Generative Neural Samplers for the Quantum Heisenberg Chain

TL;DR

This paper explores the use of generative neural samplers to estimate physical observables in quantum spin chains, demonstrating their effectiveness compared to traditional Monte Carlo methods within a classical approximation scheme.

Contribution

It introduces autoregressive neural models for sampling quantum Heisenberg chains and validates their accuracy against established Monte Carlo results.

Findings

Neural samplers accurately estimate energy, specific heat, and susceptibility.

Results align well with Monte Carlo within the Suzuki-Trotter approximation.

Demonstrates potential of neural methods in quantum statistical physics.

Abstract

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.