• Condensed Matter > Strongly Correlated Electrons [Submitted on 22 Aug 2025 (v1), last revised 24 Feb 2026 (this version, v5)] Title:Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU View PDF HTML (experimental)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 operat

Article Summaries:

  • Condensed Matter > Strongly Correlated Electrons [Submitted on 22 Aug 2025 (v1), last revised 24 Feb 2026 (this version, v5)] Title:Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU View PDF HTML (experimental)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 im

Sources: