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Quantum quench in non-relativistic fermionic field theory: harmonic traps and 2d string theory

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  • Published: 30 August 2019
  • Volume 2019, article number 176, (2019)
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Quantum quench in non-relativistic fermionic field theory: harmonic traps and 2d string theory
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  • Sumit R. Das1,
  • Shaun Hampton1 &
  • Sinong Liu1 

  • 440 Accesses

  • 12 Citations

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A preprint version of the article is available at arXiv.

Abstract

We investigate a class of exactly solvable quantum quench protocols with a finite quench rate in systems of one dimensional non-relativistic fermions in external harmonic oscillator or inverted harmonic oscillator potentials, with time dependent masses and frequencies. These hamiltonians arise, respectively, in harmonic traps, and the c = 1 Matrix Model description of two dimensional string theory with time dependent string coupling. We show how the dynamics is determined by a single function of time which satisfies a generalized Ermakov-Pinney equation. The quench protocols we consider asymptote to constant masses and frequencies at early times, and cross or approach a gapless potential. In a right side up harmonic oscillator potential we determine the scaling behavior of the one point function and the entanglement entropy of a subregion by obtaining analytic approximations to the exact answers. The results are consistent with Kibble-Zurek scaling for slow quenches and with perturbation calculations for fast quenches. For cis-critical quench protocols the entanglement entropy oscillates at late times around its initial value. For end-critical protocols the entanglement entropy monotonically goes to zero inversely with time, reflecting the spread of fermions over the entire line. For the inverted harmonic oscillator potential, the dual collective field description is a scalar field in a time dependent metric and dilaton background.

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  1. Department of Physics and Astronomy, University of Kentucky, Lexington, KY, 40506, U.S.A.

    Sumit R. Das, Shaun Hampton & Sinong Liu

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Das, S.R., Hampton, S. & Liu, S. Quantum quench in non-relativistic fermionic field theory: harmonic traps and 2d string theory. J. High Energ. Phys. 2019, 176 (2019). https://doi.org/10.1007/JHEP08(2019)176

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  • Received: 02 May 2019

  • Revised: 08 July 2019

  • Accepted: 06 August 2019

  • Published: 30 August 2019

  • DOI: https://doi.org/10.1007/JHEP08(2019)176

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Keywords

  • Field Theories in Lower Dimensions
  • Holography and condensed matter physics (AdS/CMT)
  • Matrix Models
  • Nonperturbative Effects
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