Disorder in one-dimensional (1D) many-body systems facilitates abundant phases such as many-body localization (MBL) and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder compared to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of a MBL phase in the JCH model that strongly violates the eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in the weak disorder regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.
Disorder in one-dimensional (1D) many-body systems facilitates abundant phases such as many-body localization (MBL) and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder compared to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of a MBL phase in the JCH model that strongly violates the eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in the weak disorder regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.
Disorder in one-dimensional (1D) many-body systems emerges abundant phases such as many-body localization (MBL), and thermalization. However, it remains unclear regarding their existence and behavior within hybrid quantum systems. Here, based on a simple bosonic-spin hybrid model, as known as the Jaynes-Cummings-Hubbard (JCH) array, we investigate the effect of disorder comparing to the phenomena in the clean system with the variation of atom-photon coupling strength. By using the level-spacing ratio, entanglement entropy, and the properties of observable diagonal and off-diagonal matrix elements, we find that strong disorder results in the appearance of MBL phase in the JCH model that strongly violate eigenstate thermalization hypothesis (ETH), while a conditional prethermal behavior can exist in weak disorder or weak coupling regime. The conditional prethermal dynamics is based on the choice of initial product states. This work systematically reveals abundant many-body phases in the 1D JCH model and clarifies the discrepancies in the thermalization properties of systems with and without disorder.
Abstract The eigenstate thermalization hypothesis (ETH) is a mechanism for the thermalization of quantum chaotic systems. Most researches on quantum chaotic systems involve the two-body interaction between spins, fermions, and bosons, but for the JCH model, the emergence of quantum-chaotic properties comes from the competition between the hopping strength of the photon and the photon-atom coupling strength. We use exact diagonalization to prove that the JCH system has the property of the quantum chaotic system and verify the validity of ETH ansatz both for diagonal and off-diagonal matrix elements of the photon observables with reasonable experimental parameters.
In the one-dimensional low-density Jaynes-Cummings Hubbard (JCH) model, we find that when the hopping strength is much smaller than the coupling strength, the average restricted energy gap ratio exhibits an abnormal statistical behavior that is neither a Poisson nor a Gaussian orthogonal ensemble. But the average half-chain entanglement entropy exhibits ergodicity, and the eigenstate thermalization hypothesis (ETH) is valid for the observable. These results are quite different from those of the standard JCH model. In addition, when the hopping and the coupling strengths are of the same order, quantum chaos still appears in the low-density JCH model, which is in contrast to the integrability of the one-dimensional hard-core bosons. Finally, the dipole-dipole interaction breaks the particle-hole symmetry and leads the abnormal statistical properties to be closer to those of the integrable system at the weak hopping strength limit, but the quantum chaos properties cannot be affected when the hopping strength is of the same order as the coupling strength. Our results demonstrate the counterintuitive behavior in the low-density JCH model and explain the physics behind them from the perspective of the energy spectrum.
Abstract Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase , in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. The last decades of research have brought an unprecedented new variety of tools and indicators to study the breakdown of ergodicity, ranging from spectral and wave function measures, matrix elements of observables, through quantities probing unitary quantum dynamics, to transport and quantum information measures. We give a comprehensive overview of these approaches and attempt to provide a unified understanding of their main features. We emphasize general trends towards ergodicity with increasing length and time scales, which exclude naive single-parameter scaling hypothesis, necessitate the use of more refined scaling procedures, and prevent unambiguous extrapolations of numerical results to the asymptotic limit. Providing a concise description of numerical methods for studying ETH and MBL, we explore various approaches to tackle the question of the MBL phase. Persistent finite size drifts towards ergodicity consistently emerge in quantities derived from eigenvalues and eigenvectors of disordered many-body systems. The drifts are related to continuous inching towards ergodicity and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede the understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength provides premises suggesting the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.
Closed generic quantum many-body systems may fail to thermalize under certain conditions even after long times, a phenomenon called many-body localization (MBL). Numerous studies support the stability of the MBL phase in strongly disordered one-dimensional systems. However, the situation is much less clear when a small part of the system is ergodic, a scenario which also has important implications for the existence of many-body localization in higher dimensions. Here we address this question experimentally using a large-scale quantum simulator of ultracold bosons in a two-dimensional optical lattice. We prepare two-component mixtures of varying relative population and implement a disorder potential which is only experienced by one of the components. The second non-disordered ''clean'' component plays the role of a bath of adjustable size that is collisionally coupled to the ''dirty'' component. Our experiments show how the dynamics of the dirty component, which, when on its own, show strong evidence of localization, become affected by the coupling to the clean component. For a high clean population, the clean component appears to behave as an effective bath for the system which leads to its delocalization, while for a smaller clean population, the ability of the bath to destabilize the system becomes strongly reduced. Our results reveal how a finite-sized quantum system can bring another one towards thermalization, in a regime of complex interplay between disorder, tunneling and intercomponent interactions. They provide a new benchmark for effective theories aiming to capture the complex physics of MBL in the weakly localized regime.
The many-body localization (MBL) proximity effect is an intriguing phenomenon where a thermal bath localizes due to the interaction with a disordered system. The interplay of thermal and nonergodic behavior in these systems gives rise to a rich phase diagram, whose exploration is an active field of research. In this paper, we study a bosonic Hubbard model featuring two particle species representing the bath and the disordered system. Using state-of-the-art numerical techniques, we investigate the dynamics of the model in different regimes, based on which we obtain a tentative phase diagram as a function of coupling strength and bath size. When the bath is composed of a single particle, we observe clear signatures of a transition from an MBL proximity effect to a delocalized phase. Increasing the bath size, however, its thermalizing effect becomes stronger and eventually the whole system delocalizes in the range of moderate interaction strengths studied. In this regime, we characterize particle transport, revealing diffusive behavior of the originally localized bosons.