Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite density
Lattice gauge theories coupled to fermionic matter account for many interesting phenomena in both high-energy physics and condensed-matter physics. Certain regimes, e.g., at finite fermion density, are difficult to simulate with traditional Monte Carlo algorithms due to the so-called sign problem. W...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2023-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.043128 |
| _version_ | 1797210401293729792 |
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| author | Julian Bender Patrick Emonts J. Ignacio Cirac |
| author_facet | Julian Bender Patrick Emonts J. Ignacio Cirac |
| author_sort | Julian Bender |
| collection | DOAJ |
| description | Lattice gauge theories coupled to fermionic matter account for many interesting phenomena in both high-energy physics and condensed-matter physics. Certain regimes, e.g., at finite fermion density, are difficult to simulate with traditional Monte Carlo algorithms due to the so-called sign problem. We present a variational, sign-problem-free Monte Carlo method for lattice gauge theories with continuous gauge groups and apply it to (2+1)-dimensional compact QED with dynamical fermions at finite density. The variational ansatz is formulated in the full gauge-field basis, i.e., without having to resort to truncation schemes for the U(1) gauge-field Hilbert space. The ansatz consists of two parts: first, a pure gauge part based on Jastrow-type ansatz states (which can be connected to certain neural-network ansatz states) and, second, a fermionic part based on gauge-field-dependent fermionic Gaussian states. These are designed in such a way that the gauge-field integral over all fermionic Gaussian states is gauge-invariant and at the same time still efficiently tractable. To ensure the validity of the method we benchmark the pure gauge part of the ansatz against another variational method and the full ansatz against an existing Monte Carlo simulation where the sign problem is absent. Moreover, in limiting cases where the exact ground state is known we show that our ansatz is able to capture this behavior. Finally, we study a sign-problem affected regime by probing density-induced phase transitions. |
| first_indexed | 2024-04-24T10:10:00Z |
| format | Article |
| id | doaj.art-c2f1670288f7442e9f8ad84383fec6e9 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:00Z |
| publishDate | 2023-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-c2f1670288f7442e9f8ad84383fec6e92024-04-12T17:35:47ZengAmerican Physical SocietyPhysical Review Research2643-15642023-11-015404312810.1103/PhysRevResearch.5.043128Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite densityJulian BenderPatrick EmontsJ. Ignacio CiracLattice gauge theories coupled to fermionic matter account for many interesting phenomena in both high-energy physics and condensed-matter physics. Certain regimes, e.g., at finite fermion density, are difficult to simulate with traditional Monte Carlo algorithms due to the so-called sign problem. We present a variational, sign-problem-free Monte Carlo method for lattice gauge theories with continuous gauge groups and apply it to (2+1)-dimensional compact QED with dynamical fermions at finite density. The variational ansatz is formulated in the full gauge-field basis, i.e., without having to resort to truncation schemes for the U(1) gauge-field Hilbert space. The ansatz consists of two parts: first, a pure gauge part based on Jastrow-type ansatz states (which can be connected to certain neural-network ansatz states) and, second, a fermionic part based on gauge-field-dependent fermionic Gaussian states. These are designed in such a way that the gauge-field integral over all fermionic Gaussian states is gauge-invariant and at the same time still efficiently tractable. To ensure the validity of the method we benchmark the pure gauge part of the ansatz against another variational method and the full ansatz against an existing Monte Carlo simulation where the sign problem is absent. Moreover, in limiting cases where the exact ground state is known we show that our ansatz is able to capture this behavior. Finally, we study a sign-problem affected regime by probing density-induced phase transitions.http://doi.org/10.1103/PhysRevResearch.5.043128 |
| spellingShingle | Julian Bender Patrick Emonts J. Ignacio Cirac Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite density Physical Review Research |
| title | Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite density |
| title_full | Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite density |
| title_fullStr | Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite density |
| title_full_unstemmed | Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite density |
| title_short | Variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: A study of (2+1)-dimensional compact QED with dynamical fermions at finite density |
| title_sort | variational monte carlo algorithm for lattice gauge theories with continuous gauge groups a study of 2 1 dimensional compact qed with dynamical fermions at finite density |
| url | http://doi.org/10.1103/PhysRevResearch.5.043128 |
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