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/2508.16298v3 (pdf) |
| Code repository: | https://github.com/KexinFeng/qed_fermion |
| Date submitted: | Nov. 7, 2025, 4:26 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 $O(N_{\tau} V_s)$, where $N_\tau$ is the imaginary time dimension and $V_s$ is spatial volume, which is much more efficient than determinant QMC with scaling behavior of $O(N_\tau V_s^3)$. 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 $N_\tau\times L\times L = 660\times66\times66$, 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. 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
Current status:
Reports on this Submission
Strengths
(ii) Original and innovative methodological developments enabling record large simulations
(iii) Results substantially improve our understanding of the fate of U(1) gauge field couplied to fermions
Weaknesses
(ii) Complementary and additional quantities need to be analyzed to conclusively establish the obtained results
Report
The manuscript is well-written and I would recommend its publication in SciPost Physics after the authors have answered the following concerns/questions and addressed these issues in an appropriately revised manuscript:
(i) The manuscript would benefit from quantitative measurements of autocorrelation times for gauge fields, fermionic bilinears, and energy. Could the authors provide τ_L or acceptance-rate scaling with L, and comment on whether critical slowing down is suppressed or only reduced?
(ii) The authors fix N_τ = 10 L (thus β = L).
Questions: Why is this particular scaling chosen?
Has the dependence on Δτ been checked?
Are the power-law exponents stable as Δτ → 0?
Could the authors provide a small-Δτ extrapolation or a consistency check?
(iii) While Fig. 2(b) shows small-L comparisons, no quantitative error analysis is given.
Could the authors provide explicit differences between HQMC and exact/ED or DQMC observables (e.g., energies, correlation functions) to demonstrate correctness and absence of systematic biases?
(iv) The scaling fits are done on a small number of large-distance points due to noise limitations.
Can the authors quantify the fitting range and systematic drift of exponents as the fitting window is varied? Are the statistical uncertainties (including covariance between data points) properly propagated?
(v) Since DSL/QED3 physics emerges only in the infrared, the accessible L may still be in a crossover regime. Are there indicators (e.g., scaling collapse, monotonic drift of exponents with 1/L) that the simulations have indeed reached the asymptotic scaling regime?
(vi) The paper interprets matching exponents for spin and bond operators as evidence for emergent SU(4). Can the authors provide a quantitative comparison (e.g., exponent difference Δ_spin − Δ_bond with uncertainty)? Is the agreement within error bars expected theoretically at these lattice sizes? Are there other operators (e.g., adjoint vs singlet channels) that could strengthen the SU(4) conclusion?
(vii) The τ⁻⁴ behaviour is associated with conserved current scaling Δ_J = 2. Can the authors distinguish τ⁻⁴ from possible τ⁻³ (free photon) or τ⁻⁵ behaviors within error bars? Are the results sensitive to gauge coupling J or to anisotropy in temporal vs spatial discretization?
Requested changes
Please see points raised in the Report
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)