Dynamical quantum phase transition in a bosonic system with long-range interactions

TL;DR

This paper studies dynamical quantum phase transitions in a bosonic system with long-range interactions, revealing how the generation of a mass gap after a quench leads to distinct dynamical phases and nonanalytic behavior in the Loschmidt echo.

Contribution

It introduces an analytical approximation for late-time dynamics and links the emergence of dynamical quantum phase transitions to the formation of a finite mass gap post-quench.

Findings

Dynamical phase transitions depend on the post-quench mass gap.

Loschmidt echo shows periodic nonanalytic cusps with specific initial and final states.

Two dynamical phases are characterized by the presence or absence of a finite mass gap.

Abstract

In this paper, we investigate the dynamical quantum phase transitions appearing in the Loschmidt echo and the time-dependent order parameter of a quantum system of harmonically coupled degenerate bosons as a function of the power-law decay $\sigma$ of long-range interactions. Following a sudden quench, the nonequilibrium dynamics of this system are governed by a set of nonlinear coupled Ermakov equations. To solve them, we develop an analytical approximation valid at late times. Based on this approximation, we show that the emergence of a dynamical quantum phase transition hinges on the generation of a finite mass gap following the quench, starting from a massless initial state. In general, we can define two distinct dynamical phases characterized by the finiteness of the post-quench mass gap. The Loschmidt echo exhibits periodical nonanalytic cusps whenever the initial state has a vanishing mass gap and the final state has a finite mass gap. These cusps are shown to coincide with the maxima of the time-dependent long-range correlations.