Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains

TL;DR

This paper applies entanglement perturbation theory (EPT) to study antiferromagnetic Heisenberg spin chains, accurately reproducing known results and exploring effects of anisotropy and magnetic fields, including phase diagrams and correlation functions.

Contribution

The paper demonstrates EPT's high accuracy in modeling spin chains, confirming asymptotic correlation behaviors and mapping phase diagrams for anisotropic models.

Findings

EPT reproduces Bethe Ansatz results for ground state energy and correlations

Confirms asymptotic spin correlation behavior predicted by conformal field theory

Determines phase diagram for spin-1 model using finite-size scaling

Abstract

A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z-axis anisotropy $\lambda$ and magnetic field B. To demonstrate the accuracy, we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg model, and find that EPT successfully reproduces the exact Bethe Ansatz results for the ground state energy, the local magnetization, and the spin correlation functions (Bethe ansatz result is available for the first 7 lattice separations). In particular, EPT confirms for the first time the asymptotic behavior of the spin correlation functions predicted by the conformal field theory, which realizes only for lattice separations larger than 1000. Next, turning on the z-axis anisotropy and the magnetic field, the 2-spin and 4-spin correlation functions are calculated, and the results are compared with those obtained by Bosonization and density matrix renormalization group methods. Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state phase diagram in $\lambda$ space is determined with help of the Roomany-Wyld RG finite-size-scaling. The results are in good agreement with those obtained by the level-spectroscopy method.