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Symmetry breaking and the geometry of reduced density matrices

Autor(en)
V. Zauner, D. Draxler, L. Vanderstraeten, J. Haegeman, F. Verstraete
Abstrakt

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.

Organisation(en)
Quantenoptik, Quantennanophysik und Quanteninformation
Externe Organisation(en)
Ghent University
Journal
New Journal of Physics
Band
18
Anzahl der Seiten
21
ISSN
1367-2630
DOI
https://doi.org/10.1088/1367-2630/18/11/113033
Publikationsdatum
11-2016
Peer-reviewed
Ja
ÖFOS 2012
103025 Quantenmechanik, 103015 Kondensierte Materie, 103029 Statistische Physik
Schlagwörter
ASJC Scopus Sachgebiete
Allgemeine Physik und Astronomie
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/8bf54496-7030-4522-8298-9414315af809