Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough Letter of Verstraete and Cirac [Phys. Rev. Lett. 104, 190405 (2010).PRLTAO0031-900710.1103/PhysRevLett.104.190405], provides a powerful variational ansatz for the ground state of strongly interac...
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| Published in: | Physical review letters Vol. 118; no. 22; p. 220402 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
American Physical Society
02.06.2017
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| ISSN: | 0031-9007, 1079-7114, 1079-7114 |
| Online Access: | Get full text |
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| Summary: | The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough Letter of Verstraete and Cirac [Phys. Rev. Lett. 104, 190405 (2010).PRLTAO0031-900710.1103/PhysRevLett.104.190405], provides a powerful variational ansatz for the ground state of strongly interacting quantum field theories in one spatial dimension. A continuous MPS (cMPS) approximation to the ground state can be obtained by simulating a Euclidean time evolution. In this Letter we propose a cMPS optimization algorithm based instead on energy minimization by gradient methods and demonstrate its performance by applying it to the Lieb-Liniger model (an integrable model of an interacting bosonic field) directly in the thermodynamic limit. We observe a very significant computational speed-up, of more than 2 orders of magnitude, with respect to simulating a Euclidean time evolution. As a result, a much larger cMPS bond dimension D can be reached (e.g., D=256 with moderate computational resources), thus helping unlock the full potential of the cMPS representation for ground state studies. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 USDOE |
| ISSN: | 0031-9007 1079-7114 1079-7114 |
| DOI: | 10.1103/PhysRevLett.118.220402 |