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Physical review. B./Physical review. B

Dynamical l-bits and persistent oscillations in Stark many-body localization

Thivan M. Gunawardana, Berislav Buča

Published Oct 21, 2022• 21 citations
Publisher

Abstract

Stark many-body localization (MBL) occurs when interacting quantum particles are placed in a strong linear field gradient. Localization of excitations, coherent Bloch oscillations, Hilbert-space fragmentation, and scarring have been observed numerically and experimentally, but their origin is not understood. The authors explain these features analytically by perturbatively constructing an algebraic structure of Stark MBL Hamiltonians they name ``dynamical l-bits''. These structures are exponentially stable in the field gradient strength. Thus, the work has potential implications for quantum information processing.

DOI
10.1103/physrevb.106.l161111

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Stark many-body localization (MBL) occurs when interacting quantum particles are placed in a strong linear field gradient. Localization of excitations, coherent Bloch oscillations, Hilbert-space fragmentation, and scarring have been observed numerically and experimentally, but their origin is not understood. The authors explain these features analytically by perturbatively constructing an algebraic structure of Stark MBL Hamiltonians they name ``dynamical l-bits''. These structures are exponentially stable in the field gradient strength. Thus, the work has potential implications for quantum information processing.
Stark many-body localized (SMBL) systems have been shown both numerically and experimentally to have Bloch many-body oscillations, quantum many-body scars, and fragmentation in the large field tilt limit. Likewise, they are believed to show localization similar to disordered MBL. We explain and analytically prove all these observations by rigorously showing the existence of novel algebraic structures that are exponentially stable in time, which we call dynamical l-bits. Moreover, we show that many-body Bloch oscillations persist even at infinite temperature for exponentially long-times. We numerically confirm our results by studying the prototypical Stark MBL model of a tilted XXZ spin chain. Our work explains why thermalization was observed in a recent 2D tilted experiment. As dynamical l-bits are stable, localized and quantum coherent excitations, our work opens new possibilities for quantum information processing in Stark MBL systems.
Many-body localization (MBL), a transportless phase in disordered interacting quantum systems, has recently been observed in systems without disorder but instead with a strong linear potential, a phenomenon known as Stark MBL. Here, the authors show how several experimental setups devised to study conventional MBL can also be used for Stark MBL, due to their almost identical phenomenologies. They then discuss Stark MBL as a possible experimental setting to explore Hilbert space fragmentation in systems with conserved dipole moment.
Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the nonergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case where the quenched on-site energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of 29 functional superconducting qubits, faithfully reproducing the relaxation dynamics of a nonintegrable spin model. At large Stark potentials, local observables display periodic Bloch oscillations, a manifesting characteristic of the fragmentation of the Hilbert space in sectors that conserve dipole moments. The flexible programmability of our quantum emulator highlights its potential in helping the understanding of nontrivial quantum many-body problems, in direct complement to simulations in classical computers.
In one-dimensional (1D) disorder-free interacting systems, a sufficiently strong linear potential can induce localization of the many-body eigenstates, a phenomenon dubbed as Stark many-body localization (MBL). In this paper, we investigate the fate of Stark MBL in 1D spinless fermions systems with long-range interactions, specifically focusing on the role of interaction strength. We obtain the Stark MBL phase diagrams by computing the mean gap ratio and many-body inverse participation ratio at half-filling. We show that, for short-range interactions, there is a qualitative symmetry between the limits of weak and strong interactions. However, this symmetry is absent in the case of long-range interactions, where the system is always Stark many-body localized at strong interactions, regardless of the linear potential strength. Furthermore, we study the dynamics of imbalance and entanglement with various initial states using time-dependent variational principle (TDVP) numerical methods. We reveal that the dynamical quantities display a strong dependence on the initial conditions, which suggests that the Hilbert-space fragmentation precludes thermalization. Our results demonstrate the robustness of Stark MBL even in the presence of long-range interactions and offer an avenue to explore MBL in disorder-free systems with long-range interactions.
We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined DC as well as a square wave AC electric field. First, the condition for the dynamical coherent destruction of Wannier-Stark localization and super Bloch oscillations in the non-interacting limit, are obtained semi-classically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to Stark many-body localization, for sufficiently large field strengths. We find that in the presence of an additional high-frequency AC field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive (A/ωA/\omegaA/ω) is tuned at the dynamical localization point of the non-interacting limit or by off-resonant drive. Remarkably, resonant drive with A/ωA/\omegaA/ω tuned away from the dynamical localization point leads to a \emph{coherent destruction of Stark-MBL}. Moreover, a pure (high-frequency) AC field can also give rise to the MBL phase if A/ωA/\omegaA/ω is tuned at the dynamical localization point of the zero dc field problem.
Stark Many-Body Localization (MBL) is a phenomenon observed in quantum systems in the absence of disorder, where the presence of a linear potential, known as the Stark field, causes the localization. Our study aims to provide novel insight into the properties of Stark MBL and to discover unique entanglement characteristics specific to this phenomenon. The phase diagram analysis reveals different behavior with varying interaction strengths. Furthermore, we highlight the influence of domain wall structures on the breakdown of the entanglement entropy of the system. Moreover, the investigation of Out-of-Time-Ordered Correlator (OTOC) behavior demonstrates distinct responses to interactions based on domain wall configurations. Our findings contribute to a better understanding of Stark MBL and offer valuable insights into the entanglement properties of systems subjected to Stark potentials.