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

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.

6 pages including supplementary material, 3 figures

References in corpus (6)

• Resonating valence bond states in the PEPS formalism
• Transfer Matrices and Excitations with Matrix Product States
• Generalization of the matrix product ansatz for integrable chains
• Spinon excitation spectra of the $J_1$-$J_2$ chain from analytical calculations in the dimer basis and exact diagonalization
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
• SU(4) topological RVB spin liquid on the square lattice