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.

arXiv comment6 pages including supplementary material, 3 figures

References in corpus (30)

• Quantum Spin Liquid States
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• A Field Guide to Spin Liquids
• Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Post-Matrix Product State Methods: To tangent space and beyond
• Resonating valence bond states in the PEPS formalism
• Variational matrix product ansatz for dispersion relations
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Transfer Matrices and Excitations with Matrix Product States
• Soliton Approach to Spin-Peierls Antiferromagnets: Large-Scale Numerical Results
• Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics
• Dynamical structure factor of the $J_1-J_2$ Heisenberg model in one dimension: the variational Monte Carlo approach
• The Bethe ansatz as a matrix product ansatz
• The Algebraic Bethe Ansatz and Tensor Networks
• Numerical Contraction of the Tensor Network generated by the Algebraic Bethe Ansatz
• Generalization of the matrix product ansatz for integrable chains
• Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz
• Entanglement and corner Hamiltonian spectra of integrable open spin chains
• Spinon confinement and deconfinement in spin-1 chains
• A Plaquette Basis for the Study of Heisenberg Ladders
• Elementary excitations in the gapped phase of a frustrated S=1/2 spin ladder: from spinons to the Haldane triplet
• Spinon excitation and Möbius boundary condition in S=1/2 antiferromagnetic Heisenberg spin ladder with zigzag structure
• A gapped SU(3) spin liquid with Z_3 topological order
• Spinon excitation spectra of the $J_1$-$J_2$ chain from analytical calculations in the dimer basis and exact diagonalization
• SU(3) trimer resonating-valence-bond state on the square lattice
• Quantum trimer models and topological SU(3) spin liquids on the kagome lattice
• SU(4) topological RVB spin liquid on the square lattice
• Massive spinons in $S=1/2$ spin chains: spinon-pair operator representation