Time-crystalline long-range order in chiral fermionic vacuum
- URL: http://arxiv.org/abs/2111.08127v1
- Date: Mon, 15 Nov 2021 22:52:05 GMT
- Title: Time-crystalline long-range order in chiral fermionic vacuum
- Authors: Nobuyuki Okuma
- Abstract summary: It is widely believed that there is no macroscopic time-crystalline order in the ground states of short-range interacting systems.
We consider a time-dependent correlation function for an order operator with a spatially discontinuous weight in a one-dimensional chiral fermionic system.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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