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Exploring the many-body localization transition in two dimensions (1604.04178v1)

Published 14 Apr 2016 in cond-mat.quant-gas, cond-mat.dis-nn, cond-mat.stat-mech, and cond-mat.str-el

Abstract: One fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept, challenging our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single site resolved measurements we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments mark the first demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.

Citations (770)

Summary

  • The paper experimentally validates many-body localization (MBL) in a two-dimensional system using rubidium-87 bosons in a disordered optical lattice, investigating its transition from thermal to localized phases.
  • Key findings include identifying a critical disorder strength for the MBL transition and observing a divergence in the density profile decay length near this critical point, indicating a continuous phase transition.
  • The study highlights the significant role of interactions in enabling thermalization at low disorder and shows potential implications for understanding quantum coherence in complex materials and for applications like quantum computing.

Examination of Many-Body Localization Transition in Two-Dimensional Systems

The paper entitled "Exploring the many-body localization transition in two dimensions" provides a rigorous empirical investigation into the many-body localization (MBL) phenomenon in a two-dimensional (2D) regime, specifically using bosons in a disordered optical lattice. This research contributes to understanding the conditions under which a closed quantum many-body system fails to thermalize, thus challenging the conventionally accepted principles of statistical physics. This paper focuses on validation of MBL in higher dimensions, an area that poses significant challenges to current analytical and computational methods.

Methodology and Experimental Setup

The experiment was meticulously designed to track the relaxation dynamics of quantum states beyond current classical simulation capabilities. Utilizing a sophisticated 2D setup, the authors prepared a Mott insulator of rubidium-87 atoms in under a disordered potential created by a digital mirror device to project a controllable random optical lattice onto the sample. The dynamics of these systems were scrutinized under variable disorder strengths to elucidate the characteristics and conditions leading to MBL.

Findings and Analysis

Evidence from measuring the imbalance and examining the density profiles clearly indicates the onset of localization transitioning from thermal to localized phases at critical disorder strengths. Several critical observations were made:

  • Diverging Length Scale: The paper identified a divergence in the decay length of density profiles when approaching the MBL transition, suggestive of an underlying critical phenomenon and indicative of a continuous phase transition.
  • Critical Disorder Strengths: Through extensive measurement of imbalance over various disorder strengths, a critical disorder magnitude was identified, where the system transitions to a localized phase, no longer thermalizing, underlining the significant role of interaction-induced changes in dynamics.
  • Interaction Influence: The reduction in effective interaction via lowering initial occupant densities verified that interactions promote thermalization under low disorder, enabling localization only beyond a certain disorder threshold. This distinction showcases the salient role of interactions in determining many-body phase dynamics.

Implications and Future Directions

The implications of this work are threefold. Practically, these findings enhance our ability to predict and manage quantum coherence in complex materials, with potential implications for quantum computing and storage. Theoretically, this experimental result challenges current understanding and anticipates that quantum systems in higher dimensions harbor rich phenomena not present in 1D analogs. The results advocate for renewed theoretical and computational efforts to further dissect and comprehensively characterize transitions in finite dimensions.

Future explorations could focus on more refined characterizations of density-density correlations and spectral properties, which could further bridge gaps in the understanding of many-body eigenstates and their dynamical evolution. Additionally, the possibility of exploring Griffiths phases and sub-diffusive transport phenomena near the MBL transition holds promise for deepened insights into disorder-based quantum phase transitions.

In conclusion, the research presented compelling evidence for many-body localization in two dimensions, setting a precedent for subsequent experimental and theoretical studies aimed at a holistic understanding of localization phenomena in quantum systems.

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