Symmetry breaking and the geometry of reduced density matrices

The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all p...

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Main Authors: V Zauner, D Draxler, L Vanderstraeten, J Haegeman, F Verstraete
Format: Article
Language:English
Published: IOP Publishing 2016-01-01
Series:New Journal of Physics
Subjects:
Online Access:https://doi.org/10.1088/1367-2630/18/11/113033
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author V Zauner
D Draxler
L Vanderstraeten
J Haegeman
F Verstraete
author_facet V Zauner
D Draxler
L Vanderstraeten
J Haegeman
F Verstraete
author_sort V Zauner
collection DOAJ
description The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of these convex bodies exhibit non-analyticities, which signal the emergence of symmetry breaking and of an associated order parameter and also show different characteristics for different types of phase transitions. We illustrate this with three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model, the classical q -state Potts model in two-dimensions at finite temperature and the ideal Bose gas in three-dimensions at finite temperature. This state based viewpoint on phase transitions provides a unique novel tool for studying exotic many body phenomena in quantum and classical systems.
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spelling doaj.art-b7e6fcbea1d949079d1986c03a28382c2023-08-08T14:34:15ZengIOP PublishingNew Journal of Physics1367-26302016-01-01181111303310.1088/1367-2630/18/11/113033Symmetry breaking and the geometry of reduced density matricesV Zauner0D Draxler1L Vanderstraeten2J Haegeman3F Verstraete4Vienna Center for Quantum Technology, University of Vienna , Boltzmanngasse 5, A-1090 Wien, AustriaVienna Center for Quantum Technology, University of Vienna , Boltzmanngasse 5, A-1090 Wien, AustriaGhent University , Krijgslaan 281, B-9000 Gent, BelgiumGhent University , Krijgslaan 281, B-9000 Gent, BelgiumVienna Center for Quantum Technology, University of Vienna , Boltzmanngasse 5, A-1090 Wien, Austria; Ghent University , Krijgslaan 281, B-9000 Gent, BelgiumThe concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of these convex bodies exhibit non-analyticities, which signal the emergence of symmetry breaking and of an associated order parameter and also show different characteristics for different types of phase transitions. We illustrate this with three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model, the classical q -state Potts model in two-dimensions at finite temperature and the ideal Bose gas in three-dimensions at finite temperature. This state based viewpoint on phase transitions provides a unique novel tool for studying exotic many body phenomena in quantum and classical systems.https://doi.org/10.1088/1367-2630/18/11/113033strongly correlated systemsphase transitionssymmetry breakingconvex setsthermodynamic surfacestensor network states
spellingShingle V Zauner
D Draxler
L Vanderstraeten
J Haegeman
F Verstraete
Symmetry breaking and the geometry of reduced density matrices
New Journal of Physics
strongly correlated systems
phase transitions
symmetry breaking
convex sets
thermodynamic surfaces
tensor network states
title Symmetry breaking and the geometry of reduced density matrices
title_full Symmetry breaking and the geometry of reduced density matrices
title_fullStr Symmetry breaking and the geometry of reduced density matrices
title_full_unstemmed Symmetry breaking and the geometry of reduced density matrices
title_short Symmetry breaking and the geometry of reduced density matrices
title_sort symmetry breaking and the geometry of reduced density matrices
topic strongly correlated systems
phase transitions
symmetry breaking
convex sets
thermodynamic surfaces
tensor network states
url https://doi.org/10.1088/1367-2630/18/11/113033
work_keys_str_mv AT vzauner symmetrybreakingandthegeometryofreduceddensitymatrices
AT ddraxler symmetrybreakingandthegeometryofreduceddensitymatrices
AT lvanderstraeten symmetrybreakingandthegeometryofreduceddensitymatrices
AT jhaegeman symmetrybreakingandthegeometryofreduceddensitymatrices
AT fverstraete symmetrybreakingandthegeometryofreduceddensitymatrices