General theory for discrete symmetry-breaking equilibrium states
- URL: http://arxiv.org/abs/2303.18020v1
- Date: Fri, 31 Mar 2023 12:52:36 GMT
- Title: General theory for discrete symmetry-breaking equilibrium states
- Authors: \'Angel L. Corps, Armando Rela\~no
- Abstract summary: Spontaneous symmetry-breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation.
We show that when a discrete symmetry is spontaneously broken in a quantum system, the time evolution necessarily conserves two additional and non-commuting quantities.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Spontaneous symmetry-breaking in phase transitions occurs when the system
Hamiltonian is symmetric under a certain transformation, but the equilibrium
states observed in nature are not. Here, we prove that when a discrete symmetry
is spontaneously broken in a quantum system, then the time evolution
necessarily conserves two additional and non-commuting quantities, besides the
one linked to the symmetry. This implies the existence of equilibrium states
consisting in superpositions of macroscopic configurations. Then, we propose an
experimental realization of such equilibrium states with the current
state-of-the art in quantum technologies. Through numerical calculations, we
show that they survive as very long-lived pre-thermal states, even very far
away from the thermodynamic limit. Finally, we also show that a small
symmetry-breaking perturbation in the Hamiltonian stabilizes the conservation
of one of the two former quantities, implying that symmetry-breaking
equilibrium states become stable even in small quantum systems.
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