Quantum transverse-field Ising model on an infinite tree from matrix product states
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PhysRevB_77_214431.pdf
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1009.86 KB
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Author(s)
Nagaj, Daniel
Farhi, Edward
Goldstone, Jeffrey
Shor, Peter W.
Sylvester, Igor
Date Issued
June 2008
Journal
Physical Review B
Publisher
American Physical Society
Citation
Nagaj, Daniel et al. “Quantum transverse-field Ising model on an infinite tree from matrix product states.” Physical Review B 77.21 (2008): 214431. (C) 2010 The American Physical Society.
Version
Final published version
Abstract
We give a generalization to an infinite tree geometry of Vidal’s infinite time-evolving block decimation (iTEBD) algorithm [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)] for simulating an infinite line of quantum spins. We numerically investigate the quantum Ising model in a transverse field on the Bethe lattice using the matrix product state ansatz. We observe a second order phase transition, with certain key differences from the transverse field Ising model on an infinite spin chain. We also investigate a transverse field Ising model with a specific longitudinal field. When the transverse field is turned off, this model has a highly degenerate ground state as opposed to the pure Ising model whose ground state is only doubly degenerate.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Materials Science and Engineering
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevB.77.214431
