Observable-Based Learning of Effective Entanglement Hamiltonians
Abstract
Determining the entanglement Hamiltonian (EH) of an interacting quantum many-body system remains a fundamental challenge beyond special analytically tractable cases. Here we develop an observable-matching framework for learning effective EHs, which we demonstrate using response estimates from quantum Monte Carlo. As applications of this framework, we first calibrate the overall prefactor of the lattice Bisognano--Wichmann (LBW) construction using equal-time correlations and then learn spatially resolved couplings beyond its prescribed profile, without assuming a specific functional form for their spatial dependence. Trained solely on local correlations, the learned EHs reproduce benchmarked von Neumann and second Rényi entropies in $1$D and second Rényi entropies in $2$D. For a strong-bond cut associated with special surface criticality at the (2+1)D O(3) Wilson--Fisher critical point, free-form learning outperforms the calibrated LBW ansatz in predicting the second Rényi entropy and reveals spatially nonuniform coupling renormalizations. Importantly, the learned EH also provides access to the von Neumann entropy in this setting, revealing a negative subleading correction and extending previous Rényi entropy findings to the von Neumann case. Directly evaluating the von Neumann entropy in such (2+1)D interacting quantum many-body systems remains challenging for conventional numerical methods. These results establish observable-based learning as a route to constructing effective entanglement Hamiltonians beyond prescribed spatial profiles in higher-dimensional interacting systems.
Related
- Sharp universal death of entanglement threshold for Pauli Hamiltonians
- Autonomous stabilization of many-body entanglement with Floquet Hamiltonians and weak measurement
- Entanglement dynamics after quenches with inhomogeneous Hamiltonians
- Effective Hamiltonians and non-Hermitian physics
- Static Effective Hamiltonians for Molecular Systems through RPA-Based Downfolding.
BibTeX
@misc{yang2026observablebased,
title = {{Observable-Based Learning of Effective Entanglement Hamiltonians}},
author = {Siyi Yang and Yuzhi Liu and Yi-Ming Ding and Zheng Yan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07353},
eprint = {2611.07353},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07353},
}
RIS
TY - UNPB
TI - Observable-Based Learning of Effective Entanglement Hamiltonians
AU - Siyi Yang
AU - Yuzhi Liu
AU - Yi-Ming Ding
AU - Zheng Yan
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07353
UR - https://arxiv.org/abs/2611.07353
AB - Determining the entanglement Hamiltonian (EH) of an interacting quantum many-body system remains a fundamental challenge beyond special analytically tractable cases. Here we develop an observable-matching framework for learning effective EHs, which we demonstrate using response estimates from quantum Monte Carlo. As applications of this framework, we first calibrate the overall prefactor of the lattice Bisognano--Wichmann (LBW) construction using equal-time correlations and then learn spatially resolved couplings beyond its prescribed profile, without assuming a specific functional form for their spatial dependence. Trained solely on local correlations, the learned EHs reproduce benchmarked von Neumann and second Rényi entropies in $1$D and second Rényi entropies in $2$D. For a strong-bond cut associated with special surface criticality at the (2+1)D O(3) Wilson--Fisher critical point, free-form learning outperforms the calibrated LBW ansatz in predicting the second Rényi entropy and reveals spatially nonuniform coupling renormalizations. Importantly, the learned EH also provides access to the von Neumann entropy in this setting, revealing a negative subleading correction and extending previous Rényi entropy findings to the von Neumann case. Directly evaluating the von Neumann entropy in such (2+1)D interacting quantum many-body systems remains challenging for conventional numerical methods. These results establish observable-based learning as a route to constructing effective entanglement Hamiltonians beyond prescribed spatial profiles in higher-dimensional interacting systems.
ER -