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Quantum transverse-field Ising model on an infinite tree from matrix product states

2008; American Physical Society; Volume: 77; Issue: 21 Linguagem: Inglês

10.1103/physrevb.77.214431

1550-235X

Daniel Nagaj, Edward Farhi, Jeffrey Goldstone, Peter W. Shor, Igor Andrade Sylvester,

Quantum Computing Algorithms and Architecture

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.