The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States

Details The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States

2007-12-11

arxiv.org/abs/0712.1806v1

Phys. Rev. B 77, 214431 (2008)

Physics

Condensed Matter

Statistical Mechanics

28 pages, 23 figures, PDFlatex

Scientific paper

10.1103/PhysRevB.77.214431

We give a generalization to an infinite tree geometry of Vidal's infinite time-evolving block decimation (iTEBD) algorithm 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.

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