基于受限玻尔兹曼机（RBM）的非可积非厄米横场伊辛链中纵向场驱动的相变
Longitudinal-Field-Driven Transition in a non-integrable Non-Hermitian Transverse-Field Ising Chain via RBMs
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中文总结 AI 辅助
本研究采用受限玻尔兹曼机（RBM）结合变分蒙特卡洛采样，研究受纵向与复杂横场作用的非可积非厄米横场伊辛链，确定了PT对称性破缺驱动的非厄米量子相变，证实实值神经量子态是研究非厄米量子临界现象的有效框架。
中文摘要 AI 辅助
我们研究了受纵向场和复杂横场作用的非厄米横场伊辛链的基态性质与量子临界行为。为解决这一相互作用多体问题，我们采用基于受限玻尔兹曼机（RBM）的实值神经量子态，通过变分蒙特卡洛（VMC）采样进行优化。对有限链的谱分析揭示了与自发宇称-时间（PT）对称性破缺相关的例外点。我们开发了实值RBM框架以重构非厄米哈密顿量的基态本征态。与精确对角化的基准对比表明，RBM方法可准确复现基态能量、磁化强度及自旋-自旋关联。将分析扩展至更大系统尺寸后，我们确定了以PT对称性破缺和磁有序出现为特征的非厄米量子相变。我们的结果证实，实值神经量子态是研究相互作用非厄米量子系统临界现象的高效且可扩展框架。
英文摘要
We investigate the ground-state properties and quantum critical behavior of a non-Hermitian transverse-field Ising chain subjected to longitudinal and complex transverse magnetic fields. To address this interacting many-body problem, we employ real-valued neural quantum states based on Restricted Boltzmann Machines (RBMs), optimized using Variational Monte Carlo (VMC) sampling. Spectral analysis of finite chains reveals exceptional points associated with spontaneous parity-time (PT) symmetry breaking. A real-valued RBM framework is developed to reconstruct the ground-state eigenstates of the non-Hermitian Hamiltonian. Benchmark comparisons with exact diagonalization demonstrate that the RBM approach accurately reproduces the ground-state energy, magnetization, and spin-spin correlations. Extending the analysis to larger system sizes, we identify a non-Hermitian quantum phase transition characterized by PT-symmetry breaking and the emergence of magnetic order. Our results establish real-valued neural quantum states as an efficient and scalable framework for investigating critical phenomena in interacting non-Hermitian quantum systems.
