Time-crystalline long-range order in chiral fermionic vacuum

TL;DR

This paper demonstrates the existence of time-crystalline long-range order in the ground state of a one-dimensional chiral fermionic system, challenging previous beliefs about short-range systems.

Contribution

It reveals that spatial discontinuities and infinite dimensionality can induce time-crystalline order in ground states of fermionic systems.

Findings

Time-dependent correlation functions diverge logarithmically at equal times.

Breakdown of the inequality prohibiting time-crystalline order in ground states.

Connection to divergence in bosonic correlation functions via bosonization.

Abstract

It is widely believed that there is no macroscopic time-crystalline order in the ground states of short-range interacting systems. In this paper, we consider a time-dependent correlation function for an order operator with a spatially discontinuous weight in a one-dimensional chiral fermionic system. Although both the Hamiltonian and the order parameter are composed of spatially local operators, the time-dependent correlation function diverges logarithmically in equal time intervals. This result implies a breakdown of an inequality that claims the absence of time-crystalline long-range order in the ground states, unless the upper-bound constant is set to be infinity. This behavior is due to the combination of the discontinuity of the order operator and the infinite dimensionality of quantum field theory. In the language of bosonization, it can also be related to the divergence of a space-time-resolved bosonic correlation function.