Entanglement Perturbation Theory for Antiferromagnetic Heisenberg Spin Chains

Abstract

A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z -axis anisotropy λ and magnetic field B . To demonstrate its 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 seven 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- 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 λ space is determined by Roomany–Wyld renormalization group (RG) finite size scaling. The results are in good agreement with those obtained by the level-spectroscopy method.