Entanglement guided search for parent Hamiltonians

TL;DR

This paper presents an entanglement-based method for efficiently identifying parent Hamiltonians of complex quantum ground states by leveraging their reduced density matrices and an exact ansatz, successfully applied to various non-trivial phases.

Contribution

The authors introduce a novel entanglement-guided search method that simplifies finding parent Hamiltonians, applicable to diverse quantum phases and critical points, based on a convex minimization of relative entropy.

Findings

Successfully reconstructs parent Hamiltonians for complex ground states

Applicable to conformal, topological, and critical quantum phases

Demonstrates the entanglement structure simplifies Hamiltonian search

Abstract

We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several non-trivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave-functions considerably simplifies the search for parent Hamiltonians.