A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions

Abstract

We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of Östlund and Rommer [1], we separate the Hilbert space of the system into subspaces with different momentum. This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation. Surprisingly, many branches of the dispersion relation are approximated to a very good precision. We benchmark the accuracy of the algorithm by comparison with the exact solutions of the quantum Ising and the antiferromagnetic Heisenberg spin-1/2 model.

13 pages, 11 figures, 5 tables

References in corpus (3)

• DMRG and periodic boundary conditions: a quantum information perspective
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions

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