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Time-reversal symmetry adaptation in relativistic density matrix renormalization group algorithm.

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We introduce time-reversal symmetry adaptation for relativistic density matrix renormalization group (R-DMRG) algorithms. This method halves computational costs and avoids artificial breaking of Kramers degeneracy in relativistic quantum chemistry calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Nonrelativistic quantum mechanics uses spin symmetry (S, M) as good quantum numbers.
  • Relativistic Hamiltonians with spin-dependent interactions, like spin-orbit coupling, break spin symmetry.
  • Standard relativistic density matrix renormalization group (R-DMRG) is computationally expensive and can artificially break Kramers degeneracy for systems with an odd number of electrons.

Purpose of the Study:

  • To develop a more efficient and accurate R-DMRG algorithm.
  • To overcome the limitations of standard R-DMRG, particularly for systems with odd numbers of electrons.
  • To introduce time-reversal symmetry adaptation into R-DMRG.

Main Methods:

  • Proposed time-reversal symmetry adaptation for R-DMRG.
  • Introduced a time-reversal symmetry-adapted renormalized basis.
  • Developed strategies to maintain basis function structure during sweep optimization.

Main Results:

  • Reduced the number of renormalized operators needed by half.
  • Halved the computational costs for Hamiltonian-wavefunction multiplication and renormalization.
  • Successfully adapted R-DMRG to handle time-reversal symmetry, avoiding artificial Kramers degeneracy breaking.

Conclusions:

  • Time-reversal symmetry adaptation significantly improves the efficiency of R-DMRG.
  • The developed method is applicable to other tensor network states without loops.
  • This advancement enables more accurate relativistic quantum chemistry calculations.