Time crystal in non-Hermitian quantum systems

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). We numerically and analytically demonstrate that considering integrability breaking interactions will shift the phase diagram but leave the quasi time crystal phase for weak interactions. We will provide initial results on realizing this phase on a noisy quantum computer.

[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.