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Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
by Fanjie Sun and Xiao Yan Xu
Submission summary
| Authors (as registered SciPost users): | Fanjie Sun |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202409_00036v2 (pdf) |
| Date submitted: | 2024-12-25 12:57 |
| Submitted by: | Sun, Fanjie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
Determinant Quantum Monte Carlo (DQMC) provides numerically exact solutions for strongly correlated fermionic systems but faces significant computational challenges with increasing system size. While submatrix updates were originally developed for Hirsch-Fye QMC with onsite interactions at finite temperatures, their comprehensive application in DQMC has remained unexplored despite noted algorithmic similarities. We present the first comprehensive application of submatrix updates in DQMC, significantly extending beyond the original scope by enabling simulations with extended interactions and at zero temperature. Building upon conventional fast updates and delay updates, our generalized implementation achieves an order-of-magnitude improvement in computational efficiency, enabling simulations of the half-filled Hubbard model on lattices up to 8,000 sites - a scale previously challenging with standard DQMC implementations. This enhanced computational capability allows us to accurately determine the finite-temperature phase diagram of the 3D Hubbard model at half-filling. Our findings not only shed light on the phase transitions within these complex systems but also pave the way for more effective simulations of strongly correlated electrons, potentially guiding experimental efforts in cold atom simulations of the 3D Hubbard model.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Thank you very much for the editorial assessment and forwarding the report from the respected referees on November 28th.
Below are our point-to-point responses to the suggestions from the respected referees, and we have made corresponding changes in the revised manuscript. With these, we would humbly like to resubmit our manuscript to SciPost Physics.
Sincerely,
Fanjie Sun and Xiao Yan Xu
List of changes
According to the respected referees’ comments, we made the following revisions.
• We make our contribution in the abstract and introduction clearer.
• We have added reference Phys. Rev. B 99, 125145 (2019).
• We have added the appendix G to explain the universality class and finite-size effects of the model.
• Some typos are fixed.