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Annual review of condensed matter physics

Journal of Statistical Mechanics: theory and experiment

A review is given on the foundations and applications of non-Hermitian classical and quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra, including Jordan normal form, biorthogonality, exceptional points, pseudo-Hermiticity and parity-time symmetry, are delineated in a pedagogical and mathematically coherent manner. Building on these, we provide an overview of how diverse classical systems, ranging from photonics, mechanics, electrical circuits, acoustics to active matter, can be used to simulate non-Hermitian wave physics. In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility, enhanced sensitivity, topological energy transfer, coherent perfect absorption, single-mode lasing, and robust biological transport. We then explain in detail how non-Hermitian operators emerge as an effective description of open quantum systems on the basis of the Feshbach projection approach and the quantum trajectory approach. We discuss their applications to physical systems relevant to a variety of fields, including atomic, molecular and optical physics, mesoscopic physics, and nuclear physics with emphasis on prominent phenomena/subjects in quantum regimes, such as quantum resonances, superradiance, continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field theories. Finally, we introduce the notion of band topology in complex spectra of non-Hermitian systems and present their classifications by providing the proof, firstly given by this review in a complete manner, as well as a number of instructive examples. Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.

Non-Hermitian Physics

Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1  +  1 and 2  +  1 dimensions using ultracold atoms in optical lattices.

https://iopscience.iop.org/article/10.1088/0034-4885/79/1/014401/pdf

Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices.

We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced many-body localizated phase. Physical picture of this crossover is investigated in detail. We also observe non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.

https://iopscience.iop.org/article/10.1088/1367-2630/ab6352/pdf

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

We present a theoretical study of quantum simulations of ($1+1$)-dimensional U(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and a Higgs matter field, by using ultracold bosonic gases on a one-dimensional optical lattice. Starting from the extended Bose-Hubbard model with on-site and nearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model as a low-energy effective theory. The derived gauge-Higgs model exhibits nontrivial phase transitions between the confinement and Higgs phases, and we discuss the relation with the phase transition in the extended Bose-Hubbard model. Finally, we study the real-time dynamics of an electric flux by the Gross-Pitaevskii equations and the truncated Wigner approximation. The dynamics is governed by a bosonic analog of the Schwinger mechanism---i.e., the shielding of an electric flux by a condensation of Higgs fields, which occurs differently in the Higgs and the confinement phases. These results, together with the obtained phase diagrams, shall guide experimentalists in designing quantum simulations of the gauge-Higgs models by using cold gases.

Quantum simulation of ( 1 + 1 )-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases

We show that a quantum scar state, an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum, can be constructed in flat band systems. The key idea of our construction is to make use of orthogonal compact localized states. We concretely discuss our construction scheme, taking a sawtooth flat lattice system as an example, and numerically demonstrate the presence of a quantum scar state. Examples of higher-dimensional systems are also addressed. Our construction method of quantum scar has broad applications to various flat band systems.

Flat band quantum scar

Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge–Higgs model is a quite important one because it describes a wide variety of phenomena/models related to the Anderson–Higgs mechanism, such as superconductivity, the standard model of particle physics, and the inflation process of the early Universe. In this paper, we first show that atomic description of the lattice gauge model allows us to explore real-time dynamics of the gauge variables by using the Gross–Pitaevskii equations. Numerical simulations of the time development of an electric flux reveal some interesting characteristics of the dynamic aspect of the model and determine its phase diagram. Next, to realize a quantum simulator of the U(1) lattice gauge–Higgs model on an optical lattice filled by cold atoms, we propose two feasible methods: (i) Wannier states in the excited bands and (ii) dipolar atoms in a multilayer optical lattice. We pay attention to the constraint of Gauss's law and avoid nonlocal gauge interactions.

https://iopscience.iop.org/article/10.1088/1367-2630/17/6/063005/pdf

Real-time dynamics and proposal for feasible experiments of lattice gauge–Higgs model simulated by cold atoms

The $N$-flavor interacting Su-Schrieffer-Heeger (i-SSH) model realizable in cold atoms in an optical lattice is studied. We clarify the relationship between the i-SSH model and the Chiral-Gross-Neveu-Wilson (CGNW) model. Following the previous study of the CGNW model in the high-energy physics community, the ground-state phases of the i-SSH model are investigated and interpreted from the viewpoint of the phases of the CGNW model. The interaction effect on the i-SSH model, belonging to the topological BDI class, is grasped by following the view of the dynamical breakdown of chiral symmetry in the CGNW model. Furthermore, we compare the large-$N$ ground-state phase diagram with that of the $N=1$ case obtained by exact diagonalization, and then we propose a tabletop cold-atom quantum simulator to test the model.

Yoshihito Kuno

Papers

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

Quantum simulation of ( 1 + 1 )-dimensional U(1) gauge-Higgs model on a lattice by cold Bose gases

Flat band quantum scar

Real-time dynamics and proposal for feasible experiments of lattice gauge–Higgs model simulated by cold atoms

Phase structure of the interacting Su-Schrieffer-Heeger model and the relationship with the Gross-Neveu model on lattice