Instanton Crystal Phase*

We propose a class of models exhibiting instanton crystal phase. In this
phase, the minimum of the free energy corresponds to a configuration with an
imaginary-time-dependent order parameter in a form of a chain of alternating
instantons-and antiinstantons. The resulting characteristic feature of this
state is that the average of the order parameter vanishes, however, two- and
higher-order correlation functions of the order parameter show non-decaying
oscillations in imaginary time. In order to study the model in a broad
region of parameters of the model quantitatively, and 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 phase are obtained also
analytically. The numerical study of the model shows that there is a quantum
phase transition between the instanton crystal and the state with the
imaginary-time-independnet order parameter at zero temperature.