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arXiv · 0712.1806

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

Daniel Nagaj·Edward Farhi·Jeffrey Goldstone·Peter Shor·Igor Sylvester
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Abstract

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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Daniel Nagaj, Edward Farhi, Jeffrey Goldstone, Peter Shor, Igor Sylvester. 2007-12-11. The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States. https://doi.org/10.1103/physrevb.77.214431

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