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arXiv:1904.03463 · New Journal of Physics

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

Yoshihito Kuno, Takahiro Orito, Ikuo Ichinose

Published Dec 18, 2019• 88 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1088/1367-2630/ab6352

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Abstract 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.
We find that a flat-band fermion system with interactions and without disorders exhibits nonthermalized ergodicity-breaking dynamics, an analog of many-body localization (MBL). In the previous works we observed flat-band many-body localization (FMBL) in the Creutz ladder model. The origin of FMBL is a compact localized state governed by local integrals of motion (LIOMs), which are to be obtained explicitly. In this work we clarify the dynamical aspects of FMBL. We first study dynamics of two particles, and find that the states are not substantially modified by weak interactions, but the periodic time evolution of entanglement entropy emerges as a result of a specific mechanism inherent in the system. On the other hand, as the strength of the interactions is increased, the modification of the states takes place with inducing instability of the LIOMs. Furthermore, many-body dynamics of the system at finite fillings is numerically investigated by the time-evolving block decimation (TEBD) method. For a suitable choice of the filling, nonthermal and low entangled dynamics appears. This behavior is a typical example of the disorder-free FMBL.
We clarify the interplay and competition between disorder and flat band in the Creutz ladder with interparticle interactions focusing on the system's dynamics. Without disorder, the Creutz ladder exhibits flat-band many-body localization (FMBL). In this work, we find that disorder generates drastic effects on the system, i.e., addition of it induces a thermal phase first and further increase of it leads the system to the conventional many-body-localized (MBL) phase. The competition gives novel localization properties and unconventional quench dynamics to the system. We first draw the global sketch of the localization phase diagram by focusing on the two-particle system. The thermal phase intrudes between the FMBL and MBL phases, the regime of which depends on the strength of disorder and interactions. Based on the two-particle phase diagram and the properties of the quench dynamics, we further investigate finite-filling cases in detail. At finite-filling fractions, we again find that the interplay and competition between the interactions and disorder in the original flat-band Creutz ladder induces a thermal phase, which separates the FMBL and MBL phases. We also verify that the time evolution of the system coincides with the static phase diagrams. For suitable fillings, the conservation of the initial-state information and low-growth entanglement dynamics are also observed. These properties depend on the strength of disorder and interactions.
Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.
The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with transverse hopping that possesses such stable flat bands and show that many-body localization appears in the presence of interactions without quenched disorder. We numerically demonstrate that the eigenstate thermalization hypothesis is violated. We show that the influence of degenerate flat band states spreads across the full energy spectrum and grows extensively in the thermodynamic limit. Furthermore, we verify localization in terms of time evolution of some local observable, revival probability, participation ratio, and entanglement entropy.
We investigate the properties of a few interacting bosons in a Creutz ladder, which has become a standard model for topological systems, and which can be realized in experiments with cold atoms in optical lattices. At the single-particle level, this system may exhibit a completely flat energy landscape with nontrivial topological properties. In this scenario, we identify topological two-body edge states resulting from the bonding of single-particle edge and flat-band states. We also explore the formation of two- and three-body bound states in the strongly interacting limit, and we show how these quasiparticles can be engineered to replicate the flat-band and topological features of the original single-particle model. Furthermore, we show that in this geometry perfect Aharonov-Bohm caging of two-body bound states may occur for arbitrary interaction strengths, and we provide numerical evidence that the main features of this effect are preserved in an interacting many-body scenario resulting in many-body Aharonov-Bohm caging. Published by the American Physical Society 2024
The most recent manifestation of cold Rydberg atom quantum simulators that employs tailored optical tweezer arrays enables the study of many-body dynamics under so-called facilitation conditions. We show how the facilitation mechanism yields a Hilbert space structure in which the many-body states organize into synthetic lattices which feature in general one or several flat bands and may support immobile localized states. We focus our discussion on the case of a ladder geometry for which we analyze the influence of disorder generated by the uncertainty of the atomic positions. The localization properties of this system are characterized through two length scales (localization lengths) which are found to display anomalous scaling behavior at certain energies. Moreover, we discuss the experimental preparation of an immobile localized state, and analyze disorder-induced propagation effects.