Surrogate models for quantum spin systems based on reduced-order modeling

Area of Science:

• Quantum Mechanics
• Computational Physics
• Condensed Matter Physics

Background:

• Investigating phase diagrams of quantum models is computationally intensive due to large Hilbert spaces.
• Accurate calculation of ground states and physical observables is crucial for phase diagram determination.

Purpose of the Study:

• To present a novel methodology for efficiently investigating quantum model phase diagrams.
• To reduce the computational complexity associated with mapping quantum phase diagrams.

Main Methods:

• The reduced basis method (RBM) is employed, constructing a basis from ground-state snapshots.
• A greedy strategy is utilized for selecting optimal points in parameter space for snapshot computation.
• Physical observables are computed using the assembled RBM basis, reducing computational cost.

Main Results:

• The RBM accurately approximates the ground-state manifold with a moderate number of basis functions.
• The required basis size grows mildly with the number of microscopic constituents.
• Computational complexity is significantly lower than methods requiring the full Hilbert space.

Conclusions:

• The reduced basis method offers an efficient and accurate approach for quantum model phase diagram investigation.
• This methodology provides a substantial computational advantage over traditional methods.
• Future work may combine RBM with tensor network methods for further computational savings.