Condensed matter physics in time crystals

• Published in: New journal of physics Vol. 22; no. 7; pp. 75003 - 75025
• Main Authors: Guo, Lingzhen, Liang, Pengfei
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.07.2020
• Subjects: Band theory; Broken symmetry; condensed matter; Condensed matter physics; Crystal lattices; discrete time crystals; Floquet engineering; Floquet time crystals; noncommutative geometry; phase space crystals; Physics; Symmetry; symmetry breaking; Topology
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ab9d54

Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the discrete time-translation symmetry in periodically driven (Floquet) systems is allowed to be spontaneously broken, resulting in the so-called Floquet or discrete time crystals. While most works so far searching for time crystals focus on the symmetry breaking process and the possible stabilising mechanisms, the many-body physics from the interplay of symmetry-broken states, which we call the condensed matter physics in time crystals, is not fully explored yet. This review aims to summarise the very preliminary results in this new research field with an analogous structure of condensed matter theory in solids. The whole theory is built on a hidden symmetry in time crystals, i.e., the phase space lattice symmetry, which allows us to develop the band theory, topology and strongly correlated models in phase space lattice. In the end, we outline the possible topics and directions for the future research.