An instanton-like excitation of a discrete time crystal

TL;DR

This paper investigates instanton-like excitations in a non-equilibrium discrete time crystal, revealing tunneling phenomena between degenerate phases and a critical transition point with diverging instanton size.

Contribution

It introduces the concept of instanton-like excitations in discrete time crystals and analyzes their properties, including a dynamical transition with diverging instanton size.

Findings

Identification of instanton-like tunneling between degenerate time crystal phases

Observation of a dynamical transition with diverging instanton size

Proposal of a phenomenological theory for phase dynamics

Abstract

Spontaneous symmetry breaking and elementary excitation are two of the pillars of condensed matter physics that are closely related to each other. The symmetry and its spontaneous breaking not only control the dynamics and spectrum of elementary excitations, but also determine their underlying structures. In this paper, we study the excitation properties of a non-equilibrium quantum matter: a discrete time crystal phase that spontaneously breaks the temporal translational symmetry. It is shown that such an intriguing symmetry breaking allows an instanton-like excitation that represents a tunneling between two "degenerate" time crystal phases. Furthermore, we also observe a dynamical transition point at which the instanton "size" diverges, a reminiscence of the critical slowing down phenomenon in nonequilibrium statistic physics. A phenomenological theory has been proposed to understand the phase dynamics of the proposed system and the experimental realization and detection have also been discussed.