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arXiv · 1307.3253

The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality

David Pekker·Gil Refael·Ehud Altman·Eugene Demler·Vadim Oganesyan
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Abstract

We consider a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. A possible example is the recently proposed many-body localization transition, in which transport coefficients vanish at a critical temperature. Describing this unconventional quantum criticality has been technically challenging as understanding the finite-temperature dynamics requires the knowledge of a large number of many-body eigenstates. Here we develop a real-space renormalization group method for excited state (RSRG-X), that allow us to overcome this challenge, and establish the existence and universal properties of such temperature-tuned dynamical phase transitions. We characterize a specific example: the 1D disordered transverse field Ising model with interactions. Using RSRG-X, we find a finite-temperature transition, between two localized phases, characterized by non-analyticities of the dynamic spin correlation function and the low frequency heat conductivity.

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David Pekker, Gil Refael, Ehud Altman, Eugene Demler, Vadim Oganesyan. 2013-08-15. The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality. https://doi.org/10.1103/physrevx.4.011052

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