Learning the Effective Spin Hamiltonian of a Quantum Magnet

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