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The cumulant Green's functions method for the Hubbard model.

R N Lira1, P S Riseborough2, J Silva-Valencia3

  • 1Instituto de Física, Universidade Federal Fluminense, Niterói, RJ, Brazil.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 21, 2023
PubMed
Summary
This summary is machine-generated.

The cumulant Green's functions method (CGFM) accurately models strongly correlated electrons in the Hubbard model. This direct calculation method shows reliable results for various physical properties, improving upon existing techniques.

Keywords:
Green’s functionsHubbard modelMott insulatorcumulant expansion

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Theory

Background:

  • The Hubbard model is crucial for understanding strongly correlated electron systems.
  • Accurate and efficient computational methods are needed to solve complex models.

Purpose of the Study:

  • To introduce and validate the cumulant Green's functions method (CGFM) for the single-band Hubbard model.
  • To demonstrate the CGFM's capability in calculating key physical properties and its applicability to experimental systems.

Main Methods:

  • Diagonalization of a correlated cluster ('seed') to compute cumulants.
  • Direct calculation of lattice Green's functions using cluster-derived cumulants.
  • Benchmarking against established methods like the thermodynamic Bethe ansatz and quantum transfer matrix.

Main Results:

  • CGFM accurately reproduces the gap, double occupancy, and ground-state energy.
  • Fulfillment of particle-hole symmetry in the density of states.
  • Systematic convergence to known results with increasing cluster size.

Conclusions:

  • CGFM provides a direct, non-variational, and non-self-consistent approach for strongly correlated models.
  • The method is applicable to various dimensions and can be extended to other models like Anderson and t-J.
  • Successful simulation of an optical lattice experiment highlights practical utility.