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

Author(s): B. Pirvu, J. Haegeman, F. Verstraete

Journal: Phys. Rev. B

Volume: 85

Page(s): 13 pp.

Year: 2012

DOI Number: 10.1103/PhysRevB.85.035130

Link: Link to publication


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 Östlund and Rommer [see S. Östlund and S. Rommer Phys. Rev. Lett. 75 3537 (1995); S. Rommer and S. Östlund Phys. Rev. B 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.


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