The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States
Statistical Mechanics
2009-11-13 v1 Quantum Physics
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.
Keywords
Cite
@article{arxiv.0712.1806,
title = {The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States},
author = {Daniel Nagaj and Edward Farhi and Jeffrey Goldstone and Peter Shor and Igor Sylvester},
journal= {arXiv preprint arXiv:0712.1806},
year = {2009}
}
Comments
28 pages, 23 figures, PDFlatex