Quantum transverse-field Ising model on an infinite tree from matrix product states
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...
| Asıl Yazarlar: | , , , , |
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| Diğer Yazarlar: | |
| Materyal Türü: | Makale |
| Dil: | en_US |
| Baskı/Yayın Bilgisi: |
American Physical Society
2010
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| Online Erişim: | http://hdl.handle.net/1721.1/51347 https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0003-4626-5648 |
| Özet: | 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. |
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