Ground-state properties via machine learning quantum constraints
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on suffi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.L032043 |
| _version_ | 1797210652587065344 |
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| author | Pei-Lin Zheng Si-Jing Du Yi Zhang |
| author_facet | Pei-Lin Zheng Si-Jing Du Yi Zhang |
| author_sort | Pei-Lin Zheng |
| collection | DOAJ |
| description | Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on sufficiently large system sizes. Here, we propose an alternative strategy based upon the expectation values of an ensemble of operators and the elusive yet vital quantum constraints between them where the search for ground-state properties simply equates to classical constrained minimization. These quantum constraints are generally obtainable via sampling and then machine learning on a large number of systematically consistent quantum many-body states. We showcase our perspective on one-dimensional fermion chains and spin chains for applicability, effectiveness, caveats, and unique advantages especially for strongly correlated systems, thermodynamic-limit systems, property designs, etc. |
| first_indexed | 2024-04-24T10:14:00Z |
| format | Article |
| id | doaj.art-71eeb199a6d24c20aea9d440d976f735 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:14:00Z |
| publishDate | 2022-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-71eeb199a6d24c20aea9d440d976f7352024-04-12T17:24:41ZengAmerican Physical SocietyPhysical Review Research2643-15642022-09-0143L03204310.1103/PhysRevResearch.4.L032043Ground-state properties via machine learning quantum constraintsPei-Lin ZhengSi-Jing DuYi ZhangGround-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on sufficiently large system sizes. Here, we propose an alternative strategy based upon the expectation values of an ensemble of operators and the elusive yet vital quantum constraints between them where the search for ground-state properties simply equates to classical constrained minimization. These quantum constraints are generally obtainable via sampling and then machine learning on a large number of systematically consistent quantum many-body states. We showcase our perspective on one-dimensional fermion chains and spin chains for applicability, effectiveness, caveats, and unique advantages especially for strongly correlated systems, thermodynamic-limit systems, property designs, etc.http://doi.org/10.1103/PhysRevResearch.4.L032043 |
| spellingShingle | Pei-Lin Zheng Si-Jing Du Yi Zhang Ground-state properties via machine learning quantum constraints Physical Review Research |
| title | Ground-state properties via machine learning quantum constraints |
| title_full | Ground-state properties via machine learning quantum constraints |
| title_fullStr | Ground-state properties via machine learning quantum constraints |
| title_full_unstemmed | Ground-state properties via machine learning quantum constraints |
| title_short | Ground-state properties via machine learning quantum constraints |
| title_sort | ground state properties via machine learning quantum constraints |
| url | http://doi.org/10.1103/PhysRevResearch.4.L032043 |
| work_keys_str_mv | AT peilinzheng groundstatepropertiesviamachinelearningquantumconstraints AT sijingdu groundstatepropertiesviamachinelearningquantumconstraints AT yizhang groundstatepropertiesviamachinelearningquantumconstraints |