发表机构
University of Washington; Boston College（华盛顿大学; 波士顿学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出相位无关的HyperDet波函数拟设，通过可学习融合张量构建，在分数陈绝缘体等多相中实现高基态重叠，可追踪相变并提取拓扑信息，为强关联系统研究提供新变分平台。
AI 中文摘要
描述强关联系统的竞争相位通常需要基于特定相位假设构建的试探波函数。我们提出超行列式（HyperDet）波函数，作为适用于玻色子和费米子量子多体系统的相位无关拟设，可处理具有自发对称破缺序、分数化和/或含任意子激发的拓扑序的系统。HyperDet结构通过一个完全可学习的融合张量$\boldsymbol{\rm F}$，将辅助费米子部分子的斯莱特行列式融合到物理轨道中而自然产生。使用变分蒙特卡洛方法优化后，单个HyperDet架构在玻色子和费米子模型的整个分数陈绝缘体相，以及其附近的竞争相中，都能与精确对角化得到的基态达到≥99.9%的极高重叠度。我们引入二分融合矩阵的奇异值谱作为融合张量的结构诊断工具，发现其谱的重分布可以追踪多体相变，无需计算特定相位的可观测量。优化后的融合张量还编码了部分子层面的拓扑数据：它重现了玻色子和费米子FCI态预期的部分子陈数，完善了其场论描述及由此产生的拓扑序。其内在规范结构进一步决定了物理对称性是否允许虚提升，并且当存在忠实提升时，可提取其投影类；对于玻色子FCI，这恢复了预期的部分子平移分数化。因此我们预期，HyperDet波函数将成为一个有前景的变分平台，可用于跨强关联相的精确基态搜索和相图探索，还能提供从部分子层面微观机制到场论描述的可解释理论洞见。
英文摘要
Competing phases of strongly correlated systems are often described by trial wavefunctions built on phase-specific assumptions. We propose the \emph{hyperdeterminant (HyperDet) wavefunction} as a phase-agnostic ansatz for both bosonic and fermionic quantum many-body systems exhibiting spontaneous symmetry-breaking, fractionalization, and/or topological order. The HyperDet structure emerges by fusing auxiliary fermionic parton Slater determinants into physical orbitals through a learnable \emph{fusion tensor $\mathcal F$}. Optimized using variational Monte Carlo, a single HyperDet architecture achieves overlaps exceeding $99.9\%$ with exact-diagonalization ground states for nearly all sampled parameters across fractional Chern insulator (FCI) phases and their neighboring competing phases in both bosonic and fermionic models. Beyond its variational expressiveness, the optimized fusion tensor also provides rich interpretability. We show that, (i) the singular-value spectra of the \emph{bipartite fusion matrix} can be used to track phase transitions; (ii) the reconstructed Bott indices reproduce the parton Chern numbers expected for the FCI states without parton-Hamiltonian input; and (iii) faithful lifts of physical translations to the parton degrees of freedom recover the expected translation fractionalization in the bosonic FCI without projective symmetry class assignment. These results establish HyperDet wavefunction as a promising framework for both variational ground-state searches and phase-diagram explorations across strongly correlated phases, and for providing theoretical insights by connecting the optimized wavefunction with parton microscopics and field-theory descriptions.
Commentsadd weighted Tucker reconstruction and determinant expansion; update discussion
