Accurate Gauge-Invariant Tensor Network Simulations for Abelian Lattice Gauge Theory in (2+1)D: ground state and real-time dynamics
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arXiv
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| Formato: | Preprint |
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2025
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| _version_ | 1866912529216700416 |
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| author | Wu, Yantao Liu, Wen-Yuan |
| author_facet | Wu, Yantao Liu, Wen-Yuan |
| contents | We propose a novel tensor network method to achieve accurate and efficient simulations of Abelian lattice gauge theories (LGTs) in (2+1)D for both ground state and real-time dynamics. The first key is to identify a gauge canonical form (GCF) of gauge-invariant tensor network states, which already simplifies existing algorithms for (1+1)D LGTs. The second key is to employ the GCF of projected entangled-pair state (PEPS) combining with variational Monte Carlo (VMC), enabling efficient computations for (2+1)D LGTs. We demonstrate the versatile capability of this approach for accurate ground state simulation of pure $Z_2$, $Z_3$ and $Z_4$ gauge theory, odd-$Z_2$ gauge theories, and $Z_2$ gauge theory coupled to hard-core bosons, on square lattices up to $32 \times 32$. Furthermore, we demonstrate that it allows for accurate simulations of real-time dynamics up to long-time, exemplified by the dynamics of elementary excitations of the deconfined $Z_2$ gauge field on a $10\times10$ lattice. This is also the first example of using VMC to simulate the real-time dynamics of PEPS, whose impact may extend beyond gauge theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accurate Gauge-Invariant Tensor Network Simulations for Abelian Lattice Gauge Theory in (2+1)D: ground state and real-time dynamics Wu, Yantao Liu, Wen-Yuan Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice Quantum Physics We propose a novel tensor network method to achieve accurate and efficient simulations of Abelian lattice gauge theories (LGTs) in (2+1)D for both ground state and real-time dynamics. The first key is to identify a gauge canonical form (GCF) of gauge-invariant tensor network states, which already simplifies existing algorithms for (1+1)D LGTs. The second key is to employ the GCF of projected entangled-pair state (PEPS) combining with variational Monte Carlo (VMC), enabling efficient computations for (2+1)D LGTs. We demonstrate the versatile capability of this approach for accurate ground state simulation of pure $Z_2$, $Z_3$ and $Z_4$ gauge theory, odd-$Z_2$ gauge theories, and $Z_2$ gauge theory coupled to hard-core bosons, on square lattices up to $32 \times 32$. Furthermore, we demonstrate that it allows for accurate simulations of real-time dynamics up to long-time, exemplified by the dynamics of elementary excitations of the deconfined $Z_2$ gauge field on a $10\times10$ lattice. This is also the first example of using VMC to simulate the real-time dynamics of PEPS, whose impact may extend beyond gauge theory. |
| title | Accurate Gauge-Invariant Tensor Network Simulations for Abelian Lattice Gauge Theory in (2+1)D: ground state and real-time dynamics |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2503.20566 |