Hirschfeld, Peter J.
|Title:||Lower Bounds for the Ground-State Energies of the 2D Hubbard and t-J Models|
|Abstract:||We present simple lower bounds on the ground-state energy of the two-dimensional (2D) Hubbard and t-J models for arbitrary values of band filling and coupling constant. For the Hubbard model we derive two types of bounds, both based on decomposing the model Hamiltonian into a sum of sub-Hamiltonians. For a decomposition into local cluster sub-Hamiltonians, we perform a generalized Legendre transform on previously derived bounds for the grand-canonical potential. For a decomposition into spin-up and spin-down parts, previous results on the spinless Falicov-Kimball model may be used to obtain bounds for the Hubbard model, generalizing a result of Langer and Mattis to arbitrary filling. For the 2D t-J model we have only considered the decomposition into clusters. The 1D Hubbard model is used as a test case. The bounds may be improved by diagonalizing the Hamiltonian for larger clusters.|
|Rights:||©1991 The American Physical Society|
|Publisher:||The American Physical Society|
|Citation:||Valenti, Roser; Stolze, Joachim; Hirschfeld, Peter J.: Lower Bounds for the Ground-State Energies of the 2D Hubbard and t-J Models. In: Physical Review B Nr. 16, Jg. 43(1991), S. 13743-13746, doi: 10.1103/PhysRevB.43.13743 .|
|Appears in Collections:||Stolze, Joachim Prof. Dr.|
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