SciPost Physics Core

SciPost Phys. Core 5, 004 (2022) · published 27 January 2022

• doi: 10.21468/SciPostPhysCore.5.1.004
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Abstract

We study the dissipative dynamics of one-dimensional fermions, described in terms of the sine-Gordon model in its free massive boson or semi-classical limit, while keeping track of forward scattering processes. The system is prepared in the gapped ground state, and then coupled to environment through local currents within the Lindblad formalism. The heating dynamics of the system is followed using bosonization. The single particle density matrix exhibits correlations between the left and right moving particles. While the density matrix of right movers and left movers is translationally invariant, the left-right sector is not, corresponding to a translational symmetry breaking charge density wave state. Asymptotically, the single particle density matrix decays exponentially with exponent proportional to $-\gamma t|x|\Delta^2$ where $\gamma$ and $\Delta$ are the dissipative coupling and the gap, respectively. The charge density wave order parameter decays exponentially in time with an interaction independent decay rate. The second R\'enyi entropy grows linearly with time and is essentially insensitive to the presence of the gap.

• Gunawardana et al., Dynamical l-bits and persistent oscillations in Stark many-body localization
  Phys. Rev. B 106, L161111 (2022) [Crossref]
• Yamamoto et al., Universal description of dissipative Tomonaga-Luttinger liquids with SU(N) spin symmetry: Exact spectrum and critical exponents
  Phys. Rev. B 107, 045110 (2023) [Crossref]
• Yamamoto et al., Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
  Phys. Rev. B 105, 205125 (2022) [Crossref]
• Rao et al., Generalized sine-Gordon model for coupled condensates and phase transition
  Phys. Rev. B 108, 115106 (2023) [Crossref]