SCIENCE@home

O-Sensing: Operator Sensing for Interaction Geometry and Symmetries

Ye-Ming Meng,Zheng Shi

Published 2026 in Unknown venue

ABSTRACT

We ask whether the Hamiltonian, interaction geometry, and symmetries of a quantum many-body system can be inferred from a few low-lying eigenstates without knowing which sites interact with each other. Directly solving the eigenvalue equations imposes constraints that yield a highly degenerate subspace of candidate operators, where the local Hamiltonian is hidden among an extensive family of conserved quantities, obscuring the interaction geometry. Here we introduce O-Sensing, a protocol designed to extract the Hamiltonian and symmetries directly from these states. Specifically, O-Sensing employs parsimony-driven optimization to extract a maximally sparse operator basis from the degenerate subspace. The Hamiltonian is then selected from this basis by maximizing spectral entropy (effectively minimizing degeneracy) within the sampled subspace. We validate O-Sensing on Heisenberg models on connected Erd\H{o}s--R\'enyi graphs, where it reconstructs the interaction geometry and uncovers additional long-range conserved operators. We establish a learnability phase diagram across graph densities, featuring a pronounced ``confusion''regime where parsimony favors a dual description on the complement graph. These results show that sparsity optimization can reconstruct interaction geometry as an emergent output, enabling simultaneous recovery of the Hamiltonian and its symmetries from low-energy eigenstates.

PUBLICATION RECORD

CITATION MAP

EXTRACTION MAP

CLAIMS

  • No claims are published for this paper.

CONCEPTS

  • No concepts are published for this paper.

REFERENCES

Showing 1-37 of 37 references · Page 1 of 1

CITED BY

  • No citing papers are available for this paper.

Showing 0-0 of 0 citing papers · Page 1 of 1