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arXiv:2305.15471 · Physical review. B./Physical review. B

Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions

Yi-Ting Tu, DinhDuy Vu, S. Das Sarma

Published Aug 30, 2023• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.108.064313

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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.
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 provide real-space and Fock-space (FS) characterizations of ergodic, nonergodic extended (NEE) and many-body localized (MBL) phases in an interacting quasiperiodic system, namely, the generalized Aubry-Andr\'e-Harper model, which possesses a mobility edge in the noninteracting limit. We show that a mobility edge in the single-particle (SP) excitations survives even in the presence of interaction in the NEE phase. In contrast, all single-particle excitations get localized in the MBL phase due to the MBL proximity effect. We give complementary insights into the distinction of the NEE states from the ergodic and MBL states by computing local FS self-energies and decay length associated, respectively, with the local and the nonlocal FS propagators. Based on a finite-size scaling analysis of the typical local self-energy across the NEE to ergodic transition, we show that MBL and NEE states exhibit qualitatively similar multifractal character. However, we find that the NEE and MBL states can be distinguished in terms of the distribution of local self-energy and the decay of the nonlocal propagator in the FS, whereas the typical local FS self-energy cannot tell them apart.
Many-body eigenstates that are neither thermal nor many-body localized (MBL) have been numerically found in certain interacting chains with moderate quasiperiodic potentials. The energy regime consisting of these nonergodic but extended (NEE) eigenstates has been extensively studied as a possible many-body mobility edge between the energy-resolved MBL and thermal phases. Recently, the NEE regime was proposed to be a prethermal phenomenon that generally occurs when different operators spread on sizably different timescales. Here, we numerically examine the mutual independence among the NEE, MBL, and thermal regimes through the lens of eigenstate entanglement spectra (ES). Given the complexity and rich information embedded in ES, we develop an unsupervised learning approach designed to quantify the mutual independence among general phases. Our method is first demonstrated on an illustrative toy example that uses RGB color data to represent phases, and then applied to the ES of an interacting generalized Aubry-Andre model from weak to strong potential strength. We find that while the MBL and thermal regimes are mutually independent, the NEE regime is dependent on the former two and smoothly emerges as the potential strength decreases. We attribute this numerical finding to the fact that the ES data in the NEE regime exhibit both an MBL-like fast decay and a thermal-like long tail.
A mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. The Aubry-André (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for a mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of a mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our Letter also offers new possibilities to engineer quantum transport and phase transitions in disordered systems.
We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge.
We investigate the quantum dynamics of a one-dimensional quasiperiodic system featuring a single-particle mobility edge (SPME), described by the generalized Aubry-André (GAA) model. This model offers a unique platform to study the consequences of coexisting localized and extended eigenstates, which contrasts sharply with the abrupt localization transition in the standard Aubry-André model. We analyze the system's response to a quantum quench through two complementary probes: entanglement entropy (EE) and subsystem information capacity (SIC). We find that the SPME induces a smooth crossover in all dynamical signatures. The EE saturation value exhibits a persistent volume-law scaling in the mobility-edge phase, with an entropy density that continuously decreases as the number of available extended states decreases. Complementing this, the SIC profile interpolates between the linear ramp characteristic of extended systems and the information trapping behavior of localized ones, directly visualizing the mixed nature of the underlying spectrum. Our results establish unambiguous dynamical fingerprints of a mobility edge, providing a crucial non-interacting benchmark for understanding information and entanglement dynamics in more complex systems with mixed phases.