Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions

Abstract

A one-dimensional quantum spin model with the competing two-spin and three-spin interactions is investigated in the context of a tensor network algorithm based on the infinite matrix product state representation. The algorithm is an adaptation of Vidal's infinite time-evolving block decimation algorithm to a translation-invariant one-dimensional lattice spin system involving three-spin interactions. The ground-state fidelity per lattice site is computed, and its bifurcation is unveiled, for a few selected values of the coupling constants. We succeed in identifying critical points and deriving local order parameters to characterize different phases in the conventional Ginzburg-Landau-Wilson paradigm.

4+ pages, 5 figures

References in corpus (19)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Scaling of entanglement support for Matrix Product States
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Ground state fidelity from tensor network representations
• Quantum fidelity and quantum phase transitions in matrix product states
• Ground-state fidelity in one-dimensional gapless model
• Statistical mechanics of the Cluster-Ising model
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Quantum fidelity in the thermodynamic limit
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Finite temperature fidelity susceptibility for one-dimensional quantum systems
• Competing many-body interactions in systems of trapped ions
• Oscillating fidelity susceptibility near a quantum multicritical point

Cited by in corpus (4)

• Quantum fidelity for degenerate groundstates in quantum phase transitions
• Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model
• Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
• Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries