using-qmbcertify

To compute certified ground-state energy bounds for Heisenberg spin models, you solve a structured semidefinite program using the NPA hierarchy. This Skill leverages symmetry exploitation and reduced-density-matrix positivity to generate rigorous numeric energy bounds.

The NPA hierarchy for quantum many-body spin systems is a structured noncommutative-polynomial-optimization method. It targets 1D and 2D Heisenberg models by enforcing reduced-density-matrix positivity to solve large-scale semidefinite programs.

Yes, you can use Mosek and JuMP in Julia for semidefinite program optimization. This Skill requires the Mosek solver and Julia environment to perform numeric SDP optimization for bounding ground-state properties of spin models.

To convert numeric SDP optima into exact rational certificates for 1D Heisenberg chains, the Skill applies an exact rational post-processing layer. This uses Arblib to mathematically verify ground-state energy bounds rather than relying on numeric approximations.

Yes, this approach works for both 1D and 2D Heisenberg models by implementing a specialized noncommutative-polynomial-optimization hierarchy. However, the exact rational post-certification layer is specifically provided for 1D chains.

You need the Mosek solver to bound ground-state properties because calculating these limits requires solving large-scale semidefinite programs. Mosek handles the numeric SDP optimization necessary before exact rational post-certification can occur.