Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915289057198080 |
|---|---|
| author | Wang, Zhe Wang, Zhiyan Ding, Yi-Ming Mao, Bin-Bin Yan, Zheng |
| author_facet | Wang, Zhe Wang, Zhiyan Ding, Yi-Ming Mao, Bin-Bin Yan, Zheng |
| contents | We propose a quantum Monte Carlo scheme capable of extracting large-scale data of Rényi entanglement entropy (EE) with high precision and low technical barrier. Instead of directly computing the ratio of two partition functions within different space-time manifolds, we obtain them separately via a reweight-annealing scheme and connect them from the ratio of a reference point. The incremental process can thus be designed along a path of real physical parameters within this framework, and all intermediates are meaningful EEs corresponding to these parameters. In a single simulation, we can obtain many multiples ($\sim βL^d$, d is the space dimension) of EEs, which has been proven to be powerful for determining phase transition points and critical exponents. Additionally, we introduce a formula to calculate the derivative of EE without resorting to numerical differentiation from dense EE data. This formula only requires computing the difference of energies in different space-time manifolds. The calculation of EE and its derivative becomes much cheaper and simpler in our scheme. We then demonstrate the feasibility of using EE and its derivative to find phase transition points, critical exponents, and various phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative Wang, Zhe Wang, Zhiyan Ding, Yi-Ming Mao, Bin-Bin Yan, Zheng Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Computational Physics Quantum Physics We propose a quantum Monte Carlo scheme capable of extracting large-scale data of Rényi entanglement entropy (EE) with high precision and low technical barrier. Instead of directly computing the ratio of two partition functions within different space-time manifolds, we obtain them separately via a reweight-annealing scheme and connect them from the ratio of a reference point. The incremental process can thus be designed along a path of real physical parameters within this framework, and all intermediates are meaningful EEs corresponding to these parameters. In a single simulation, we can obtain many multiples ($\sim βL^d$, d is the space dimension) of EEs, which has been proven to be powerful for determining phase transition points and critical exponents. Additionally, we introduce a formula to calculate the derivative of EE without resorting to numerical differentiation from dense EE data. This formula only requires computing the difference of energies in different space-time manifolds. The calculation of EE and its derivative becomes much cheaper and simpler in our scheme. We then demonstrate the feasibility of using EE and its derivative to find phase transition points, critical exponents, and various phases. |
| title | Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2406.05324 |