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

Abstract

We study a matrix product state 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 Astlund and Rommer [see S. Astlund and S. Rommer, Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.75.353775, 3537 (1995);S. Rommer and S. Astlund, Phys. Rev. B1098-012110.1103/PhysRevB.55.2164 55, 2164 (1997)], 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 and previous numerical results for the quantum Ising, the antiferromagnetic Heisenberg spin-1/2, and the bilinear-biquadratic spin-1 models. © 2012 American Physical Society.