The boundary effects of transverse field Ising model

Abstract

Advance in quantum simulations using trapped ions or superconducting elements allows detailed analysis of the transverse field Ising model (TFIM), which can exhibit a quantum phase transition and has been a paradigm in exactly solvable quantum systems. The Jordan-Wigner transformation maps the one-dimensional TFIM to a fermion model, but additional complications arise in finite systems and introduce a fermion-number parity constraint when periodic boundary condition (PBC) is imposed. By constructing the free energy and spin correlations with the fermion-number parity constraint and comparing the results to the TFIM with open boundary condition, we show that the boundary effects can become significant for the anti-ferromagnetic TFIM with odd number of sites at low temperature.

arXiv comment17 pages, 3 figures

References in corpus (6)

• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Digital quantum simulation of spin models with circuit quantum electrodynamics
• Quantum transport in ultracold atoms
• Recent progress in quantum simulation using superconducting circuits
• Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space

Cited by in corpus (12)

• Variational Quantum Linear Solver
• Fermionic Gaussian states: an introduction to numerical approaches
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Enhancing correlation times for edge spins through dissipation
• Trajectory phase transitions in non-interacting spin systems
• Strong zero modes in a class of generalised Ising spin ladders with plaquette interactions
• Ring frustration and factorizable correlation functions of critical spin rings
• Loschmidt-amplitude wave function spectroscopy and the physics of dynamically driven phase transitions
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Quaternary Jordan-Wigner mapping and topological extended-kink phase in the interacting Kitaev ring
• Simulation of the 1d XY model on a quantum computer
• Seeding neural network quantum states with tensor network states