Quasi time crystal

TL;DR

This paper explores the concept of quasi time crystals, demonstrating their existence through a simple two-state model and the transverse field Ising model, highlighting periodic temporal behavior in quantum systems.

Contribution

It introduces the idea of quasi time crystals, analyzing their properties via a two-state model and applying the concept to the transverse field Ising model with exact solutions.

Findings

Periodic probability variations in superpositions of quantum states.

Existence of quasi time crystal behavior near quantum phase transitions.

Exact solution of oscillating magnetization in the transverse field Ising model.

Abstract

We discuss the possibility of making a quasi time crystal. A simple two-state model is studied to clarify our definition. In a superposition of the ground state and the excited state and the probability of observation varies periodically in time during the lifetime of the excited state. The quasi time crystal is also discussed around the first order quantum phase transition, which is characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. Our results have broad validity. As an example, the one-dimensional transverse field Ising model with surface fields is shown to have similar behavior. The oscillating magnetization profile is solved exactly.