Abstract
We study a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. One example of such a transition is the recently proposed many-body localization-delocalization transition, in which transport coefficients vanish at a critical temperature with no singularities in thermodynamic observables. Describing this purely dynamical quantum criticality is technically challenging as understanding the finite-temperature dynamics necessarily requires averaging over a large number of matrix elements between many-body eigenstates. Here, we develop a real-space renormalization group method for excited states that allows us to overcome this challenge in a large class of models. We characterize a specific example: the 1 D disordered transverse-field Ising model with generic interactions. While thermodynamic phase transitions are generally forbidden in this model, using the real-space renormalization group method for excited states we find a finite-temperature dynamical transition between two localized phases. The transition is characterized by nonanalyticities in the low-frequency heat conductivity and in the long-time (dynamic) spin correlation function. The latter is a consequence of an up-down spin symmetry that results in the appearance of an Edwards-Anderson-like order parameter in one of the localized phases.
- Received 20 September 2013
DOI:https://doi.org/10.1103/PhysRevX.4.011052
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Published by the American Physical Society
Popular Summary
Upon heating, a compass needle loses its magnetization, or a liquid turns into vapor, at a particular material-dependent temperature. These are the two everyday examples of conventional phase transitions. These known phase transitions all have one property in common: There is at least one thermodynamic observable undergoing a qualitative or dramatic change, such as the magnetization in the case of a compass needle or the density in the case of a liquid. In this theoretical paper, we demonstrate a new type of quantum phase transition that leaves no signature in any thermodynamic observable, showing a fundamental departure from the conventional types.
The system where we find such an unusual phase transition is actually rather simple: a one-dimensional chain of quantum spins with nearest-neighbor interactions and local magnetic fields, both of random magnitude. The disorder immobilizes magnetic excitations, and this effect ultimately enables a novel athermal symmetry-breaking phase transition. An analysis of this phase transition is challenging since the transition involves nonequilibrium quantum properties of the system rather than its ground state, and its signatures through time-dependent transport properties, such as low-frequency heat conductivity, become unambiguously clear only in large systems..
Nonequilibrium behavior of a quantum system is determined by its excitations; the key is therefore to gain the knowledge of the excited many-spin eigenstates of a large system with disorder. Up to now, only systems with fewer than 100 spins could be reliably explored. Using the real-space renormalization-group method that we have developed for this purpose, however, we are able to construct excited eigenstates of systems having thousands of spins and hence obtain definitive results.
The transition we have analyzed is perhaps the simplest member of a new class of quantum dynamical transitions that could be realized in ultracold atom systems or, utilizing ultrafast lasers, in condensed matter systems. Our work opens the door to future exploration and classification.