%0 Journal Article %D 2023 %T Colloquium: Quantum and Classical Discrete Time Crystals %A Michael P. Zaletel %A Mikhail Lukin %A Christopher Monroe %A Chetan Nayak %A Frank Wilczek %A Norman Y. Yao %X

The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. We focus on the breaking of ergodicity as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the AC Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there exists a diverse array of strategies to stabilize time crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits will be reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

%8 5/15/2023 %G eng %U https://arxiv.org/abs/2305.08904 %0 Journal Article %J Journal of High Energy Physics %D 2018 %T Entanglement of purification: from spin chains to holography %A Phuc Nguyen %A Trithep Devakul %A Matthew G. Halbasch %A Michael P. Zaletel %A Brian Swingle %X

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

%B Journal of High Energy Physics %P 98 %8 2018/01/22 %G eng %U https://link.springer.com/article/10.1007%2FJHEP01%282018%29098#citeas %R 10.1007/JHEP01(2018)098