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Density matrix renormalization group in the Heisenberg picture.

Michael J Hartmann1, Javier Prior, Stephen R Clark

  • 1Physik Department I, Technische Universität München, James Franck Strasse, 85748 Garching, Germany. michael.hartmann@ph.tum.de

Physical Review Letters
|March 5, 2009
PubMed
Summary

Density-matrix renormalization group (DMRG) calculations are more efficient in the Heisenberg picture. This method focuses on observables, potentially offering exact results for quantum systems with finite bond dimensions.

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Area of Science:

  • Quantum mechanics
  • Computational physics

Background:

  • The density-matrix renormalization group (DMRG) is a powerful method for approximating the state of quantum systems with many subsystems.
  • DMRG leverages redundancies in state descriptions for computational efficiency.

Purpose of the Study:

  • To investigate a more efficient approach for density-matrix renormalization group calculations.
  • To explore the benefits of using the Heisenberg picture in DMRG.

Main Methods:

  • Performing density-matrix renormalization group calculations in the Heisenberg picture.
  • Focusing computational efforts on the observable of interest rather than the entire quantum state.

Main Results:

  • The Heisenberg picture approach significantly enhances the efficiency of DMRG calculations.
  • This method can achieve exact results for certain nontrivial quantum systems, even with finite bond dimensions.

Conclusions:

  • Calculating observables in the Heisenberg picture offers a substantial improvement in efficiency for DMRG.
  • This optimized DMRG approach provides a more exact and computationally feasible method for studying complex quantum systems.