Transcorrelated density matrix renormalization group

Area of Science:

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

Background:

• Strongly correlated systems present significant computational challenges for traditional quantum chemistry methods.
• The Density Matrix Renormalization Group (DMRG) is effective for quasi-one-dimensional systems but struggles with higher dimensions.
• Accurate energy approximation is crucial for understanding the behavior of these complex materials.

Purpose of the Study:

• To develop an efficient theoretical framework for approximating the energy of strongly correlated systems.
• To extend the applicability of DMRG methods to systems beyond quasi-one-dimension.
• To address the dynamic correlation problem in DMRG calculations.

Main Methods:

• Introduction of the transcorrelated Density Matrix Renormalization Group (tcDMRG) theory.
• Encoding the wave function as a product of a Jastrow or Gutzwiller correlator and a matrix product state.
• Optimization of the matrix product state using the imaginary-time variant of time-dependent DMRG applied to a non-Hermitian transcorrelated Hamiltonian.

Main Results:

• Demonstrated the efficiency of tcDMRG using the two-dimensional Fermi-Hubbard Hamiltonian.
• Showcased fast energy convergence across various system sizes, occupation numbers, and interaction strengths.
• Validated tcDMRG as a powerful approach for dynamic correlation problems.

Conclusions:

• tcDMRG significantly enhances the efficiency of standard DMRG, particularly for systems beyond quasi-one-dimension.
• The method provides a generally powerful approach to tackling dynamic correlation problems.
• tcDMRG offers a promising avenue for accurate energy approximation in complex, strongly correlated systems.