Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains

TL;DR

This paper investigates how non-equilibrium fluctuations influence pre-thermal dynamical phase transitions in long-range interacting quantum spin chains, revealing chaotic dynamics and signatures in correlation functions and Loschmidt echo.

Contribution

It introduces a combined analytical and numerical approach to study the impact of fluctuations on dynamical phase transitions in non-integrable spin models with long-range interactions.

Findings

Fluctuations can induce chaotic evolution near critical points.

Dynamical phase signatures appear in correlation functions.

Cusps in Loschmidt echo correspond to order parameter vanishing.

Abstract

We study the non-equilibrium phase diagram and the dynamical phase transitions occurring during the pre-thermalization of non-integrable quantum spin chains, subject to either quantum quenches or linear ramps of a relevant control parameter. We consider spin systems in which long-range ferromagnetic interactions compete with short-range, integrability-breaking terms. We capture the pre-thermal stages of the non-equilibrium evolution via a time-dependent spin wave expansion at leading order in the spin waves density. In order to access regimes with strong integrability breaking, instead, we perform numerical simulations based on the time-dependent variational principle with matrix product states. By investigating a large class of quantum spin models, we demonstrate that non-equilibrium fluctuations can significantly affect the dynamics near critical points of the phase diagram, resulting in a chaotic evolution of the collective order parameter, akin to the dynamics of a classical particle in a multiple-well potential subject to quantum friction. We also elucidate the signature of this novel dynamical phase on the time-dependent correlation functions of the local order parameter. We finally establish a connection with the notion of dynamical quantum phase transition associated with a possible non-analytic behavior of the return probability amplitude, or Loschmidt echo, showing that the latter displays cusps whenever the order parameter vanishes during its real-time evolution.