Generative Neural Samplers for the Quantum Heisenberg Chain
This research provides an incremental validation of generative neural samplers as an alternative for estimating observables in quantum spin systems for physicists.
This work explores the use of generative neural samplers to estimate observables for low-dimensional spin systems, specifically the quantum Heisenberg chain. By employing autoregressive models and a classical approximation via the Suzuki-Trotter transformation, the authors achieved results for energy, specific heat, and susceptibility that align well with Monte Carlo methods under the same approximation.
Generative neural samplers offer a complementary approach to Monte Carlo methods for problems in statistical physics and quantum field theory. This work tests the ability of generative neural samplers to estimate observables for real-world low-dimensional spin systems. It maps out how autoregressive models can sample configurations of a quantum Heisenberg chain via a classical approximation based on the Suzuki-Trotter transformation. We present results for energy, specific heat and susceptibility for the isotropic XXX and the anisotropic XY chain that are in good agreement with Monte Carlo results within the same approximation scheme.