PaperPanorama

HEP Lattice·hep-lat

Mon·Jul 20, 2026

3 papers—1 primary·2 cross-listed

All3Primary1Cross-lists2
  1. 01

    Path optimization method for the sign problem: Insights from random matrix models

    Kouji Kashiwa🇯🇵 · Yusuke Namekawa🇯🇵 · Hayato Takase

    The path optimization method is applied to the Stephanov model and the chiral random matrix model, both of which share several properties with QCD, to mitigate the sign problem caused by the fermion determinant. The Stephanov model serves as a prototypical model of finite-density QCD, while the chiral random matrix model represents an ideal system featuring the Silver Blaze phenomenon. We show that the path optimization successfully improves the average phase factor in the Stephanov model at high chemical potential, reproducing the analytical results with reduced statistical errors. However, it fails to improve the average phase factor in the Stephanov model at low chemical potential, as well as in the chiral random matrix model. This tendency in the phase factor behavior seems to be closely related to the global sign problem.

    hep-lathep-ph0 citations
  2. 02

    Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling

    Moxian Qian🇨🇳

    Sampling from an unnormalized Boltzmann density requires proposals that move probability mass globally while retaining enough path-probability information for statistical correction. We introduce Neural Non-Equilibrium Hamiltonian Monte Carlo (NHMC), a train-then-correct learned Hamiltonian sampler. Starting from a tractable base distribution, NHMC learns stochastic Hamiltonian-style paths toward the target. Once training is complete, the learned proposal parameters are fixed; the proposal then generates complete paths and endpoint configurations, which are statistically corrected using the recorded non-equilibrium work. This dimensionless generalized work is determined by the probability ratio between the forward proposal path and a reverse reference path. During training, minimizing its mean reduces a path-space KL divergence and controls an upper bound on endpoint mismatch. During evaluation, the same quantity defines weights for self-normalized importance sampling on paths (path-SNIS), estimates normalizing constants or free-energy differences, and gives the acceptance ratio for path-space independent Metropolis--Hastings (path-IMH). We further derive a shared-bridge round-trip NHMC--MH kernel and prove that its configuration-space transition preserves the Boltzmann target. On double-well, finite-volume lattice , compact non-Abelian gauge, and Lennard--Jones cluster targets, the NHMC construction gives corrected estimates when path overlap is sufficient; when overlap is poor, weight degeneracy, low acceptance, and long autocorrelation expose proposal failure. We additionally report a molecular internal-coordinate feasibility study using a molecular-dynamics prior and learned-force path proposal.

    ↳ cs.LGcond-mat.stat-mechhep-lat1 citation
  3. 03

    Conditional Euclidean-Hamiltonian reductions for sign-problem toy models

    Tsogtgerel Gantumur🇨🇦

    Euclidean Monte Carlo methods are effective when the path-integral weight is real and nonnegative, but finite-density fermion systems often produce sign-changing or complex scalar weights after the fermionic sector is traced out. Hamiltonian formulations avoid this complex-weight sampling problem but face rapid Hilbert-space growth. This paper studies a conditional Euclidean-Hamiltonian (CEH) reduction that combines these two descriptions. The calculation is organized around a Monte Carlo-tractable reference problem and a residual active sector. Instead of tracing the active sector into a determinant or scalar weight, CEH keeps it operator-valued and uses the reference calculation to determine projected correlation or transfer matrices. These matrices define a finite effective Hamiltonian, with the remaining finite-density dependence introduced after projection. At finite rank, the result is an effective model whose accuracy must be tested through basis enlargement, metric conditioning, stochastic matrix-element errors, and number-sector diagnostics. The construction is examined in three finite benchmarks. A two-channel oscillator tests conditional basis compression; a positive-measure stochastic calculation tests correlation-matrix harvesting and GEVP extraction, including a comparison with a PDMS-style estimator; and a four-site Hubbard ring combines a finite-budget determinant-sign stress test with finite-density continuation in non-target active spaces. The benchmarks support the proposed trade from scalar sign reweighting to a monitored active-space approximation in structured finite models, but they do not provide an end-to-end stochastic CEH treatment of the Hubbard sign problem or establish favorable scaling. Usefulness requires both low-rank approximability and efficient extraction of the required projected matrix data.

    ↳ quant-phcond-mat.str-elhep-lat0 citations

Affiliations

first authorsco-authorsvia INSPIRE