Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics
The statistics of gap ratios between consecutive energy levels is a widely used tool—in particular, in the context of many-body physics—to distinguish between chaotic and integrable systems, described, respectively, by Gaussian ensembles of random matrices and Poisson statistics. In this work, we ex...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-01-01
|
| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.12.011006 |
| _version_ | 1818750341586354176 |
|---|---|
| author | Olivier Giraud Nicolas Macé Éric Vernier Fabien Alet |
| author_facet | Olivier Giraud Nicolas Macé Éric Vernier Fabien Alet |
| author_sort | Olivier Giraud |
| collection | DOAJ |
| description | The statistics of gap ratios between consecutive energy levels is a widely used tool—in particular, in the context of many-body physics—to distinguish between chaotic and integrable systems, described, respectively, by Gaussian ensembles of random matrices and Poisson statistics. In this work, we extend the study of the gap ratio distribution P(r) to the case where discrete symmetries are present. This is important since in certain situations it may be very impractical, or impossible, to split the model into symmetry sectors, let alone in cases where the symmetry is not known in the first place. Starting from the known expressions for surmises in the Gaussian ensembles, we derive analytical surmises for random matrices comprised of several independent blocks. We check our formulas against simulations from large random matrices, showing excellent agreement. We then present a large set of applications in many-body physics, ranging from quantum clock models and anyonic chains to periodically driven spin systems. In all these models, the existence of a (sometimes hidden) symmetry can be diagnosed through the study of the spectral gap ratios, and our approach furnishes an efficient way to characterize the number and size of independent symmetry subspaces. We finally discuss the relevance of our analysis for existing results in the literature, as well as its practical usefulness, and point out possible future applications and extensions. |
| first_indexed | 2024-12-18T04:18:08Z |
| format | Article |
| id | doaj.art-8b88b3ad833b406588f400fc3f354577 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-18T04:18:08Z |
| publishDate | 2022-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-8b88b3ad833b406588f400fc3f3545772022-12-21T21:21:17ZengAmerican Physical SocietyPhysical Review X2160-33082022-01-0112101100610.1103/PhysRevX.12.011006Probing Symmetries of Quantum Many-Body Systems through Gap Ratio StatisticsOlivier GiraudNicolas MacéÉric VernierFabien AletThe statistics of gap ratios between consecutive energy levels is a widely used tool—in particular, in the context of many-body physics—to distinguish between chaotic and integrable systems, described, respectively, by Gaussian ensembles of random matrices and Poisson statistics. In this work, we extend the study of the gap ratio distribution P(r) to the case where discrete symmetries are present. This is important since in certain situations it may be very impractical, or impossible, to split the model into symmetry sectors, let alone in cases where the symmetry is not known in the first place. Starting from the known expressions for surmises in the Gaussian ensembles, we derive analytical surmises for random matrices comprised of several independent blocks. We check our formulas against simulations from large random matrices, showing excellent agreement. We then present a large set of applications in many-body physics, ranging from quantum clock models and anyonic chains to periodically driven spin systems. In all these models, the existence of a (sometimes hidden) symmetry can be diagnosed through the study of the spectral gap ratios, and our approach furnishes an efficient way to characterize the number and size of independent symmetry subspaces. We finally discuss the relevance of our analysis for existing results in the literature, as well as its practical usefulness, and point out possible future applications and extensions.http://doi.org/10.1103/PhysRevX.12.011006 |
| spellingShingle | Olivier Giraud Nicolas Macé Éric Vernier Fabien Alet Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics Physical Review X |
| title | Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics |
| title_full | Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics |
| title_fullStr | Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics |
| title_full_unstemmed | Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics |
| title_short | Probing Symmetries of Quantum Many-Body Systems through Gap Ratio Statistics |
| title_sort | probing symmetries of quantum many body systems through gap ratio statistics |
| url | http://doi.org/10.1103/PhysRevX.12.011006 |
| work_keys_str_mv | AT oliviergiraud probingsymmetriesofquantummanybodysystemsthroughgapratiostatistics AT nicolasmace probingsymmetriesofquantummanybodysystemsthroughgapratiostatistics AT ericvernier probingsymmetriesofquantummanybodysystemsthroughgapratiostatistics AT fabienalet probingsymmetriesofquantummanybodysystemsthroughgapratiostatistics |