An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929358743011328 |
|---|---|
| author | Zhang, Xu Pan, Gaopei Chen, Bin-Bin Sun, Kai Meng, Zi Yang |
| author_facet | Zhang, Xu Pan, Gaopei Chen, Bin-Bin Sun, Kai Meng, Zi Yang |
| contents | Exponential observables, formulated as $\log \langle e^{\hat{X}}\rangle$ where $\hat{X}$ is an extensive quantity, play a critical role in study of quantum many-body systems, examples of which include the free-energy and entanglement entropy. Given that $e^{X}$ becomes exponentially large (or small) in the thermodynamic limit, accurately computing the expectation value of this exponential quantity presents a significant challenge. In this Letter, we propose a comprehensive algorithm for quantifying these observables in interacting fermion systems, utilizing the determinant quantum Monte Carlo (DQMC) method. We have applied this novel algorithm to the 2D half-filled Hubbard model. At the strong coupling limit, our method showcases a significant accuracy improvement compared to conventional methods that are derived from the internal energy. We also illustrate that this novel approach delivers highly efficient and precise measurements of the nth Rényi entanglement entropy. Even more noteworthy is that this improvement comes without incurring increases in computational complexity. This algorithm effectively suppresses exponential fluctuations and can be easily generalized to other models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03448 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation Zhang, Xu Pan, Gaopei Chen, Bin-Bin Sun, Kai Meng, Zi Yang Strongly Correlated Electrons Statistical Mechanics Quantum Physics Exponential observables, formulated as $\log \langle e^{\hat{X}}\rangle$ where $\hat{X}$ is an extensive quantity, play a critical role in study of quantum many-body systems, examples of which include the free-energy and entanglement entropy. Given that $e^{X}$ becomes exponentially large (or small) in the thermodynamic limit, accurately computing the expectation value of this exponential quantity presents a significant challenge. In this Letter, we propose a comprehensive algorithm for quantifying these observables in interacting fermion systems, utilizing the determinant quantum Monte Carlo (DQMC) method. We have applied this novel algorithm to the 2D half-filled Hubbard model. At the strong coupling limit, our method showcases a significant accuracy improvement compared to conventional methods that are derived from the internal energy. We also illustrate that this novel approach delivers highly efficient and precise measurements of the nth Rényi entanglement entropy. Even more noteworthy is that this improvement comes without incurring increases in computational complexity. This algorithm effectively suppresses exponential fluctuations and can be easily generalized to other models. |
| title | An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation |
| topic | Strongly Correlated Electrons Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2311.03448 |