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Quantum Physics

arXiv:1103.2735 (quant-ph)
[Submitted on 14 Mar 2011]

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

Authors:Bogdan Pirvu, Jutho Haegeman, Frank Verstraete
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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.
Comments: 13 pages, 11 figures, 5 tables
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)
Cite as: arXiv:1103.2735 [quant-ph]
  (or arXiv:1103.2735v1 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1103.2735
Journal reference: Phys. Rev. B 85, 035130 (2012)
Related DOI: https://doi.org/10.1103/PhysRevB.85.035130

Submission history

From: Bogdan Pirvu [view email]
[v1] Mon, 14 Mar 2011 18:36:44 UTC (1,032 KB)
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