Trajectory-resolved Weiss fields for quantum spin dynamics
We explore the dynamics of quantum spin systems in two and three dimensions using an exact mapping to classical stochastic processes. In recent work, we explored the effectiveness of sampling around the mean-field evolution as determined by a stochastically averaged Weiss field. Here, we show that t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-12-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043288 |
| _version_ | 1797210315866243072 |
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| author | S. E. Begg A. G. Green M. J. Bhaseen |
| author_facet | S. E. Begg A. G. Green M. J. Bhaseen |
| author_sort | S. E. Begg |
| collection | DOAJ |
| description | We explore the dynamics of quantum spin systems in two and three dimensions using an exact mapping to classical stochastic processes. In recent work, we explored the effectiveness of sampling around the mean-field evolution as determined by a stochastically averaged Weiss field. Here, we show that this approach can be significantly extended by sampling around the instantaneous Weiss field associated with each stochastic trajectory taken separately. This trajectory-resolved approach incorporates sample to sample fluctuations and allows for longer simulation times. We demonstrate the utility of this approach for quenches in the two-dimensional and three-dimensional quantum Ising model. We show that the method is particularly advantageous in situations where the average Weiss field vanishes, but the trajectory-resolved Weiss fields are nonzero. We discuss the connection to the gauge-P phase-space approach, where the trajectory-resolved Weiss field can be interpreted as a gauge degree of freedom. |
| first_indexed | 2024-04-24T10:08:39Z |
| format | Article |
| id | doaj.art-7b6ae99cb5574546828ae79dc9822d10 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:08:39Z |
| publishDate | 2023-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-7b6ae99cb5574546828ae79dc9822d102024-04-12T17:37:24ZengAmerican Physical SocietyPhysical Review Research2643-15642023-12-015404328810.1103/PhysRevResearch.5.043288Trajectory-resolved Weiss fields for quantum spin dynamicsS. E. BeggA. G. GreenM. J. BhaseenWe explore the dynamics of quantum spin systems in two and three dimensions using an exact mapping to classical stochastic processes. In recent work, we explored the effectiveness of sampling around the mean-field evolution as determined by a stochastically averaged Weiss field. Here, we show that this approach can be significantly extended by sampling around the instantaneous Weiss field associated with each stochastic trajectory taken separately. This trajectory-resolved approach incorporates sample to sample fluctuations and allows for longer simulation times. We demonstrate the utility of this approach for quenches in the two-dimensional and three-dimensional quantum Ising model. We show that the method is particularly advantageous in situations where the average Weiss field vanishes, but the trajectory-resolved Weiss fields are nonzero. We discuss the connection to the gauge-P phase-space approach, where the trajectory-resolved Weiss field can be interpreted as a gauge degree of freedom.http://doi.org/10.1103/PhysRevResearch.5.043288 |
| spellingShingle | S. E. Begg A. G. Green M. J. Bhaseen Trajectory-resolved Weiss fields for quantum spin dynamics Physical Review Research |
| title | Trajectory-resolved Weiss fields for quantum spin dynamics |
| title_full | Trajectory-resolved Weiss fields for quantum spin dynamics |
| title_fullStr | Trajectory-resolved Weiss fields for quantum spin dynamics |
| title_full_unstemmed | Trajectory-resolved Weiss fields for quantum spin dynamics |
| title_short | Trajectory-resolved Weiss fields for quantum spin dynamics |
| title_sort | trajectory resolved weiss fields for quantum spin dynamics |
| url | http://doi.org/10.1103/PhysRevResearch.5.043288 |
| work_keys_str_mv | AT sebegg trajectoryresolvedweissfieldsforquantumspindynamics AT aggreen trajectoryresolvedweissfieldsforquantumspindynamics AT mjbhaseen trajectoryresolvedweissfieldsforquantumspindynamics |