Machine learning matrix product state ansatz for strongly correlated systems.

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• Strongly correlated systems require advanced methods for accurate wavefunction description.
• Matrix Product States (MPS) are a powerful ansatz for such systems.
• Traditional optimization of MPS can be computationally intensive.

Purpose of the Study:

• To apply machine learning (ML) for optimizing the MPS ansatz.
• To develop a computationally efficient alternative to variational optimization for MPS.
• To test the ML-optimized MPS approach on relevant physical systems.

Main Methods:

• Supervised machine learning was employed to optimize MPS.
• Input descriptors were lattice configurations; output was configuration interaction coefficients.
• Data was generated using exact diagonalization, full configuration interaction, and Monte Carlo Configuration Interaction.

Main Results:

• ML optimization was successfully tested on the Heisenberg Hamiltonian for 1D and ladder lattices.
• These lattices model conjugated molecular systems.
• The ML approach avoids calculating energy and operator expectation values.

Conclusions:

• Machine learning provides a computationally efficient method for MPS optimization.
• This ML-based approach circumvents computationally expensive calculations.
• The method is applicable to strongly correlated systems, including molecular systems.