Incommensurate Charge Density Wave as Quantum Space-Time Crystal

TL;DR

This paper proposes that incommensurate charge density waves can form quantum space-time crystals, extending the concept of quantum time crystals into spatial and temporal domains, with potential real-world observations.

Contribution

It introduces the idea that ICDWs can create quantum space crystals, combining spatial and temporal symmetry breaking, and suggests experimental realizations in materials like TaS3.

Findings

QSTC can form in ring-shaped ICDWs.

Model predicts observable QSTC states in real materials.

Breaking of space-time symmetry demonstrated via density matrices.

Abstract

A quantum time crystal (QTC) is a novel quantum mechanical ground state that was recently proposed by Wilczek. Although many QTC models have been proposed, it is not clear yet if such states are possible. We propose the idea that an incommensurate charge density wave (ICDW) forms a quantum space crystal (QSC), which is an extension of a QTC in the spatial domain. Consequently, a rotating ring-shaped ICDW naturally forms a quantum space-time crystal (QSTC), which combines the two concepts of QTC and QSC. The breaking of space-time translation symmetry is understood using time-dependent density matrices. Furthermore, we show that this model can be observed in real systems such as TaS$_3$ ring crystals at finite temperature. Our results suggest that QTC/QSTC can exist.