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Real-time evolution using the density matrix renormalization group.

Steven R White1, Adrian E Feiguin

  • 1Department of Physics and Astronomy, University of California, Irvine, California 92697, USA.

Physical Review Letters
|August 25, 2004
PubMed
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We present a new real-time evolution method for the density matrix renormalization group. This technique simulates transport in non-equilibrium systems and generates entangled wave functions in spin chains.

Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • The density matrix renormalization group (DMRG) is a powerful method for studying quantum many-body systems.
  • Simulating real-time dynamics and systems out of equilibrium remains a challenge for traditional DMRG.

Purpose of the Study:

  • To extend the density matrix renormalization group (DMRG) method to incorporate real-time evolution.
  • To apply this extended method to transport problems in non-equilibrium systems.
  • To calculate frequency-dependent correlation functions.

Main Methods:

  • Developed an extension to the density matrix renormalization group (DMRG) algorithm to include real-time evolution.
  • Applied the method to simulate a scattering process in a spin chain.

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Main Results:

  • Successfully incorporated real-time evolution into the DMRG framework.
  • Demonstrated the method's applicability to transport problems in systems out of equilibrium.
  • Illustrated the calculation of frequency-dependent correlation functions.
  • Simulated a scattering process generating a spatially nonlocal entangled wave function.

Conclusions:

  • The extended DMRG method provides a viable approach for studying real-time dynamics in quantum systems.
  • This advancement enables the investigation of non-equilibrium phenomena and entanglement generation.
  • The method is effective for analyzing transport properties and correlation functions.