Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain

TL;DR

This paper introduces a variational matrix product state approach for the spin-1/2 Heisenberg model, accurately capturing the ground state and elementary excitations, and extends to related models with high precision.

Contribution

It develops a simple yet accurate vMPS method that reflects the RVB picture and effectively models both ground states and excitations in spin chains.

Findings

Ground state energy within 0.024% of Bethe ansatz

Dispersion of elementary excitations matches exact spectrum

Method applicable to models interpolating between Heisenberg and Majumdar-Ghosh

Abstract

We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond (RVB) picture of the spin liquid, with the energy only 0.024% higher than the exact value given by Bethe ansatz. Building on the ground-state vMPS, the one-spin wave function is constructed in a simple manner with the dispersion that matches well with the exact spectrum. The vMPS scheme is applied to the family of Hamiltonian extrapolating between the Heisenberg model and the Majumdar-Ghosh model.