Time crystal in non-Hermitian system

Time crystals are an interesting new non-equilibrium phase of matter formed by repeating patterns in time, featuring time-translation symmetry breaking. Recently, Basu et al. [1] have opened the door to more interesting forms of symmetry breaking by non-unitary dynamics, such as a time crystal with quasi-long-range order. We consider an interacting form of this model and numerically solve it via time evolving block decimation (TEBD), comparing this to an analytical treatment via mean-field theory. Our findings, both numerical and analytical, consistently show that considering integrability breaking interactions will shift the phase diagram but maintain the existence of the quasi time crystal phase for weak interactions. One intriguing discovery from numeric is the emergence of a new phase transition appearing to be associated with a new, unexpected symmetry breaking. We comment on progress understanding this additional symmetry breaking.



[1] Sankhya Basu, Daniel P. Arovas, Sarang Gopalakrishnan, Chris A. Hooley, and Vadim Oganesyan. Fisher zeros and persistent temporal oscillations in nonunitary quantum circuits. Phys. Rev. Research, 4:013018, Jan 2022.