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A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions
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
\"Ostlund 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.Comment: 13 pages, 11 figures, 5 table
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