New Trends in Quantum Condensed Matter Theory 2021 @ ISSP U-Tokyo


Date and time

July 26th-30th 
9pm - midnight (Japan) 
2pm - 5pm (Central Europe) 
8am - 11am (US East Coast)

Introduction

This workshop will focus on diverse exotic phenomena that emerge in quantum materials.
The materials are characterized by strong interactions between charge and spin degrees
of freedom accompanying non-trivial electronic structures.
Studies on these complex systems have also led to surprisingly rich theoretical concepts
which encompass other areas of physics such as high-energy physics and quantum information.
In this workshop, we highlight the latest progress to stimulate future developments.
Due to the recent covid-19 pandemic, there are fewer opportunities for international exchange
and presentation of research results, especially by young researchers.
We aim to compensate this situation by organizing this workshop in online format
with young theorists who have made significant achievements in Japan and abroad.

Topics:
Quantum materials, Superconductivity, Magnetism, Statistical mechanics,
Quantum dynamics, Quantum information

Invited Speakers

Owen Benton (MPIPKS)
Subhro Bhattacharjee (ICTS)
Akito Daido (Kyoto U)
Zongping Gong (MPIQO)
Satoru Hayami (UTokyo)
Shintaro Hoshino (Saitama U)
Tatsuhiko Ikeda (ISSP)
Tatsuya Kaneko (Columbia U)
Jian Kang (Soochow U)
Anna Keselman (Technion)
Patrick Ledwith (Harvard U)
Kosuke Mitarai (Osaka U)
Takashi Mori (RIKEN)
Masaya Nakagawa (UTokyo)
Laimei Nie (UIUC)
Tokiro Numasawa (UTokyo)
Adrian(Hoi-Chun) Po (HKUST)
Naoto Shiraishi (Gakushuin U)
Ruben Verresen (Harvard U)
Pavel Volkov (Rutgers U)
Xueda Wen (Harvard/ UColorado)
Fengcheng Wu (Wuhan U)
Tsuneya Yoshida (Tsukuba U)
Yizhi You (Princeton U)
Long Zhang (KITS) 

Organizers

Masaki Oshikawa (ISSP, University of Tokyo)
Takashi Oka (ISSP, University of Tokyo)
Gang Chen (Hong Kong University)
Roderich Moessner (Max-Planck Institute PKS)
Ashvin Vishwanath (Harvard University) 

Registration

This workshop will be held online using zoom.
Please register from this form to obtain the Zoom information for access.

Program

Note: The talks 1-5 on 26th Monday are shifted by 10mins.

July 26th 2021   

1. Patrick Ledwith (Harvard)
The geometry of Chern bands in twisted bilayer graphene and implications for fractional Chern insulator phases

Abstract (Click) Moiré systems have emerged as a tunable platform for strongly correlated phenomena since the discovery of correlated insulators and superconductivity in twisted bilayer graphene in 2018. In twisted bilayer graphene, much of this physics has been traced to the appearance of flat Chern bands in an appropriate basis. In this talk I will discuss the band geometry of these Chern bands. In a simplified limiting case, the chiral model, the wavefunctions are very similar to those of the lowest Landau level. We make this connection precise and show that the chiral model has ideal momentum space "quantum geometry." We will also write down a direct analogue of the Laughlin state in real space and argue that it is a zero energy ground state of a short range interaction potential. Finally, we comment on the implications for realistic twisted bilayer graphene.

2. Jian Kang (Soochow U)
A new perspective on the Bistritzer-MacDonald model and the emergent itinerancy in twisted bilayer graphene

Abstract (Click) The Bistritzer-MacDonald (BM) model predicted the existence of the narrow bands in the twisted bilayer graphene (TBG), and nowadays is a starting point for most theoretical works. In this talk, this model with Coulomb interactions will be reviewed from a rather different perspective. We treat this model as an effective field theory defined at atomic energy scale and find that the theory flows toward a fixed point in which the bands are exactly flat [1]. Additionally, our theory explains the consistency of the magic angle between the theoretical value and the experimentally discovered one. With the Hamiltonian obtained, we further derived the exact excitation spectrum in the strong coupling limit at the even integer fillings [1]. Combined with the variational method, we studied the Landau fan, the electron mass measured by quantum oscillations, and the recently discovered cascade transitions near the integer fillings [2]. Our results not only qualitatively agree with the measurements, but also reveal the emergence of the Fermi liquid at the fractional fillings.

1. Oskar Vafek and Jian Kang, Phys. Rev. Lett, 122, 257602 (2020).
2. Jian Kang, B. Andrei Bernevig, and Oskar Vafek, arXiv:2104.01145.

3. Kosuke Mitarai (Osaka U)
Quantum algorithms for quantum many-body systems on near-term quantum computers

Abstract (Click) Noisy intermediate scale quantum (NISQ) devices refer to current and near-term quantum devices with ~100 qubits and sufficiently high gate fidelity. Simulations of NISQ devices with a sufficient number of qubits are believed to be intractable for classical computers. In this talk, I discuss some recent ideas on how to exploit their power for simulating quantum many-body systems. Along with the concrete algorithms for such applications, I will also present general methodologies for efficient use of NISQ devices whose quantum resource is still very limited.

4. Zongping Gong (MPIQO)
Topological aspects of quantum cellular automata in one dimension

Abstract (Click) Quantum cellular automata (QCA) are unitary transformations that preserve locality. In one dimension, QCA are known to be fully characterized by a topological chiral index that takes on arbitrary rational numbers [1]. QCA with nonzero indices are anomalous, in the sense that they are not finite-depth quantum circuits of local unitaries, yet they can appear as the edge dynamics of two-dimensional chiral Floquet topological phases [2].

In this talk, I will focus on the topological aspects of one-dimensional QCA. First, I will talk about how the topological classification of QCA will be enriched by finite unitary symmetries [3]. On top of the cohomology character that applies equally to topological states, I will introduce a new class of topological numbers termed symmetry-protected indices. The latter, which include the chiral index as a special case, are genuinely dynamical topological invariants without state counterparts [4].

In the second part, I will show that the chiral index lower bounds the operator entanglement of QCA [5]. This rigorous bound enforces a linear growth of operator entanglement in the Floquet dynamics governed by nontrivial QCA, ruling out the possibility of many-body localization. In fact, this result gives a rigorous proof to a conjecture in Ref. [2]. Finally, I will present a generalized entanglement membrane theory that captures the large-scale (hydrodynamic) behavior of typical (chaotic) QCA.

References:
[1] D. Gross, V. Nesme, H. Vogts, and R. F. Werner, Commun. Math. Phys. 310, 419 (2012).
[2] H. C. Po, L. Fidkowski, T. Morimoto, A. C. Potter, and A. Vishwanath, Phys. Rev. X 6, 041070 (2016).
[3] Z. Gong, C. Sünderhauf, N. Schuch, and J. I. Cirac, Phys. Rev. Lett. 124, 100402 (2020).
[4] Z. Gong and T. Guaita, arXiv: 2106.05044.
[5] Z. Gong, L. Piroli, and J. I. Cirac, Phys. Rev. Lett. 126, 160601 (2021).

5. Ruben Verresen (Harvard U)
Towards realizing toric code topological order in the lab

Abstract (Click) One of the most paradigmatic phases of matter with intrinsic topological order is the Z2 spin liquid. Made famous by Kitaev's toric code model, its experimental realization has proven to be an elusive goal. In this talk, I will explain how it is now possible to realize this state in the lab by using strongly-interacting Rydberg atoms. The effective Hamiltonian, also known as a "PXP" model, realizes a dimer model on the kagome lattice, thereby encoding the Hilbert space of a Z2 gauge theory. We will see how defects of the dimer covering (monomer fluctuations) can stabilize the deconfined phase of this gauge theory---the desired Z2 spin liquid. Detecting such an exotic phase of matter is a highly non-trivial task; fortunately, in this set-up it is possible to probe the nonlocal string correlations associated to a dimer Hilbert space, giving access to the string order parameter discovered by Fredenhagen-Marcu and Gregor-Huse-Moessner-Sondhi. Such nonlocal correlations are measurable in the cold atom platform by using a particular quantum quench. In the first part of this talk, I will focus on the conceptual ideas behind this theoretical prediction of the spin liquid [1]; in the second part, I will showcase some recent experimental results in this direction [2].

[1] R. Verresen, M. D. Lukin, A. Vishwanath, Phys. Rev. X 11, 031005 (2021)
[2] G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletic, M. D. Lukin, arXiv:2104.04119

July 27th 2021   

6. Fencheng Wu (Wuhan U)
Quantum Simulation in Moiré Bilayers

Abstract (Click) Van der Waals bilayers with a small lattice mismatch or misalignment have a moiré superlattice that generates spatial modulation for both electrons and collective excitations. In this talk, I will present our theoretical proposals of using moiré bilayers as a quantum simulation platform to realize model Hamiltonians, for examples, Hubbard model, Kane-Mele model and Haldane model for electrons, as well as Bose-Hubbard model for excitons. A series of experiments in which our theoretical proposals have been realized will be discussed.

7. Pavel Volkov (Rutgers U)
Twisted Nodal Superconductors

Abstract (Click) “Twistronics” paradigm has been tremendously successful in realizing strongly correlated and topological phases of electrons in two-dimensional semiconductors or semimetals. In my talk, I will show that twisted bilayers of nodal superconductors allow a similar degree of control over the neutral quasiparticles in a superconductor.
I will demonstrate that the twist strongly affects the dispersion of the low-energy Bogoliubov-de Gennes quasiparticles, allowing further manipulation with magnetic fields, current, or interlayer voltage. In particular, application of an interlayer current transforms the system into a topological superconductor, opening a topological gap and resulting in a quantized thermal Hall effect with gapless, neutral edge modes. Close to a “magic” value of the twist angle, interactions between quasiparticles further lead to the emergence of a time-reversal symmetry breaking superconducting state. I will also discuss the possible experimental realization of this proposal, with a particular focus on high-Tc cuprates, already available in monolayer form.

8. Tatsuya Kaneko (Columbia U)
Light-induced η-pairing in Mott-Hubbard systems

Abstract (Click) Light-induced states out of equilibrium can induce intriguing phenomena in correlated electron systems. Among them, experimental observation of light-induced superconducting behavior [1] has attracted attention and activated many theoretical studies. In our recent work [2], we find a new pathway to access an unconventional electron-electron pairing state in an optically driven system. Here, we focus on η-pairing, which was originally proposed by C. N. Yang [3]. The η-pairing state is an exact eigenstate of the Hubbard model and possesses staggered off-diagonal long-range correlations. However, this pairing state is hidden in the excited states of the Hubbard model and is not realized in the equilibrium state. Our study shows that photoexcitation can induce the η-pairing state in the Hubbard model out of equilibrium. In my talk, first, I show the numerical results that demonstrate that the η-pairing correlation is induced in the photoexcited Mott insulator. Then, I introduce the optical selection rule in the Hubbard model and explain the mechanism of light-induced η-pairing.

[1] M. Mitrano et al., Nature 530, 461 (2016).
[2] T. Kaneko T. Shirakawa, S. Sorella, S. Yunoki, Phys. Rev. Lett. 122, 077002 (2019).
[3] C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989).

9. Laimei Nie (UIUC)
Many-body quantum chaos: an entanglement perspective

Abstract (Click) From the three-body problem to the butterfly effect, chaos is one of the most mathematically fascinating yet tangible phenomena in nature. Recent years have seen a surge of interest in the concept of quantum chaos in many-body systems, largely due to its potential connections with fundamental questions ranging from the mechanism of quantum thermalization, to black hole information paradox. However, unlike its classical counterpart, the description of quantum chaos remains debatable - even its definition is not clear despite decades of efforts. In this talk, we will discuss a new way to look at the problem: instead of focusing on quantum states, we aim to uncover the chaotic behavior of a many-body quantum system by studying the entanglement of operators. We will test this idea in a variety of systems, including the Sachdev-Ye-Kitaev model and the 2D conformal field theories, and reveal a hierarchy of chaos of their dynamics. In particular, we will show that nature may have a bound on chaos, and illustrate how certain systems are prohibited from saturating the bound due to conservation laws. We will also discuss the relation and distinction between our entanglement measure and other probes of chaos.

10. Tokiro Numasawa (U Tokyo)
Symmetry breaking, Quantum chaos and wormholes in coupled SYK models

Abstract (Click) The Sachdev-Ye-Kitaev (SYK) model has attracted much attention in various fields.
From a condensed matter perspective, it is an interesting strongly correlated quantum system though it is still solvable at large N.
From a high energy perspective, it is interesting since it has a lot to do with quantum black holes.
Variants of the SYK model, in particular the coupled SYK models, are also interesting because they exhibit interesting entanglement structures and also are related to wormholes.
In this talk, we study aspects of coupled SYK models with wormhole interpretations in a high energy theory context.
After reviewing some important properties of two coupled SYK models, we first study quantum chaos (Lyapunov exponents) of the models.
Then, we introduce a generalization of two coupled SYK models and study the quantum phase structures and its relation to symmetry breaking at large N.
Finally we will talk about analytically continued wormholes and non unitary dynamics in the SYK model.

July 28th 2021   

11. Satoru Hayami (U Tokyo)
Bottom-up design of momentum-dependent spin-split band structures in spin-orbit-coupling free antiferromagnets

Abstract (Click) The spin-orbit coupling (SOC) in crystals has attracted great interest in various fields of condensed matter physics, such as nontrivial topological states, multipole states, and spintronics [1]. Meanwhile, studies for such SOC-related physics have been usually done in materials containing heavier elements with the large atomic SOC, such as 4d-5d and f electrons, where the novel electronic and large physical responses have been discovered. On the other hand, it tends to be difficult to control such phenomena flexibly because the atomic SOC is built in the complicated atomic orbitals and chemical composition. In order to widen the scope of materials and explore further possibilities of SOC-related physics toward applications to electronics and spintronics devices, another mechanism from a different viewpoint is desired.

In the present study, we discuss yet another intriguing interplay between the spin and orbital degrees of freedom that originates from the spontaneous crystalline symmetry breaking through a magnetic phase transition. We examine the macroscopic symmetry and microscopic model-parameter conditions for emergence of spin-split electronic band structure in collinear/noncollinear antiferromagnets without atomic SOC. By using a concept of augmented multipoles for the tight-binding models [2], we find that anisotropic kinetic motions of electrons in an AFM give rise to an effective spin-orbit interaction in momentum space, which results in symmetric spin splitting in collinear magnets [3,4] and antisymmetric spin splitting in noncollinear magnets [5]. We present that multipole descriptions are useful to understand a peculiar spin splitting in the band structure in a systematic way [6].
[1] J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Rev. Mod. Phys. 87, 1213 (2015).
[2] S. Hayami, M. Yatsushiro, Y. Yanagi, and H. Kusunose, Phys. Rev. B 98, 165110 (2018).
[3] M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Motome, and H. Seo, Nat. Commun. 10, 4305 (2019).
[4] S. Hayami, Y. Yanagi, and H. Kusunose, J. Phys. Soc. Jpn. 87, 123702 (2019).
[5] S. Hayami, Y. Yanagi, and H. Kusunose, Phys. Rev. B 101, 220403(R) (2020).
[6] S. Hayami, Y. Yanagi, and H. Kusunose, Phys. Rev. B 102, 144441 (2020).

12. Anna Keselman (Technion)
Spectral Signatures of Quasiparticle Interactions in Quantum Spin Chains

Abstract (Click) Elementary excitations in quantum magnets can be typically described in terms of long-lived quasiparticles, either simple magnons (spin waves), or more exotic fractionalized excitations such as spinons. In general, when multiple quasiparticles are present, they interact, and in a strongly correlated system, they interact strongly. We employ MPS-based techniques to uncover signatures of interactions between quasiparticles that show up in the dynamical spin correlations of antiferromagnets in presence of a magnetic field.
In this talk, I will focus on the antiferromagnetic spin-1/2 chain, addressing both the low and high magnetization regimes. In the low magnetization regime, in the gapless phase, we find that the marginally irrelevant backscattering interaction between the fractionalized spinons leaves a distinct signature in the transverse dynamical susceptibility creating a non-zero gap between two branches of excitations at small momentum. In the high magnetization regime, close to the saturation field, we show that interactions between magnons lead to a formation of two-magnon bound states which leave a sharp feature in the transverse correlations. I will then discuss how the response is altered in presence of Dzyaloshinskii-Moriya (DM) interactions in both regimes.

13. Owen Benton (MPIPKS)
Routes to Higher-Rank Coulomb Spin Liquids

Abstract (Click) Coulomb spin liquids are disordered phases of frustrated magnets, whose long wavelength description corresponds with the theory of electromagnetism. They are realised in the spin ice materials, and present a beautiful case study in emergence, with magnetic monopoles and gauge fields arising out of an interacting spin system. Recent work has highlighted the possibility of “higher rank” Coulomb phases: spin liquids where the right effective description features tensor electric and magnetic fields with rank > 1. These are particularly sought after due to an intimate connection with fractons: quasiparticles with an intrinsic inability to move when isolated.

In this context, it is natural to ask whether we can write down simple models which naturally give rise to higher-rank Coulomb phases and whether these models can ever be connected to experiment?

In this talk, I will give an introduction to higher rank Coulomb spin liquids, and discuss potential routes to their realisation, both on the level of theoretical models and in experiment. I will show how a simple model on the breathing pyrochlore lattice, featuring only commonly occurring forms of nearest-neighbour interaction, leads to a higher rank Coulomb spin liquid [1], and discuss the potential to realise this in Yb-based materials. I will then go on to discuss a systematic approach to finding models realising higher rank spin liquids, based on the creation, annihilation and coalescence of topological defects in momentum space [2]. In this latter approach, higher rank Coulomb phases are seen to occur naturally at the phase boundaries between distinct “lower-rank” spin liquids.

[1] H. Yan, O. Benton, L. D. C. Jaubert and N. Shannon, Phys. Rev. Lett. 124, 127203 (2020)
[2] O. Benton and R. Moessner, arXiv:2103.10817

14. Akito Daido (Kyoto U)
Intrinsic mechanism of superconducting diode effect

Abstract (Click) Nonreciprocal transport is attracting attention as a new functionality of matter [1,2]. An example is the magnetochiral anisotropy (MCA), which has been observed in various materials from (semi)conductors to superconductors. MCA is the inequivalence of the resistance of the rightward and leftward currents: either R(I)>R(-I)>0 or R(-I)>R(I)>0. On the other hand, such a drastic situation is possible in superconductors that either one of R(\pm I) vanishes while the other remains finite. Such a superconducting diode effect(SDE) has recently been observed in the Nb/V/Ta superlattice without an inversion center [3]. SDE is a promising building block of dissipationless electric circuits and is a fascinating phenomenon manifesting the inversion breaking and superconductivity interplay. One of the remaining issues is to identify suitable materials providing the best performance; however, the mechanisms to cause SDE have not been clarified, preventing the progress in the material search.
  In this work, we propose an intrinsic mechanism to cause SDE by studying the nonreciprocity in the depairing critical current [4]. We clarify the temperature scaling of the nonreciprocal depairing current near the critical temperature [4,5,6] and point out its significant enhancement at low temperatures. It is also found that the nonreciprocal critical current shows sign reversals upon increasing the magnetic field. These behaviors are understood by the nonreciprocity of the Landau critical momentum and the crossover of the helical superconductivity. Thereby, we propose the intrinsic SDE as a promising bulk probe of the helical superconducting states.

[1] Y. Tokura and N. Nagaosa, Nat. Commun. 9, 3740 (2018).
[2] T. Ideue and Y. Iwasa, Annu. Rev. Condens. Matter Phys. 12, 201 (2021).
[3] F. Ando et al., Nature 584, 373 (2020).
[4] A. Daido, Y. Ikeda, and Y. Yanase, arXiv:2016.03326.
[5] N. Yuan and L.Fu, arXiv:2106.01909.
[6] J. J. He, Y. Tanaka, and N. Nagaosa, arXiv:2106.03575.

15. Shintaro Hoshino (Saitama U)
Interaction and disorder effects on Bogoliubov Fermi surfaces

Abstract (Click) The superconductivity is understood as a quantum condensation of Cooper pairs. While the Fermi surface usually disappears in the pairing state, they can remain in some superconducting states [1], where the elementary excitations near the Fermi surfaces are composed not of original electrons but of Bogoliubov quasiparticles (bogolons). For the time-reversal symmetry broken system with preserved inversion symmetry, such Bogoliubov-Fermi surfaces are stable as they are topologically protected [2]. Since the bogolons can carry energy, the thermal properties such as specific heat and thermal conductivity are expected to be similar to the conventional Fermi liquid of electrons and are potentially observed in the actual materials. However, the bogolons are quasiparticles in the superconducting state, and their physical properties should be different from those of the electrons. Therefore, it is desirable to clarify the difference between the Fermi liquid and the Bogoliubov Fermi liquid, the latter of which is realized for the non-ideal bogolons generically.

We have shown that the impurity and correlation effects on this Bogoliubov Fermi surface generate purely odd-frequency pairing amplitude at low energies, which is a Cooper pair formed only at different time [3]. This property gives a clear distinction from the normal Fermi liquid state of electrons. Furthermore, at sufficiently low temperatures, it is also expected that the system shows a (even-frequency) pairing state of bogolons because of the intrinsic logarithmically divergent pair susceptibility of the Fermi surfaces [4]. In the talk, we will discuss these topics in detail.

[1] G.E. Volovik, Phys. Lett. A 142, 282 (1989).
[2] D.F. Agterberg, P.M.R. Brydon, C. Timm, Phys. Rev. Lett. 118, 127001 (2017).
[3] T. Miki, S.-T. Tamura, S. Iimura, S. Hoshino, arXiv:2103.02251 (2021).
[4] S.-T. Tamura, S. Iimura, S. Hoshino, Phys. Rev. B 102, 024505 (2020).

July 29th 2021   

16. Subhro Bhattacharjee (ICTS, Bangalore)
SU(4) Dirac fermions on honeycomb lattice

Abstract (Click) For SOC coupled systems with d^1 electronic configuration on a honeycomb lattice, it has been suggested Dirac fermions with a large SU(4) symmetry can emerge at low energies. In this talk, I shall describe our study of understanding different possible masses of these fermions and the resultant phases so obtained. Because of SOC, the symmetry transformation of the fermions are rather different from graphene.

17. Naoto Shiraishi (Gakushuin U)
Undecidability in quantum thermalization

Abstract (Click) If we leave a quantum many-body system at a nonequilibrium initial state and measure some macroscopic observable, it will relax to the unique equilibrium value. This phenomenon is called thermalization. Almost all physical systems are considered to show thermalization, while some quantum many-body systems including integrable systems are known not to thermalize. Vast literature in this field is devoted to clarify what ultimately determines the presence or absence of thermalization. In spite of prodigious efforts, a decisive answer applying any quantum system has still been elusive. We approach this problem with a completely different perspective. We examine the hardness of the problem of quantum thermalization from the viewpoint of theoretical computer science. Surprisingly, we find that the problem of quantum thermalization is an undecidable problem [1]. Namely, there is no general theorem or procedure to determine the presence or absence of thermalization in any system. This result of undecidability is valid even if the system is in one-dimension, local interaction, and shift-invariant, and the observable is a one-body observable, and the initial state is a product state. In this talk, we plan to provide a brief review of quantum thermalization and theoretical computer science first, and then explain our main result.

References: [1] N. Shiraishi and K. Matsumoto, arXiv:2012.13889/arXiv:2012.13890 (accepted to Nat. Comm.)

18. Xueda Wen (Harvard/ U Colorado)
Randomly driven quantum critical systems in (1+1)d

Abstract (Click) In this talk, I will first review recent progress in a family of exactly solvable time-dependent driven quantum critical systems that can be described by conformal field theories in (1+1)d. Then I will focus on the case of random driving. In general, there are heating phases where the entanglement entropy grows linearly in time, and “exceptional points” where the entanglement entropy grows slower. In particular, based on some mathematical theorems, I will give analytical understanding on the universal features in both the heating phase and at the exceptional points. This is a joint work in preparation with Ruihua Fan, Yingfei Gu and Ashvin Vishwanath.

19. Masaya Nakagawa (U Tokyo)
Dissipative Hubbard model: magnetism, superfluid pairing, and exact solution

Abstract (Click) While unitarity lies at the heart of quantum dynamics in closed systems, realistic quantum systems cannot avoid dissipation due to an environment and therefore undergo non-unitary dynamics. Recent progress in quantum simulations with a large number of atoms, ions, and molecules has provided an ideal experimental platform for exploring the effect of dissipation on strongly correlated quantum many-body systems. In this talk, by employing the paradigmatic Fermi-Hubbard model, we show that dissipation induces novel magnetism and superfluid pairing in nonequilibrium steady states [1-3]. The non-unitary dynamics of such dissipative systems is governed by a non-Hermitian Liouvillian superoperator. By extending the Bethe ansatz method to dissipative systems, we find an exact solution that gives the eigenspectrum of the Liouvillian of the dissipative Hubbard model in one dimension [2]. This result presents a new class of exactly solvable open quantum many-body systems, which can be experimentally realized with ultracold atoms.

[1] M. Nakagawa, N. Tsuji, N. Kawakami, and M. Ueda, Phys. Rev. Lett. 124, 147203 (2020).
[2] M. Nakagawa, N. Kawakami, and M. Ueda, Phys. Rev. Lett. 126, 110404 (2021).
[3] M. Nakagawa, N. Tsuji, N. Kawakami, and M. Ueda, arXiv:2103.13624.

20. Tsuneya Yoshida (Tsukuba U)
Correlated systems with non-Hermitian topology

Abstract (Click) Topological insulators and superconductors have been extensively studied because of characteristic band structures protected by topological properties. While these topological phases are described by a Hermitian Hamiltonian, it turned out that non-Hermitian systems induce a variety of topological phenomena for which non-Hermiticity is essential[1-3]. A typical example is an exceptional point where band touching occurs both for the real- and imaginary-parts due to defectiveness of the Hamiltonian (i.e., violation of diagonalizability of the Hamiltonian).
In this talk, we analyze effects of symmetry on exceptional points, and demonstrate the emergence of symmetry-protected exceptional rings and surfaces in correlated systems[4]. If time allows, we also see that a fractional quantum Hall state, a topologically ordered state, emerges even in a non-Hermitian system[5].

References:
[1] Z. Gong et al., PRX 8 031079 (2018).
[2] E. J. Bergholtz, J. C. Budich, F. K. Kunst, RMP 93 015005 (2021).
[3] Y. Ashida, Z. Gong, and M. Ueda, Adv. Phys. 69 249 (2020).
[4] TY, et al., PRB 99 121101 (2019); TY et al., PTEP 2020 12A109 (2020).
[5] TY, K. Kudo and Y. Hatsugai Sci. Rep. 9 16895 (2019); TY, K. Kudo, H. Katsura, and Y. Hatsugai PRR 2 033428 (2020).

July 30th 2021   

21. Long Zhang (KITS, University of Chinese Academy of Sciences)
Conformal Boundary Conditions and Boundary Criticality of Symmetric Quantum Spin Chains

Abstract (Click) "Symmetry-protected" topological phases are gapped states distinguishable only in the presence of certain symmetries. Recently, symmetric critical states with robust edge modes are under intensive exploration. In this work, we show that the conformal boundary condition at the physical and the entangling surfaces is a more generic signature of such symmetric quantum critical states. We study two families of quantum critical chains, described by the 2D Ising and the three-state Potts CFT, respectively. In each family of critical chains, on the one hand, we find an ordinary simple model and SPT counterpart exhibits a different surface critical behavior although in the same bulk universality class. On the other hand, we also observe distinct universal energy and entanglement spectra in the ordinary simple model and SPT counterpart, which indicate different conformal boundary conditions. Furthermore, we combine numerical and field theory analysis to show conformal boundary condition is closely related to the bulk critical field theory, which can be taken as the novel "bulk-boundary correspondence" in quantum critical systems, just like bulk-boundary correspondence in a surface quantum anomaly of symmetry protected topological phase.

22. Yizhi You (Princeton U)
Plaquette-dimer liquid beyond renormalization

Abstract (Click) We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a z-link or a plaquette in the x-y plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type `higher-rank electrostatics', which can exhibit a plaquette-dimer liquid and an ordered phase. We analyse this theory in detail, using height representations and T-duality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the Kosterlitz-Thouless transition. A significant new element is its UV-IR mixing, where the low energy behavior of the liquid phase and the transition out of it is dominated by local (short-wavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm.

23. Adrian (Hoi-Chun) Po (HKUST)
Symmetric Jordan-Wigner transformation in higher dimensions

Abstract (Click) Interpreted in a restricted sense, the Jordan-Wigner transformation provides a manifestly local representation of a lattice fermionic system using bosonic degrees of freedom. While locality becomes an issue in higher than one spatial dimension in the original formulation, recently it has been shown that the problem can be resolved by invoking a background Z2 gauge theory. Building on these recent developments, we will discuss a way to perform the Jordan-Wigner transformation in higher than one dimension while keeping not only locality but also the symmetries manifest.

24. Tatsuhiko Ikeda (U Tokyo)
Nonequilibrium steady states in periodically driven dissipative quantum systems

Abstract (Click) Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is one of the forefronts of quantum physics of light-matter interaction but often limited to ideal dissipationless systems. For the Floquet engineering extended to a broader class of materials, it is vital to understand the quantum states emerging in a balance of the periodic drive and energy dissipation. This talk consists of two topics: (1) a general description of nonequilibrium steady states (NESS) for high-frequency drives (Ref. [1]) and (2) time-crystalline NESS protected by "symmetry" (Ref. [2]). In Topic (1), we discuss the NESS in the time-periodic Lindblad equation solved by the high-frequency expansion technique. In Topic (2), we introduce a new "symmetry" termed the Floquet dynamical symmetry and show it leads to time-crystalline states.
Reference:
[1] T. N. Ikeda and M. Sato, Sci. Adv. 6, eabb4019 (2020).
[2] K. Chinzei and T. N. Ikeda, Phys. Rev. Lett. 125, 060601 (2020).

25. Takashi Mori (RIKEN)
Spectral analysis of the relaxation time in open quantum many-body systems

Abstract (Click) Dynamics of open quantum systems is generated by the Liouvillian, and the real part of its eigenvalue determines the decay rate of the corresponding eigenmode. It is expected that the Liouvillian gap, which is defined as the smallest non-zero real part of the Liouvillian eigenvalue, gives the inverse of the longest relaxation time. However, some counter-examples were presented in Ref. [1]: the relaxation time increases with the system size faster than the inverse Liouvillian gap, which clearly shows that the inverse Liouvillian gap does not give the longest relaxation time.

I talk about our recent work [2] resolving this "gap discrepancy problem" in open quantum many-body systems. It is found that not only the Liouvillian eigenvalue, but also the overlap between left- and right-eigenvectors crucially affects the relaxation time. I present a spectral expression of the relaxation time, which is confirmed to agree with numerics and is straightforwardly extended to classical Markov processes. Based on this result, I also discuss spectral approach to metastability [3].

[1] M. Znidaric, Phys. Rev. E 92, 042143 (2015)
[2] T. Mori and T. Shirai, Phys. Rev. Lett. 125, 230604 (2020)
[3] T. Mori, arXiv: 2102.05796



Contact

Takashi Oka (oka@issp.u-tokyo.ac.jp; ISSP, UTokyo)