Boundary time crystals

TL;DR

This paper introduces boundary time crystals, a new form of time-translation symmetry breaking in many-body quantum systems, characterized by a time-periodic steady state emerging in open quantum systems and linked to quantum synchronization.

Contribution

It defines boundary time crystals, analyzes a solvable model, and explores their connection to time-periodic steady states and quantum synchronization.

Findings

Boundary time crystals exhibit continuous time-translation symmetry breaking.

A solvable model demonstrates the existence of boundary time crystals.

Boundary time crystals are connected to time-periodic steady states in open quantum systems.

Abstract

In this work we introduce {\it boundary time-crystals}. Here {\it continuous} time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we analyse in detail a solvable model where an accurate scaling analysis can be performed. The existence of the boundary time crystals is intimately connected to the emergence of a time-periodic steady state in the thermodynamic limit of a many-body open quantum system. We also discuss connections to quantum synchronisation.