Annual review of condensed matter physics

Journal of Statistical Mechanics: theory and experiment

19세기말 애국적 담론과 新小說의 정체성

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.

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Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that phenomenon is displayed. The possibility and significance of breaking of imaginary time-translation symmetry is discussed.

Quantum Time Crystals

The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.

Many-body localization of bosons in an optical lattice: Dynamics in disorder-free potentials

Motivated by recent experiments on interacting bosons in a quasi-one-dimensional optical lattice [M. Rispoli et al., Nature (London) 573, 385 (2019)], we analyze theoretically properties of the system in the crossover between delocalized and localized regimes. Comparison of time dynamics for uniform and density-wave-like initial states enables a demonstration of the existence of the mobility edge. To this end we define a different observable, the mean speed of transport at long times. It gives us an efficient estimate of the critical disorder for the crossover. We also show that the mean velocity growth of occupation fluctuations close to the edges of the system carries similar information. Using the quantum quench procedure, we show that it is possible to probe the mobility edge for different energies.

Many-body localization in the Bose-Hubbard model: Evidence for mobility edge

This work shows that interacting particles in a one dimensional optical lattice with strong harmonic confinement behave in a unique way, resulting in an exotic coexistence between spatially separated regions of localized and extended domains. The position of the border between two regions is estimated using local static field arguments coming from Stark localization

Coexistence of localized and extended phases : many-body localization in a harmonic trap

Nonergodic dynamics in disorder-free potentials

We discuss nonergodic dynamics of interacting spinless fermions in a tilted optical lattice as modeled by a XXZ spin chain in a magnetic (or electric) field changing linearly across the chain. The time dynamics is studied using exact propagation for small chains and matrix product state techniques for larger system sizes. We consider both the initial N\'eel separable state and the quantum quench scenario, in which the initial state may be significantly entangled. We show that the entanglement dynamics is significantly different in both cases. In the former a rapid initial growth is followed by a saturation for sufficiently large tilt $F$. In the latter case the dynamics seems to be dominated by pair tunneling, and the effective tunneling rate scales as $1/{F}^{2}$. In the presence of an additional harmonic potential the imbalance is found to be entirely determined by a local effective tilt ${F}_{\text{loc}}$; the entanglement entropy growth is modulated with frequency that follows $1/{F}_{\mathrm{loc}}^{2}$ scaling first, but at long time the dynamics is determined rather by the curvature of the harmonic potential. Only for large tilts or sufficiently large curvatures, corresponding to the deeply localized regime, do we find logarithmic entanglement growth for the N\'eel initial state. The same curvature determines the long-time imbalance for large $F$, which reveals strong revival phenomena associated with the manifold of equally spaced states, degenerate in the absence of the harmonic potential.

Ruixiao Yao

Papers

Many-body localization of bosons in an optical lattice: Dynamics in disorder-free potentials

Many-body localization in the Bose-Hubbard model: Evidence for mobility edge

Coexistence of localized and extended phases : many-body localization in a harmonic trap

Nonergodic dynamics in disorder-free potentials

Many-body localization in tilted and harmonic potentials