Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement

Abstract

A systematic analysis is performed for quantum phase transitions in a two-dimensional anisotropic spin 1/2 anti-ferromagnetic XYX model in an external magnetic field. With the help of an innovative tensor network algorithm, we compute the fidelity per lattice site to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition. We also compute an entanglement estimator, defined as a ratio between the one-tangle and the sum of squared concurrences, to identify both the factorizing field and the critical point, resulting in a quantitative agreement with quantum Monte Carlo simulation. In addition, the local order parameter is "derived" from the tensor network representation of the system's ground state wave functions.

4+ pages, 3 figures

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Cited by in corpus (15)

• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Coherent and dissipative dynamics at quantum phase transitions
• Multipartite Entanglement Measures and Quantum Criticality from Matrix and Tensor Product States
• Oscillating fidelity susceptibility near a quantum multicritical point
• Ground-state fidelity at first-order quantum transitions
• Spontaneous symmetry breaking and bifurcations in ground state fidelity for quantum lattice systems
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Persistence of entanglement in thermal states of spin systems
• Glassy Behavior and Jamming of a Random Walk Process for Sequentially Satisfying a Constraint Satisfaction Formula
• Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
• Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models
• A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model