Spin-Projected Matrix Product States: Versatile Tool for Strongly Correlated Systems

Area of Science:

• Quantum Many-Body Physics
• Computational Chemistry
• Condensed Matter Theory

Background:

• Accurate description of electronic structures in molecules and materials is crucial for understanding chemical and physical properties.
• Traditional methods often struggle with systems exhibiting strong electron correlation and complex magnetic behaviors.
• Spin adaptation, ensuring wave functions are eigenfunctions of total spin, is essential for accurate magnetic property predictions.

Purpose of the Study:

• To develop a new wave function ansatz, spin-projected matrix product states (SP-MPS), that simplifies spin adaptation.
• To provide a computationally efficient method for studying strongly correlated and magnetic systems.
• To enable accurate calculations of ground and excited states, as well as various physical properties.

Main Methods:

• Constructing SP-MPS by applying a spin projector to matrix product states (MPS).
• Utilizing the matrix product operator (MPO) formalism for Hamiltonians and spin projectors.
• Developing algorithms for variational optimization, perturbation theory, and property evaluation within the SP-MPS framework.

Main Results:

• SP-MPS offers a simpler route to spin adaptation compared to explicit SU(2) symmetry incorporation in MPS.
• The ansatz connects to broken-symmetry mean-field states, facilitating exploration of complex electronic landscapes.
• An embarrassingly parallel algorithm arises naturally from the MPO representation for efficient computation.
• SP-MPS can achieve high accuracy by increasing bond dimensions and allows straightforward excited state calculations.

Conclusions:

• SP-MPS represents a significant advancement in quantum many-body methods for strongly correlated and magnetic systems.
• The method provides a versatile and efficient tool for electronic structure calculations, applicable to various models and real systems.
• This ansatz opens new avenues for quantum embedding theories and accurate prediction of molecular and material properties.