HilbertGlass Transition: New Universality of TemperatureTuned ManyBody Dynamical Quantum Criticality
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 manybody localizationdelocalization 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 finitetemperature dynamics necessarily requires averaging over a large number of matrix elements between manybody eigenstates. Here, we develop a realspace 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 transversefield Ising model with generic interactions. While thermodynamic phase transitions are generally forbidden in this model, using the realspace renormalization group method for excited states we find a finitetemperature dynamical transition between two localized phases. The transition is characterized by nonanalyticities in the lowfrequency heat conductivity and in the longtime (dynamic) spin correlation function. The latter is a consequence of an updown spin symmetry that results in the appearance of an EdwardsAndersonlike order parameter in one of the localized phases.
 Publication:

Physical Review X
 Pub Date:
 January 2014
 DOI:
 10.1103/PhysRevX.4.011052
 arXiv:
 arXiv:1307.3253
 Bibcode:
 2014PhRvX...4a1052P
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics
 EPrint:
 The previous version of the paper contained an error in the expression for T_c at low T in Sec. IIc. In addition to fixing this error we have also made small improvements throughout the text