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Symmetry breaking and the geometry of reduced density matrices

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QUTE (Quantum Tensor Networks and Entanglement)
Abstract
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.
Keywords
strongly correlated systems, phase transitions, symmetry breaking, convex sets, thermodynamic surfaces, tensor network states, ENTANGLED PAIR STATES, IDEAL BOSE-GAS, ISING-MODEL, SQUARE LATTICE, SPIN SYSTEMS, POTTS-MODEL, SEPARABILITY, STATISTICS, DIMENSIONS, TRANSITION

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Citation

Please use this url to cite or link to this publication:

Chicago
Zauner, V, D Draxler, Laurens Vanderstraeten, Jutho Haegeman, and Frank Verstraete. 2016. “Symmetry Breaking and the Geometry of Reduced Density Matrices.” New Journal of Physics 18.
APA
Zauner, V, Draxler, D., Vanderstraeten, L., Haegeman, J., & Verstraete, F. (2016). Symmetry breaking and the geometry of reduced density matrices. NEW JOURNAL OF PHYSICS, 18.
Vancouver
1.
Zauner V, Draxler D, Vanderstraeten L, Haegeman J, Verstraete F. Symmetry breaking and the geometry of reduced density matrices. NEW JOURNAL OF PHYSICS. 2016;18.
MLA
Zauner, V, D Draxler, Laurens Vanderstraeten, et al. “Symmetry Breaking and the Geometry of Reduced Density Matrices.” NEW JOURNAL OF PHYSICS 18 (2016): n. pag. Print.
@article{8513360,
  abstract     = {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.},
  articleno    = {113033},
  author       = {Zauner, V and Draxler, D and Vanderstraeten, Laurens and Haegeman, Jutho and Verstraete, Frank},
  issn         = {1367-2630},
  journal      = {NEW JOURNAL OF PHYSICS},
  keyword      = {strongly correlated systems,phase transitions,symmetry breaking,convex sets,thermodynamic surfaces,tensor network states,ENTANGLED PAIR STATES,IDEAL BOSE-GAS,ISING-MODEL,SQUARE LATTICE,SPIN SYSTEMS,POTTS-MODEL,SEPARABILITY,STATISTICS,DIMENSIONS,TRANSITION},
  language     = {eng},
  pages        = {8},
  title        = {Symmetry breaking and the geometry of reduced density matrices},
  url          = {http://dx.doi.org/10.1088/1367-2630/18/11/113033},
  volume       = {18},
  year         = {2016},
}

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