HyperDet Wavefunction: A Phase-Agnostic Ansatz for Strongly Correlated Systems
Abstract
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 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.
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BibTeX
@misc{hu2026hyperdet,
title = {{HyperDet Wavefunction: A Phase-Agnostic Ansatz for Strongly Correlated Systems}},
author = {Xiaodong Hu and Guan-Lin Lin and Ying Ran and Di Xiao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04146},
eprint = {2609.04146},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04146},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - HyperDet Wavefunction: A Phase-Agnostic Ansatz for Strongly Correlated Systems
AU - Xiaodong Hu
AU - Guan-Lin Lin
AU - Ying Ran
AU - Di Xiao
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.04146
UR - https://arxiv.org/abs/2609.04146
AB - 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 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.
ER -