Quantum critical behavior at the many-body-localization transition (1812.06959v1)

Abstract: Phase transitions are driven by collective fluctuations of a system's constituents that emerge at a critical point. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behavior is described by a general theory of phase transitions. Recently, however, fundamentally distinct phase transitions have been discovered for out-of-equilibrium quantum systems, which can exhibit critical behavior that defies this description and is not well understood. A paradigmatic example is the many-body-localization (MBL) transition, which marks the breakdown of quantum thermalization. Characterizing quantum critical behavior in an MBL system requires the measurement of its entanglement properties over space and time, which has proven experimentally challenging due to stringent requirements on quantum state preparation and system isolation. Here, we observe quantum critical behavior at the MBL transition in a disordered Bose-Hubbard system and characterize its entanglement properties via its quantum correlations. We observe strong correlations, whose emergence is accompanied by the onset of anomalous diffusive transport throughout the system, and verify their critical nature by measuring their system-size dependence. The correlations extend to high orders in the quantum critical regime and appear to form via a sparse network of many-body resonances that spans the entire system. Our results unify the system's microscopic structure with its macroscopic quantum critical behavior, and they provide an essential step towards understanding criticality and universality in non-equilibrium systems.

Overview of Quantum Critical Behavior at the Many-Body Localization Transition

This paper presents an empirical investigation into the quantum critical dynamics exhibited during the many-body localization (MBL) transition within a disordered Bose-Hubbard system. Utilizing advanced experimental protocols, the research innovatively combines site-resolved fluorescence imaging with control over disorder potentials and interaction parameters to directly observe and quantify the entanglement properties and transport phenomena inherent to this non-equilibrium quantum phase transition. These empirical results provide insight into the unique collective fluctuations and high-order correlation structures characteristic of the MBL transition, thereby advancing the understanding of criticality and universality in non-equilibrium quantum systems.

Experimental Framework and Methodology

The cornerstone of this paper is the implementation of tunable experimental setups that facilitate the exploration of dynamics via controlled Hamiltonian evolution. Researchers utilize the bosonic Aubry-André model, allowing for the inspection of systems with up to twelve lattice sites at unity filling and precise manipulation of disorder amplitude, interaction energy, and tunneling rates. The experimental protocol ensures high purity of the initial states, overcoming challenges such as rare-region effects and stochastic noise. Fluorescence imaging provides comprehensive atom-number distributions necessary for probing transport dynamics and subsequent entanglement characterization.

Key Findings and Numerical Insights

The paper reports several critical findings. First, it characterizes the slowdown of particle transport influenced by disorder strength, quantified through power-law growth exponents of the transport distance. This is indicative of anomalous diffusion occurring at intermediate disorder levels, suggesting a subdiffusive transport regime adjacent to the full localization observed at higher disorder strengths.

Further, the paper makes significant contributions by mapping the system-size dependence of observables in the long-time limit, revealing a distinctive lack of intrinsic length scales in the quantum critical regime. This finite-size dependence resonates with theoretical models suggesting a diminishing critical cone, a perspective corroborated by these experimental results.

Exploration of higher-order correlation structures reveals that all measured processes display a strong correlation within the quantum critical domain, denoting enhanced quantum fluctuations. Critical to understanding these interactions, the research illustrates a sparse network of resonances, emphasizing the criticality-related macroscopic transport processes by leveraging correlations rooted in the quasi-periodic potential structure.

Theoretical Implications and Future Directions

These findings substantiate theoretical claims about anomalous diffusion and many-body resonances around the MBL transition. The paper convincingly supports the hypothesis that many-body dynamics govern quantum critical behavior via complex resonant tunneling and correlated hopping processes, advancing the narrative of interactions facilitating critical transport.

Looking ahead, the paper posits several promising avenues for future research: examining potential jumps in entanglement entropy near transitions, probing new dynamical phases, and assessing rare-region influences. The expanded capacity for simulating larger systems computationally unavailable presents ample opportunities for deeper inquiries into non-equilibrium quantum mechanics, with ramifications for theoretical models and quantum computing architectures.

Through this detailed exploration of quantum critical phenomena at the MBL transition, the paper not only enhances experimental methodologies for studying complex quantum systems but also stimulates further theoretical debates concerning the underpinning dynamics of phase transitions out of equilibrium.