Non-equilibrium time evolution in the sine-Gordon model revisited

TL;DR

This paper introduces a novel Hamiltonian truncation method, MSTHA, to simulate non-equilibrium dynamics in the quantum sine-Gordon model, demonstrating its effectiveness across various interaction regimes and quench energies, and comparing it with semiclassical approaches.

Contribution

The paper develops MSTHA, a new Hamiltonian truncation scheme that accurately captures sine-Gordon dynamics from the hard core boson limit to weak interactions, extending previous methods.

Findings

MSTHA accurately simulates post-quench dynamics in the sine-Gordon model.

The method remains valid for mild quenches across different interaction strengths.

Semiclassical TWA approximates the dynamics well in the weakly interacting regime.

Abstract

We study the non-equilibrium dynamics of the quantum sine-Gordon model describing a pair of Josephson-coupled one-dimensional bosonic quasi-condensates. Motivated by experimentally accessible quench procedures where the zero mode of the quasi-condensates is weakly coupled to finite momentum modes, we develop a novel Hamiltonian truncation scheme relying on a mini-superspace treatment of the zero mode (MSTHA). We apply this method to simulate the time evolution after both weak and strong quantum quenches, injecting a low or high energy density into the system, and demonstrate that MSTHA accurately captures the dynamics from the hard core boson limit to the experimentally relevant weakly interacting regime for sufficiently mild quenches. In the case of high energy densities, MSTHA breaks down for weak interaction but still extends the range of validity of previous Hamiltonian truncation schemes. We also compare these results to the semiclassical truncated Wigner approximation (TWA) and establish that the dynamics can be well approximated by the semiclassical description in the weakly interacting regime realised in the experiments. In addition, we clarify the importance of the phononic modes depending on the sine-Gordon interaction strength.