Stable Determinant Monte Carlo Simulations at Large Inverse Temperature $β$
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917377388576768 |
|---|---|
| author | Luu, Thomas Ostmeyer, Johann Sinilkov, Petar Temmen, Finn L. |
| author_facet | Luu, Thomas Ostmeyer, Johann Sinilkov, Petar Temmen, Finn L. |
| contents | At low temperatures $T$ where $1/T=β\gg1$ the naïve implementation of determinant quantum Monte Carlo (DQMC) methods suffers from loss of precision and numerical instabilities when evaluating the fermion determinant.
This instability propagates into the calculation of observables that rely on the evaluation of the inverse of the fermion matrix, or the Greens function.
For DQMC methods that rely on the Hamiltonian Monte Carlo (HMC) algorithm, an additional complication comes from evaluating the force terms required for integrating Hamilton's equations of motion, since here loss of precision and numerical instabilities are also prevalent.
We show how to address all these issues using various choices of matrix decompositions, allowing us to simulate at $β\gtrsim 90$, which corresponds to room temperature for graphene structures.
Furthermore, our implementation has numerical costs that scale similarly to the naïve implementation, namely as $\mathcal{O}(N_x^3N_t)$, where $N_x$ ($N_t$) is the number of spatial (temporal) sites. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00815 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable Determinant Monte Carlo Simulations at Large Inverse Temperature $β$ Luu, Thomas Ostmeyer, Johann Sinilkov, Petar Temmen, Finn L. Computational Physics Strongly Correlated Electrons High Energy Physics - Lattice At low temperatures $T$ where $1/T=β\gg1$ the naïve implementation of determinant quantum Monte Carlo (DQMC) methods suffers from loss of precision and numerical instabilities when evaluating the fermion determinant. This instability propagates into the calculation of observables that rely on the evaluation of the inverse of the fermion matrix, or the Greens function. For DQMC methods that rely on the Hamiltonian Monte Carlo (HMC) algorithm, an additional complication comes from evaluating the force terms required for integrating Hamilton's equations of motion, since here loss of precision and numerical instabilities are also prevalent. We show how to address all these issues using various choices of matrix decompositions, allowing us to simulate at $β\gtrsim 90$, which corresponds to room temperature for graphene structures. Furthermore, our implementation has numerical costs that scale similarly to the naïve implementation, namely as $\mathcal{O}(N_x^3N_t)$, where $N_x$ ($N_t$) is the number of spatial (temporal) sites. |
| title | Stable Determinant Monte Carlo Simulations at Large Inverse Temperature $β$ |
| topic | Computational Physics Strongly Correlated Electrons High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2604.00815 |