Scaling of ground-state fidelity in the thermodynamic limit:XYmodel and beyond

2011/04/30 by Marek M. Rams, Bogdan Damski · 2 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Geometry #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Scaling #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physreva.84.032324

published as Phys. Rev. A 84, 032324 (2011) · 20 pages, 23 figures, updated references, corrected typos, version accepted in PRA

arxiv created 2011/09/16 · openalex publication_date 2011/09/16 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study ground-state fidelity defined as the overlap between two ground states of the same quantum system obtained for slightly different values of the parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY model and the neighborhood of its critical points. We describe extensively fidelity when it is dominated by the universal contribution reflecting the quantum criticality of the phase transition. We show that proximity to the multicritical point leads to anomalous scaling of fidelity. We also discuss fidelity in a regime characterized by pronounced oscillations resulting from the change in either the system size or the parameters of the Hamiltonian. Moreover, we show when fidelity is dominated by non-universal contributions, study fidelity in the extended Ising model, and illustrate how our results provide additional insight into dynamics of quantum phase transitions. Special attention is given to studies of fidelity from the momentum space perspective. All our main results are obtained analytically. They are in excellent agreement with numerics.

Citations

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Quench dynamics near a quantum critical point
• Dynamics of a quantum phase transition and relaxation to a steady state
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry
• Orthogonality Catastrophe and Shock Waves in a Nonequilibrium Fermi Gas
• Ground State Fidelity from Tensor Network Representations
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Effect of disorder on quantum phase transitions in anisotropicXYspin chains in a transverse field
• Quantum critical scaling of fidelity susceptibility
• Quantum Critical Scaling of the Geometric Tensors
• Multicritical Crossovers near the Dilute Bose Gas Quantum Critical Point
• Two soluble models of an antiferromagnetic chain
• Quantum phase transitions

Cited by

• Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results
• One- and two-dimensional quantum models: Quenches and the scaling of irreversible entropy