We propose a class of models exhibiting the instanton crystal phase. In this phase, the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in the form of a chain of alternating instantons and anti-instantons. The resulting characteristic feature of this state is that the average of the order parameter over the imaginary time vanishes. In order to study the model in a broad region of parameters of the model quantitatively, and to prove the existence of the instanton crystal phase, we develop an efficient numerical scheme, suitable for the exact treatment of the proposed models. In a certain limit, results demonstrating the existence of the instanton crystal phase are obtained also analytically. The numerical study of the model shows that there is a phase transition between the instanton crystal and the state with the imaginary-time-independent order parameter.

• Received 24 November 2020
• Accepted 22 January 2021

DOI:https://doi.org/10.1103/PhysRevB.103.075121