Generative neural samplers for the quantum Heisenberg chain

Area of Science:

• Statistical Physics
• Quantum Field Theory
• Machine Learning

Background:

• Generative neural samplers offer a novel computational approach.
• Monte Carlo methods are standard for statistical physics and quantum field theory.
• Evaluating generative models on complex systems is crucial.

Purpose of the Study:

• To assess generative neural samplers for estimating observables in low-dimensional spin systems.
• To explore autoregressive models for sampling quantum Heisenberg chain configurations.
• To compare results with established Monte Carlo techniques.

Main Methods:

• Utilized autoregressive models to sample quantum Heisenberg chain configurations.
• Employed a classical approximation based on the Suzuki-Trotter transformation.
• Calculated energy, specific heat, and susceptibility for quantum spin chains.

Main Results:

• Generative neural samplers accurately estimated observables for quantum spin systems.
• Results for the isotropic XXX and anisotropic XY chains showed good agreement with Monte Carlo.
• The Suzuki-Trotter approximation was effectively combined with neural sampling.

Conclusions:

• Generative neural samplers are a viable alternative to Monte Carlo methods.
• Autoregressive models can successfully simulate quantum spin chains.
• This approach shows potential for tackling complex problems in statistical physics.