SciPost Submission Page
Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
by Kexin Feng, Chuang Chen, Zi Yang Meng
Submission summary
| Authors (as registered SciPost users): | Kexin Feng |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2508.16298v4 (pdf) |
| Code repository: | https://github.com/KexinFeng/qed_fermion |
| Date submitted: | Jan. 13, 2026, 4:09 a.m. |
| Submitted by: | Kexin Feng |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We develop a GPU-accelerated hybrid quantum Monte Carlo (QMC) algorithm to solve the fundamental yet difficult problem of $U(1)$ gauge field coupled to fermions, which gives rise to a $U(1)$ Dirac spin liquid state under the description of (2+1)d quantum electrodynamics QED$_3$. The algorithm renders a good acceptance rate and, more importantly, nearly linear space-time volume scaling in computational complexity $O(N_τ V_s)$, where $N_τ$ is the imaginary time dimension and $V_s$ is spatial volume, which is much more efficient than determinant QMC with scaling behavior of $O(N_τV_s^3)$. Such acceleration is achieved via a collection of technical improvements, including (i) the design of the efficient problem-specific preconditioner, (ii) customized CUDA kernel for matrix-vector multiplication, and (iii) CUDA Graph implementation on the GPU. These advances allow us to simulate the $U(1)$ Dirac spin liquid state with unprecedentedly large system sizes, which is up to $N_τ\times L\times L = 660\times66\times66$, and reveal its novel properties. With these technical improvements, we see the asymptotic convergence in the scaling dimensions of various fermion bilinear operators and the conserved current operator when approaching the thermodynamic limit. The scaling dimensions find good agreement with field-theoretical expectation, which provides supporting evidence for the conformal nature of the $U(1)$ Dirac spin liquid state in the QED$_3$. Our technical advancements open an avenue to study the Dirac spin liquid state and its transition towards symmetry-breaking phases at larger system sizes and with less computational burden.
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 assessments and referee reports of our paper.
We are very grateful for the constructive comments from the three referees and have revised our manuscripts according to each suggestion. The changes have been listed below and highlighted with blue color.
Thank you in advance for your kind consideration.
Sincerely,
Kexin Feng, Chuang Chen, and Zi Yang Meng
List of changes
- In response to Report 1: (i) Section “Model and Method”, Fig. 3 has been updated where the inset in panel (a) and panels (d-f) have been added. The corresponding caption descriptions and analysis in the main text are added. In parallel, Fig. S5 in the appendix is also updated.
(ii) Appendix section “SV. The analysis of autocorrelation time”, is added along with the new Fig. S6.
- In response to Report 4: (i) Subsection “Physical observables and operator scaling dimension”, paragraph 3, the clarification about the Nf = 2 is made.
(ii) The second editorial suggestion is also taken