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...
Main Authors: | , , , , |
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Format: | Article |
Language: | English |
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IOP Publishing
2016-01-01
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Series: | New Journal of Physics |
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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. |
first_indexed | 2024-03-12T16:39:48Z |
format | Article |
id | doaj.art-b7e6fcbea1d949079d1986c03a28382c |
institution | Directory Open Access Journal |
issn | 1367-2630 |
language | English |
last_indexed | 2024-03-12T16:39:48Z |
publishDate | 2016-01-01 |
publisher | IOP Publishing |
record_format | Article |
series | New Journal of Physics |
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 |