Constraints on order and disorder parameters in quantum spin chains
M. Levin. (2019)cite arxiv:1903.09028Comment: 27 pages, 2 figures, added affiliation.
Zusammenfassung
We derive general constraints on order and disorder parameters in Ising
symmetric spin chains. Our main result is a theorem showing that every gapped,
translationally invariant, Ising symmetric spin chain has either a nonzero
order parameter or a nonzero disorder parameter. We also prove two more
constraints on order and disorder parameters: (i) it is not possible for a
gapped, Ising symmetric spin chain to have both a nonzero order parameter and a
nonzero disorder parameter; and (ii) it is not possible for a spin chain of
this kind to have a nonzero disorder parameter that is odd under the symmetry.
These constraints have an interesting implication for self-dual Ising symmetric
spin chains: every self-dual spin chain is either gapless or has a degenerate
ground state in the thermodynamic limit. All of these constraints generalize to
spin chains without translational symmetry. Our proofs rely on previously known
bounds on entanglement and correlations in one dimensional systems, as well as
the Fuchs-van de Graaf inequality from quantum information theory.
Beschreibung
Constraints on order and disorder parameters in quantum spin chains
%0 Generic
%1 levin2019constraints
%A Levin, Michael
%D 2019
%K 1d topological-order
%T Constraints on order and disorder parameters in quantum spin chains
%U http://arxiv.org/abs/1903.09028
%X We derive general constraints on order and disorder parameters in Ising
symmetric spin chains. Our main result is a theorem showing that every gapped,
translationally invariant, Ising symmetric spin chain has either a nonzero
order parameter or a nonzero disorder parameter. We also prove two more
constraints on order and disorder parameters: (i) it is not possible for a
gapped, Ising symmetric spin chain to have both a nonzero order parameter and a
nonzero disorder parameter; and (ii) it is not possible for a spin chain of
this kind to have a nonzero disorder parameter that is odd under the symmetry.
These constraints have an interesting implication for self-dual Ising symmetric
spin chains: every self-dual spin chain is either gapless or has a degenerate
ground state in the thermodynamic limit. All of these constraints generalize to
spin chains without translational symmetry. Our proofs rely on previously known
bounds on entanglement and correlations in one dimensional systems, as well as
the Fuchs-van de Graaf inequality from quantum information theory.
@misc{levin2019constraints,
abstract = {We derive general constraints on order and disorder parameters in Ising
symmetric spin chains. Our main result is a theorem showing that every gapped,
translationally invariant, Ising symmetric spin chain has either a nonzero
order parameter or a nonzero disorder parameter. We also prove two more
constraints on order and disorder parameters: (i) it is not possible for a
gapped, Ising symmetric spin chain to have both a nonzero order parameter and a
nonzero disorder parameter; and (ii) it is not possible for a spin chain of
this kind to have a nonzero disorder parameter that is odd under the symmetry.
These constraints have an interesting implication for self-dual Ising symmetric
spin chains: every self-dual spin chain is either gapless or has a degenerate
ground state in the thermodynamic limit. All of these constraints generalize to
spin chains without translational symmetry. Our proofs rely on previously known
bounds on entanglement and correlations in one dimensional systems, as well as
the Fuchs-van de Graaf inequality from quantum information theory.},
added-at = {2019-03-25T10:21:15.000+0100},
author = {Levin, Michael},
biburl = {https://www.bibsonomy.org/bibtex/2acda1281871a44c78948add7822468ec/abelion},
description = {Constraints on order and disorder parameters in quantum spin chains},
interhash = {d06e9b69f6534b5b2da6ae3078e07274},
intrahash = {acda1281871a44c78948add7822468ec},
keywords = {1d topological-order},
note = {cite arxiv:1903.09028Comment: 27 pages, 2 figures, added affiliation},
timestamp = {2019-03-25T10:21:15.000+0100},
title = {Constraints on order and disorder parameters in quantum spin chains},
url = {http://arxiv.org/abs/1903.09028},
year = 2019
}