Learning Effective Spin Hamiltonian of Quantum Magnet

TL;DR

This paper introduces an unbiased, computational approach combining optimization, differentiation, and tensor network calculations to accurately determine the effective spin Hamiltonian from experimental data, aiding the study of quantum spin liquids.

Contribution

It presents a novel Hamiltonian learning method that integrates multiple optimization techniques with advanced many-body calculations, applicable to real experimental data.

Findings

Successfully applied to synthetic data from known Hamiltonians

Accurately extracted Hamiltonians from experimental data of Copper Nitrate

Demonstrated effectiveness on complex magnetic materials

Abstract

Interacting spins in quantum magnet can cooperate and exhibit exotic states like the quantum spin liquid. To explore the materialization of such intriguing states, the determination of effective spin Hamiltonian of the quantum magnet is thus an important, while at the same time, very challenging inverse many-body problem. To efficiently learn the microscopic spin Hamiltonian from the macroscopic experimental measurements, here we propose an unbiased Hamiltonian searching approach that combines various optimization strategies, including the automatic differentiation and Bayesian optimization, etc, with the exact diagonalization and many-body thermal tensor network calculations. We showcase the accuracy and powerfulness by applying it to training thermal data generated from a given spin Hamiltonian, and then to realistic experimental data measured in the spin-chain compound Copper Nitrate and triangular-lattice materials TmMgGaO4. This automatic Hamiltonian searching constitutes a very promising approach in the studies of the intriguing spin liquid candidate magnets and correlated electron materials in general.