Nonergodic metallic and insulating phases of Josephson junction chains

Abstract

Strictly speaking, the laws of the conventional statistical physics, based on the equipartition postulate [Gibbs J W (1902) Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics] and ergodicity hypothesis [Boltzmann L (1964) Lectures on Gas Theory], apply only in the presence of a heat bath. Until recently this restriction was believed to be not important for real physical systems because a weak coupling to the bath was assumed to be sufficient. However, this belief was not examined seriously until recently when the progress in both quantum gases and solid-state coherent quantum devices allowed one to study the systems with dramatically reduced coupling to the bath. To describe such systems properly one should revisit the very foundations of statistical mechanics. We examine this general problem for the case of the Josephson junction chain that can be implemented in the laboratory and show that it displays a novel high-temperature nonergodic phase with finite resistance. With further increase of the temperature the system undergoes a transition to the fully localized state characterized by infinite resistance and exponentially long relaxation.T he remarkable feature of the closed quantum systems is the appearance of many-body localization (MBL) (1): Under certain conditions the states of a many-body system are localized in the Hilbert space resembling the celebrated Anderson localization (2) of single particle states in a random potential. MBL implies that macroscopic states of an isolated system depend on the initial conditions (i.e., the time averaging does not result in equipartition distribution and the entropy never reaches its thermodynamic value). Variation of macroscopic parameters (e.g., temperature) can delocalize the many-body state. However, the delocalization does not imply the recovery of the equipartition. Such a nonergodic behavior in isolated physical systems is the subject of this paper.We argue that regular Josephson junction arrays (JJAs) under the conditions that are feasible to implement and control experimentally demonstrate both MBL and nonergodic behavior. A great advantage of the Josephson circuits is the possibility to disentangle them from the environment, as was demonstrated by the quantum information devices (3). At low temperatures the conductivity σ of JJA is finite (below we call such behavior metallic), whereas as T → 0 JJA becomes either a superconductor ðσ → ∞Þ or an insulator ðσ → 0Þ (4, 5). We predict that at a critical temperature T = T c JJA undergoes a true phase transition into an MBL insulator (σ = 0 for T > T c ). Remarkably, already in the metallic state JJA becomes nonergodic and cannot be properly described by conventional statistical mechanics.In the bad metal regime the dynamical evolution starting from a particular initial state does not lead to the thermodynamic equilibrium, so that even extensive quantities such as entropy differ from their thermodynamic values. Starting with the seminal...

Multifractal metal in a disordered Josephson junctions array

“…The possibility of a delocalized non-ergodic behavior is very important for the interpretation of the data on atomic systems such as [10,11] because it implies that slow dynamics does not mean full localization. The non-ergodic state of the superconducting systems can be detected by the noise measurements that is expected to show strong violation of FDT [5]; in line with these expectations a giant noise was reported recently close to superconductor-insulator transition [12]. A more detailed discussion of the physical properties in this regime can be found in [5,13].…”

Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase

“…Essentially, the structure of localized wavefunctions in the Fock space of many-body quantum systems can be mapped on the localization problem of a single particle hopping on a treelike graph with quenched disorder [4][5][6] . The phenomena of many-body localization and ergodicity breaking in isolated quantum systems prevent them to equilibrate, which has serious consequences for the foundations of equilibrium statistical mechanics 7,8 .…”

Fixed Points of Wegner-Wilson Flows and Many-Body Localization

“…While the understanding of the transition between thermal and MBL phases is only beginning to emerge [8][9][10][11][12], several distinct new directions of inquiry related to MBL and the fundamental issue of ergodicity in quantum many-body systems have taken shape. These include the interplay of MBL with spontaneous symmetry breaking and topological order [13][14][15][16], selflocalization (glassiness) in translationally invariant quantum systems [17][18][19][20], and MBL in driven systems [21][22][23]. MBL has also stimulated considerable progress in developing tools for describing excited eigenstates of many-body systems [12,[24][25][26][27][28].…”