Quantum transverse-field Ising model on an infinite tree from matrix product states
Author(s)Nagaj, Daniel; Farhi, Edward; Goldstone, Jeffrey; Shor, Peter W.; Sylvester, Igor
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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.
DepartmentMassachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of Materials Science and Engineering; Massachusetts Institute of Technology. Department of Physics
Physical Review B
American Physical Society
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.
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