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arXiv:1501.03501 · Physical Review X

Universal Properties of Many-Body Delocalization Transitions

Andrew C. Potter, Romain Vasseur, S. A. Parameswaran

Published Sep 14, 2015• 331 citations
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Abstract

Developments in ultracold atomic experimental techniques highlight fundamental questions of whether quantum systems obey thermodynamics and statistical mechanics when isolated from their environment. A numerical technique is used to study phase transitions between thermal quantum fluids that obey thermodynamics and frozen quantum glasses that do not.

DOI
10.1103/physrevx.5.031033

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Developments in ultracold atomic experimental techniques highlight fundamental questions of whether quantum systems obey thermodynamics and statistical mechanics when isolated from their environment. A numerical technique is used to study phase transitions between thermal quantum fluids that obey thermodynamics and frozen quantum glasses that do not.
Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and molecules and the macroscopic properties of matter. However, statistical mechanics only describes the thermal equilibrium situation of a system, and there is no general framework to describe how equilibrium is reached or under which circumstances it can be reached at all. This problem is particularly challenging in quantum mechanics, where unitarity appears to render the very concept of thermalization counterintuitive. With the rapid experimental progress in the control and probing of ultracold quantum gases this question has become within reach of detailed experimental investigations. In these notes we present a series of experiments with ultracold one-dimensional Bose gases, which provide novel insights into this fundamental question.
氏名 池田 達彦The main theme of this thesis is the foundation of statistical mechanics in isolated quantum systems: how equilibrium states, or macroscopically unchanging states, emerge in the course of the unitary time evolution, why they are well described by the microcanonical ensemble, and how the thermodynamic entropy is interpreted from a quantum-mechanical viewpoint.Isolated quantum systems are by definition not in contact with a heat bath and, thus, they never lose their memory of the initial state to reach thermal equilibrium by throwing away the information to the bath.Therefore, to address the questions raised above, we must find out the inherent ability of isolated quantum systems to undergo thermalization.The foundation has been studied since the early 20th century because an isolated system plays the most fundamental role in statistical mechanics.Presupposing that the microcanonical ensemble describes thermal equilibrium states in isolated systems, the canonical ensemble, for example, is deduced in systems in contact with a heat bath.Despite its importance, the foundation is still only presupposed and has not been fully proven yet.Recently, the theme has attracted renewed attention because isolated quantum systems have experimentally been realized using ultracold atoms, which are trapped by lasers in a high vacuum.Until then, it had been of purely theoretical interest, and thermalization of most quantum systems in reality had often been ascribed to the coupling with their environment.Now that thermalization is actually observed in ultracold atom experiments, the theme is of interest not only theoretically but also experimentally.
We study the dynamical melting of hot one-dimensional quantum glasses. We focus on quantum glasses that emerge at strong disorder: specifically, many-body localized systems and their critical variants. The latter category includes disordered Ising, Potts, and anyonic chains whose excited-state properties and dynamics can be accessed via real-space renormalization group methods. As disorder is weakened below a critical value these non-thermal quantum glasses melt via a continuous dynamical phase transition into a classical thermal liquid. By accounting for resonant tunneling of energy, we derive and solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow sub-diffusive equilibration dynamics and energy transport, crossing over to ordinary classical diffusion at asymptotically long length scales for critical glasses. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. For non-critical, many-body localized glasses, the crossover scale diverges and subdiffusion persists to the thermodynamic limit. Our approach provides a firm microscopic basis for understanding the generic structure of many-body delocalization transitions in one dimension, and also reveals a general scaling relation among the critical exponents of the transition.