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Optimizing linked-cluster expansions by white graphs.

K Coester1, K P Schmidt1

  • 1Lehrstuhl für Theoretische Physik I, Otto-Hahn-Str. 4, TU Dortmund, D-44221 Dortmund, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 19, 2015
PubMed
Summary
This summary is machine-generated.

We developed a white-graph expansion for perturbative continuous unitary transformations. This method optimizes calculations for complex quantum models by reducing the number of graphs, simplifying analysis of spin ladders.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory

Background:

  • Perturbative continuous unitary transformations (pCUT) are powerful for studying quantum systems.
  • Linked-cluster expansions are commonly used to implement pCUT.
  • Calculating complex models can involve a large number of graphs, hindering efficiency.

Purpose of the Study:

  • Introduce a novel white-graph expansion for pCUT.
  • Improve computational efficiency for microscopic models with numerous coupling constants.
  • Demonstrate the method's applicability to a specific quantum spin model.

Main Methods:

  • Developed a white-graph expansion technique.
  • Utilized model-independent effective Hamiltonians in second quantization.
  • Exploited inherent cluster additivity for optimized bookkeeping.
  • Applied the expansion to a 2D quantum spin model of coupled two-leg XXZ ladders.

Main Results:

  • The white-graph expansion significantly reduces the number of relevant graphs.
  • This approach enhances computational efficiency for models with many coupling constants.
  • Successfully applied to analyze coupled two-leg XXZ spin ladders.

Conclusions:

  • The white-graph expansion offers an efficient alternative for pCUT calculations.
  • This method is particularly advantageous for complex quantum systems.
  • Provides a streamlined approach for studying spin ladder models.