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Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality

Pekker, David and Refael, Gil and Altman, Ehud and Demler, Eugene and Oganesyan, Vadim (2014) Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality. Physical Review X, 4 (1). Art. No. 011052. ISSN 2160-3308. doi:10.1103/PhysRevX.4.011052.

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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.

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Additional Information:© 2014 the Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 20 September 2013; revised manuscript received 23 December 2013; published 31 March 2014. It is our pleasure to thank Kedar Damle, Olexei Motrunich, David Huse, and Stefan Kehrein for useful conversations. The authors thank the KITP and the National Science Foundation under Grant No. NSF PHY11-25915 for hospitality during the conception of the paper and the Aspen Center for Physics and the NSF Grant No. 1066293 for hospitality during the writing of this paper. The computations in this paper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group at Harvard University. The authors acknowledge support from the Lee A. DuBridge prize postdoctoral fellowship (D. P.), the IQIM, an NSF center supported in part by the Moore Foundation (D. P., G. R.), DMR-0955714 (V. O.), the Packard Foundation (G. R.), BSF (E. A., E. D.), ISF and the Miller Institute for Basic Science (E. A.), Harvard-MIT CUA, the DARPA OLE program, AFOSR MURI on Ultracold Molecules, and ARO-MURI on Atomtronics (E. D.). Note added.—Recently, a paper describing a method that has some similarities to our RSRG-X appeared [37]. Another paper posted in parallel to this one explores the HGT from the complementary viewpoint of the time evolution following a quench [38].
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Aspen Center for PhysicsUNSPECIFIED
Harvard FAS Science Division Research Computing GroupUNSPECIFIED
Lee A. DuBridge prize postdoctoral fellowshipUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Miller Institute for Basic ScienceUNSPECIFIED
AFOSR MURI on Ultracold MoleculesUNSPECIFIED
Subject Keywords:Atomic and Molecular Physics; Condensed Matter Physics; Quantum Physics
Issue or Number:1
Record Number:CaltechAUTHORS:20140501-160826197
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Official Citation:Pekker, D., Refael, G., Altman, E., Demler, E., & Oganesyan, V. (2014). Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality. Physical Review X, 4(1), 011052.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45449
Deposited On:01 May 2014 23:46
Last Modified:10 Nov 2021 17:03

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