2011/03/14 by Bogdan Pirvu, Jutho Haegeman, Frank Verstraete · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.85.035130
published as Phys. Rev. B 85, 035130 (2012) · 13 pages, 11 figures, 5 tables
arxiv created 2011/03/14 · arxiv updated 2012/02/06
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.