Universal graph description for one-dimensional exchange models
We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely, Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive crucial information about those models of fundamental impo...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2020-08-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.033297 |
| _version_ | 1797211339198824448 |
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| author | Jean Decamp Jiangbin Gong Huanqian Loh Christian Miniatura |
| author_facet | Jean Decamp Jiangbin Gong Huanqian Loh Christian Miniatura |
| author_sort | Jean Decamp |
| collection | DOAJ |
| description | We demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely, Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive crucial information about those models of fundamental importance in both classical and quantum physics, and to completely characterize their algebraic structure. Notably, we prove that the spectral gap can be obtained in polynomial computational time, which has strong implications in the context of adiabatic quantum computing with quantum spin chains. This quantity also characterizes the rate to stationarity of some important classical random processes such as interchange and exclusion processes. Reciprocally, we use results derived from the celebrated Bethe ansatz to obtain mathematical results about these graphs in the unweighted case. We also discuss extensions of this unifying framework to other systems, such as asymmetric exclusion processes—a paradigmatic model in nonequilibrium physics—or the more exotic non-Hermitian quantum systems. |
| first_indexed | 2024-04-24T10:24:55Z |
| format | Article |
| id | doaj.art-76baba45f0594895811e1044d02ca7f0 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:24:55Z |
| publishDate | 2020-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-76baba45f0594895811e1044d02ca7f02024-04-12T16:59:24ZengAmerican Physical SocietyPhysical Review Research2643-15642020-08-012303329710.1103/PhysRevResearch.2.033297Universal graph description for one-dimensional exchange modelsJean DecampJiangbin GongHuanqian LohChristian MiniaturaWe demonstrate that a large class of one-dimensional quantum and classical exchange models can be described by the same type of graphs, namely, Cayley graphs of the permutation group. Their well-studied spectral properties allow us to derive crucial information about those models of fundamental importance in both classical and quantum physics, and to completely characterize their algebraic structure. Notably, we prove that the spectral gap can be obtained in polynomial computational time, which has strong implications in the context of adiabatic quantum computing with quantum spin chains. This quantity also characterizes the rate to stationarity of some important classical random processes such as interchange and exclusion processes. Reciprocally, we use results derived from the celebrated Bethe ansatz to obtain mathematical results about these graphs in the unweighted case. We also discuss extensions of this unifying framework to other systems, such as asymmetric exclusion processes—a paradigmatic model in nonequilibrium physics—or the more exotic non-Hermitian quantum systems.http://doi.org/10.1103/PhysRevResearch.2.033297 |
| spellingShingle | Jean Decamp Jiangbin Gong Huanqian Loh Christian Miniatura Universal graph description for one-dimensional exchange models Physical Review Research |
| title | Universal graph description for one-dimensional exchange models |
| title_full | Universal graph description for one-dimensional exchange models |
| title_fullStr | Universal graph description for one-dimensional exchange models |
| title_full_unstemmed | Universal graph description for one-dimensional exchange models |
| title_short | Universal graph description for one-dimensional exchange models |
| title_sort | universal graph description for one dimensional exchange models |
| url | http://doi.org/10.1103/PhysRevResearch.2.033297 |
| work_keys_str_mv | AT jeandecamp universalgraphdescriptionforonedimensionalexchangemodels AT jiangbingong universalgraphdescriptionforonedimensionalexchangemodels AT huanqianloh universalgraphdescriptionforonedimensionalexchangemodels AT christianminiatura universalgraphdescriptionforonedimensionalexchangemodels |