method-vmc

name	method-vmc
description	Use when a VMC, variational Monte Carlo, neural quantum state, NQS, NetKet, ansatz, sampler, or optimizer reproduction needs method-level route and tool selection.

Method VMC

VMC/NQS is the variational stochastic track. Use it to decide whether a paper target is an ansatz benchmark, variational energy, or neural-state training task, then invoke the right tool skills.

Sources

• Methodology reference (reproduction-grade algorithm, parameters, validation, gap analysis): references/vmc-methodology.md
• Tool skills: /using-netket, /using-jax

Route

1. Use VMC/NQS when the paper's claim is about a variational ansatz, training curve, energy benchmark, energy variance, or sign-problem regime where QMC is blocked.
2. Recommend /using-netket for NetKet model/sampler/optimizer setup and VMC timing.
3. Invoke /using-jax when CPU/GPU backend, precision, device smoke test, or compilation behavior matters.
4. Use /using-xdiag only as a small-size validation route when exact comparison is feasible; it is not the primary VMC tool.
5. If the paper uses a custom architecture or official training code, offer official code / web search before mapping it to NetKet.

Tool Handoff

Invoke /using-netket after the route is chosen. /using-netket owns ansatz, sampler, optimizer, learning rate, samples, steps, seeds, variance, error bars, and time estimate. Invoke /using-jax for backend setup.

Details

Variational method: parameterize a wavefunction ansatz, optimize parameters by minimizing energy via stochastic sampling. Neural quantum states (NQS) use neural networks as the ansatz.

Notation

• Ansatz |ψ_θ⟩: parameterized wavefunction (RBM, CNN, Transformer, ...).
• Variational energy E_θ = ⟨ψ_θ|H|ψ_θ⟩ / ⟨ψ_θ|ψ_θ⟩, estimated by Monte Carlo sampling.
• Energy variance σ²_E = ⟨H²⟩ - ⟨H⟩²: zero for exact eigenstate.

When to use

• Frustrated 2D problems where DMRG cylinder geometry biases the answer (kagome, triangular, J1-J2).
• Comparing variational energies across ansatz families.
• Sign-problem regimes where QMC is blocked.

When NOT to use

• 1D chains — DMRG is cheaper and more accurate.
• Small clusters — ED is exact.
• When the user needs a certified bound (VMC gives upper bounds only; no error bars on the gap to exact).

Pitfalls

• Local minima: VMC optimizes a non-convex landscape. Restart with different seeds; compare multiple runs.
• Sign structure: for frustrated / fermionic problems, the ansatz must capture the sign structure of the wavefunction. Marshall-sign-rule initialization helps for bipartite AFM.
• Autocorrelation: MC samples are correlated. Use decorrelation steps or check integrated autocorrelation time.
• Variance vs energy: a low energy with high variance is suspicious. Report both.
• Finite-size effects: VMC with PBC is natural (no boundary bias). Compare sizes.

Verification

• Energy upper bound: VMC energy is variational — it must be ≥ the true ground-state energy. If it's lower than a published exact result, something is wrong.
• Variance: should decrease during training and be small at convergence.
• Cross-method: compare VMC energy to DMRG (if available) on the same system. Agreement within variance is good.
• Multiple seeds: run 3–5 independent optimizations; they should converge to similar energies.

Citations

• Carleo & Troyer, Science 355, 602 (2017) — NQS with RBM.
• Becca & Sorella, Quantum Monte Carlo Approaches for Correlated Systems (Cambridge, 2017) — VMC foundations.