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

Citation Nagaj, Daniel et al. " Quantum transverse-field Ising model on an infinite tree from matrix product states. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We give a generalization to an infinite tree geometry of Vidal's infinite time-evolving block decimation ͑iTEBD͒ algorithm ͓G. Vidal, Phys. Rev. Lett. 98, 070201 ͑2007͔͒ 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.