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