AI 中文总结
本文提出变分蒙特卡洛框架，以神经量子态方法求解含动力学费米子的SU(2)格点规范理论基态，绘制相图并验证方法有效性，为相关研究提供无符号问题的变分框架。
AI 中文摘要
确定与动力学费米子耦合的非阿贝尔格点规范理论的基态，是理解禁闭效应及规范-物质系统相结构的关键。本文提出一种变分蒙特卡洛框架，用于求解L×L方格上与动力学交错费米子耦合的未截断全连续SU(2)格点规范理论的基态。我们在磁基矢下工作，采用神经网络表示规范波函数；费米子则由基于固定奈尔参考态的规范协变高斯费米子修正描述，对于每个采样的规范构型U，该修正由厄米算符生成，此算符由短威尔逊线及质量-跃迁哈密顿量的本征向量构造，变分参数数量随系统规模呈多项式增长。该高斯结构还可基于费米子占据矩阵，给出能量及相关观测量的所有费米子贡献的解析表达式。结果通过强耦合微扰理论验证，其可复现预期的有效反铁磁自旋哈密顿量。利用该框架，我们在独立电耦合与磁耦合(g², λ)平面上绘制了粗略基态相图，证明滞后分析可识别相变的存在。恢复物理关系λ=4/g²后，针对L=4、6、8的晶格规模，我们表征了系统规模增大及电耦合g²变化时，系统态偏离参考奈尔态的程度。更广泛而言，该方法为含动力学物质的连续非阿贝尔规范群提供了无符号问题的变分框架，应可扩展至其他物质内容及更高维晶格。
英文摘要
Determining the ground state of non-Abelian lattice gauge theories coupled to dynamical fermions is key to understanding confinement and the phase structure of gauge--matter systems. We present a variational Monte Carlo framework for the ground state of the untruncated fully-continuous SU$(2)$ lattice gauge theory coupled to dynamical staggered fermions on an $L\times L$ square lattice. We work in the magnetic basis with a neural-network representation of the gauge wavefunction. The fermions are described by a gauge-covariant Gaussian fermionic correction built on a fixed Néel reference state where, for each sampled gauge configuration $\mathbf{U}$, the correction is generated by a Hermitian operator. This operator is constructed from short Wilson lines and the eigenvectors of the mass--hopping Hamiltonian, with number of variational parameters polynomial in the system size. This Gaussian structure also gives analytical expressions for all fermionic contributions to the energy and related observables in terms of the fermion occupation matrix. The results are validated against strong-coupling perturbation theory, where they recover the expected effective antiferromagnetic spin Hamiltonian. Using this framework, we map a coarse ground state phase diagram in the plane of independent electric and magnetic couplings $(g^2, λ)$ and show that a hysteresis analysis can identify the existence of phase transitions. Restoring the physical relation $λ=4/g^2$, we characterize how increasing the system size and changing the electric coupling $g^2$ move the state away from the reference Néel state, for lattice sizes $L=4,6,8$. More broadly, the method offers a sign-problem-free variational framework for continuous non-Abelian gauge groups with dynamical matter that should extend to other matter content and higher-dimensional lattices.
Comments18 pages, 9 figures, 1 table
