We study the many-body localization (MBL) transition in a generalized Aubry-André model (also known as the GPD model) introduced by Ganeshan, Pixley, and Das Sarma []. In contrast to MBL in other disordered or quasiperiodic models, the interaction seems to unexpectedly enhance MBL in the GPD model in some parameter range. To understand this counterintuitive result, we demonstrate that the highest-energy single-particle band in the GPD model is unstable against weak disorder, which leads to this surprising MBL phenomenon in the interacting model. We develop a mean-field theory description to understand the coupling between extended and localized states, which we validate using extensive exact diagonalization and modified density matrix renormalization group (DMRG-X) numerical results. Published by the American Physical Society 2024
We study the many-body localization (MBL) transition in a generalized Aubry-André model (also known as the GPD model) introduced by Ganeshan, Pixley, and Das Sarma []. In contrast to MBL in other disordered or quasiperiodic models, the interaction seems to unexpectedly enhance MBL in the GPD model in some parameter range. To understand this counterintuitive result, we demonstrate that the highest-energy single-particle band in the GPD model is unstable against weak disorder, which leads to this surprising MBL phenomenon in the interacting model. We develop a mean-field theory description to understand the coupling between extended and localized states, which we validate using extensive exact diagonalization and modified density matrix renormalization group (DMRG-X) numerical results. Published by the American Physical Society 2024
We study the many-body localization (MBL) transition in an 1D exactly solvable system with long-range hopping and quasiperiodic on-site potential introduced in Phys. Rev. Lett. 131, 186303 (2023). Unlike other disorder or quasiperiodic model, an interaction-enhanced MBL happens in the moderate interaction regime, which is dubbed as the interaction-enhanced MBL. This counterintuitive phenomenon can be understood by noticing the fragility of the critical band lying at the bottom of the spectrum. The fragile band is localized by other localized states once the interaction is turned on. This mechanism can be verified by introducing a mean-field theory description which can derive highly excited states with high accuracy. The effectiveness of this mean-field theory is captured by the quasihole physics, validated by the particle entanglement spectra.
A generalization of the Aubry-Andr\'e model, the noninteracting Ganeshan-Pixley-Das Sarma model (GPD) introduced by Ganeshan et al. [Phys. Rev. Lett. 114, 146601 (2015)], is known analytically to possess a mobility edge, allowing both extended and localized eigenstates to coexist. This mobility edge has been hypothesized to survive in closed many-body interacting systems, giving rise to a new nonergodic metallic phase. In this work, coupling the interacting GPD model to a thermal bath, we provide direct numerical evidence for multiple qualitative behaviors in the parameter space of disorder strength and energy level. In particular, we look at the bath-induced saturation of entanglement entropy to classify three behaviors: thermalized, nonergodic extended, and localized. We also extract the localization length in the localized phase using the long-time dynamics of the entanglement entropy and the spin imbalance. Our work demonstrates the rich localization landscape of generalized Aubry-Andr\'e models containing mobility edges in contrast to the simple Aubry-Andr\'e model with no mobility edge.
Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension, substantial evidence for such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed avalanche instability. In quasiperiodic systems, however, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying numerically the out-of-equilibrium dynamics of large systems, we find very long-lived localization on experimentally relevant time scales. Surprisingly, we also observe large-scale transport along deterministic lines of weak potential, which appear in the investigated quasiperiodic models. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties---a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.
Anderson localization, where quenched disorder leads to the localization of single-particle wave functions, has been studied extensively. However, the effect of interaction and non-random potentials on many-body localization (MBL) has gained attention recently. We investigate the dynamics of the interacting Aubry-André model to assess the stability of the many-body localized (MBL) phase. Our motivation to consider the Aubry–André potential as the disorder potential is to eliminate the avalanche mechanism, which often destabilizes MBL in systems with quenched disorder. We analyze the time evolution and the system-size scaling across a range of disorder strengths for the entanglement entropy, number entropy, and the Hartley number entropy. In the non-interacting case, our results confirm an Anderson localization transition at a critical disorder strength Dc = 2, which is consistent with earlier studies. However, when interactions are introduced, the number entropy appears to grow unboundedly as SN ~ ln ln t in the thermodynamic limit, even for large disorder. Meanwhile, the entanglement entropy grows logarithmically, S ~ ln t, and both entropies saturate in a correlated manner at finite times td ~ e^(L·D). These findings suggest that using a quasiperiodic potential to remove the avalanche mechanism does not stabilize true MBL behavior. Instead, the long-time dynamics are qualitatively similar to those found in systems with random disorder. In this thesis, we first introduce the fundamental concepts of thermalization, quantum quench, and symmetry-resolved entropies, then provide a study of localization, specifically in the Aubry-André model. Finally, we place our numerical results in the broader context of the current debate on the stability of many-body localized phases.
Disorder free many-body localization (MBL) can occur in interacting systems that can dynamically generate their own disorder. We address the thermal-MBL phase transition of two isotropic Heisenberg spin chains that are quasiperiodically coupled to each other. The spin chains are incommensurate and are coupled through a short-range exchange interaction of the X X Z type that decays exponentially with the distance. Using exact diagonalization, matrix product states, and a density matrix renormalization group, we calculate the time evolution of the entanglement entropy at long times and extract the inverse participation ratio in the thermodynamic limit. We show that this system has a robust MBL phase. We establish the phase diagram with the onset of MBL as a function of the interchain exchange coupling and of the incommensuration between the spin chains. The Ising limit of the interchain interaction optimizes the stability of the MBL phase over a broad range of incommensurations above a given critical exchange coupling. Incorporation of interchain spin flips significantly enhances entanglement between the spin chains and produces delocalization, favoring a prethermal phase whose entanglement entropy grows logarithmically with time. Published by the American Physical Society 2024
We study many-body localization (MBL) in the quasiperiodic ${t}_{1}\text{\ensuremath{-}}{t}_{2}$ model, focusing on the role of next-nearest-neighbor (NNN) hopping t2, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction U. For weak interactions ($U\ensuremath{\ll}{t}_{1}$), this model is always nonthermal. For intermediate interactions ($U\ensuremath{\sim}{t}_{1}$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions $(U\ensuremath{\gg}{t}_{1})$, the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.