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...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2010
|
| Online Access: | http://hdl.handle.net/1721.1/51347 https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0003-4626-5648 |
| _version_ | 1826197373968187392 |
|---|---|
| author | Nagaj, Daniel Farhi, Edward Goldstone, Jeffrey Shor, Peter W. Sylvester, Igor |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Nagaj, Daniel Farhi, Edward Goldstone, Jeffrey Shor, Peter W. Sylvester, Igor |
| author_sort | Nagaj, Daniel |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:46:42Z |
| format | Article |
| id | mit-1721.1/51347 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:46:42Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/513472022-09-27T14:56:27Z Quantum transverse-field Ising model on an infinite tree from matrix product states Nagaj, Daniel Farhi, Edward Goldstone, Jeffrey Shor, Peter W. Sylvester, Igor Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Materials Science and Engineering Massachusetts Institute of Technology. Department of Physics Farhi, Edward Nagaj, Daniel Farhi, Edward Goldstone, Jeffrey Shor, Peter W. Sylvester, Igor 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. National Science Foundation Army Research Office W. M. Keck Foundation Center for Extreme Quantum Information Theory 2010-02-03T14:33:46Z 2010-02-03T14:33:46Z 2008-06 2008-04 Article http://purl.org/eprint/type/JournalArticle 1550-235X 1098-0121 http://hdl.handle.net/1721.1/51347 Nagaj, Daniel et al. “Quantum transverse-field Ising model on an infinite tree from matrix product states.” Physical Review B 77.21 (2008): 214431. (C) 2010 The American Physical Society. https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0003-4626-5648 en_US http://dx.doi.org/10.1103/PhysRevB.77.214431 Physical Review B 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. application/pdf American Physical Society APS |
| spellingShingle | Nagaj, Daniel Farhi, Edward Goldstone, Jeffrey Shor, Peter W. Sylvester, Igor Quantum transverse-field Ising model on an infinite tree from matrix product states |
| title | Quantum transverse-field Ising model on an infinite tree from matrix product states |
| title_full | Quantum transverse-field Ising model on an infinite tree from matrix product states |
| title_fullStr | Quantum transverse-field Ising model on an infinite tree from matrix product states |
| title_full_unstemmed | Quantum transverse-field Ising model on an infinite tree from matrix product states |
| title_short | Quantum transverse-field Ising model on an infinite tree from matrix product states |
| title_sort | quantum transverse field ising model on an infinite tree from matrix product states |
| url | http://hdl.handle.net/1721.1/51347 https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0003-4626-5648 |
| work_keys_str_mv | AT nagajdaniel quantumtransversefieldisingmodelonaninfinitetreefrommatrixproductstates AT farhiedward quantumtransversefieldisingmodelonaninfinitetreefrommatrixproductstates AT goldstonejeffrey quantumtransversefieldisingmodelonaninfinitetreefrommatrixproductstates AT shorpeterw quantumtransversefieldisingmodelonaninfinitetreefrommatrixproductstates AT sylvesterigor quantumtransversefieldisingmodelonaninfinitetreefrommatrixproductstates |