Reduced basis surrogates for quantum spin systems based on tensor networks

Abstract

Within the reduced basis methods approach, an effective low-dimensional subspace of a quantum many-body Hilbert space is constructed in order to investigate, e.g., the ground-state phase diagram. The basis of this subspace is built from solutions of snapshots, i.e., ground states corresponding to particular and well-chosen parameter values. Here, we show how a greedy strategy to assemble the reduced basis and thus to select the parameter points can be implemented based on matrix-product-states (MPS) calculations. Once the reduced basis has been obtained, observables required for the computation of phase diagrams can be computed with a computational complexity independent of the underlying Hilbert space for any parameter value. We illustrate the efficiency and accuracy of this approach for different one-dimensional quantum spin-1 models, including anisotropic as well as biquadratic exchange interactions, leading to rich quantum phase diagrams.

15 pages, 13 figures; extended conclusions, typos corrected

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The ITensor Software Library for Tensor Network Calculations
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Global sensitivity analysis of bulk properties of an atomic nucleus
• Phase diagram of spin-1 bosons on one-dimensional lattices
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Model reduction methods for nuclear emulators
• Self-learning Emulators and Eigenvector Continuation
• Surrogate models for quantum spin systems based on reduced order modeling
• Reduced basis emulation of pairing in finite systems
• Phase Diagram Detection via Gaussian Fitting of Number Probability Distribution

Cited by in corpus (5)

• Eigenvector Continuation and Projection-Based Emulators
• Surrogate model solver for impurity-induced superconducting subgap states
• Majorana modes in quantum dots coupled via a floating superconducting island
• Greedy Emulators for Nuclear Two-Body Scattering
• Reduced Basis Method for Driven-Dissipative Quantum Systems