Universal fidelity near quantum and topological phase transitions in finite 1D systems

We study the quantum fidelity (groundstate overlap) near quantum phase transitions of the Ising universality class in one dimensional (1D) systems of finite size L. Prominent examples occur in magnetic systems (e.g. spin-Peierls, the anisotropic XY model), and in 1D topological insulators of any top...

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Bibliographic Details
Published inarXiv.org
Main Authors König, E J, Levchenko, A, Sedlmayr, N
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 12.02.2016
Subjects
Exact solutions
Ising model
Magnetic permeability
Mathematical models
Phase transitions
Physics - Mesoscale and Nanoscale Physics
Physics - Statistical Mechanics
Topological insulators
Topology
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Summary:We study the quantum fidelity (groundstate overlap) near quantum phase transitions of the Ising universality class in one dimensional (1D) systems of finite size L. Prominent examples occur in magnetic systems (e.g. spin-Peierls, the anisotropic XY model), and in 1D topological insulators of any topologically nontrivial Altland-Zirnbauer-Kitaev universality class. The rescaled fidelity susceptibility is a function of the only dimensionless parameter LM, where 2M is the gap in the fermionic spectrum. We present analytic expressions for the fidelity susceptibility for periodic and open boundaries conditions with zero, one or two edgestates. The latter are shown to have a crucial impact and alter the susceptibility both quantitatively and qualitatively. We support our analytical solutions with numerical data.
ISSN:2331-8422
DOI:10.48550/arxiv.1602.04201