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Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions

Babadi, Mehrtash and Demler, Eugene and Knap, Michael (2015) Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions. Physical Review X, 5 (4). Art. No. 041005. ISSN 2160-3308. doi:10.1103/PhysRevX.5.041005.

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We study theoretically the far-from-equilibrium relaxation dynamics of spin spiral states in the three-dimensional isotropic Heisenberg model. The investigated problem serves as an archetype for understanding quantum dynamics of isolated many-body systems in the vicinity of a spontaneously broken continuous symmetry. We present a field-theoretical formalism that systematically improves on the mean field for describing the real-time quantum dynamics of generic spin-1/2 systems. This is achieved by mapping spins to Majorana fermions followed by a 1/N expansion of the resulting two-particle-irreducible effective action. Our analysis reveals rich fluctuation-induced relaxation dynamics in the unitary evolution of spin spiral states. In particular, we find the sudden appearance of long-lived prethermalized plateaus with diverging lifetimes as the spiral winding is tuned toward the thermodynamically stable ferro- or antiferromagnetic phases. The emerging prethermalized states are characterized by different bosonic modes being thermally populated at different effective temperatures and by a hierarchical relaxation process reminiscent of glassy systems. Spin-spin correlators found by solving the nonequilibrium Bethe-Salpeter equation provide further insight into the dynamic formation of correlations, the fate of unstable collective modes, and the emergence of fluctuation-dissipation relations. Our predictions can be verified experimentally using recent realizations of spin spiral states with ultracold atoms in a quantum gas microscope [ et al., Phys. Rev. Lett. 113, 147205 (2014)].

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Additional Information:© 2015 Published by the American Physical Society. This article is available 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 26 April 2015; published 12 October 2015. We thank S. Gopalakrishnan, B. I. Halperin, and S. Sachdev for useful discussions. We acknowledge support from Harvard-MIT CUA, NSF Grant No. DMR-1308435, AFOSR Quantum Simulation MURI, the ARO-MURI on Atomtronics, ARO MURI Quism program, Humboldt Foundation, the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation, the Austrian Science Fund (FWF) Project No. J 3361-N20, as well as Technische Universität München–Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement No. 291763. E. D. acknowledges support from Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Foundation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Army Research Office (ARO)UNSPECIFIED
Alexander von Humboldt FoundationUNSPECIFIED
Institute for Quantum Information and MatterUNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
FWF Der WissenschaftsfondsJ 3361-N20
European Union FP7291763
German Excellence InitiativeUNSPECIFIED
Walter Haefner FoundationUNSPECIFIED
Issue or Number:4
Classification Code:PACS: 75.10.Jm, 05.40.-a 05.70.Ln,
Record Number:CaltechAUTHORS:20150622-114819053
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58404
Deposited By: Ruth Sustaita
Deposited On:22 Jun 2015 19:54
Last Modified:10 Nov 2021 22:04

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