Ground-state and thermodynamic properties of the Hubbard model applied to small clusters

Abstract

The Hubbard Model with nearest-neighbor hopping and one type of orbital is applied to small clusters, with emphasis on an octahedron (six sites}. The complete eigenvalue spectrum is calculated. A rather complicated dependence of the spin of the ground state on occupation number, geometry, and model parameters is found. Thermodynamic properties are computed with use of a canonical ensemble. Results are reported for the specific heat, spin susceptibility, and spin-spin correlation functions.

Correlated electron systems on the Apollonian network

“…The low-temperature peak arises due to low-lying collective excitations, while the high-temperature broad peak comes from single-particle excitations. This behavior is quite general and has been noticed for different structures [9,10].…”

“…It is important to observe the discontinuous change of L 1 and L 2 . This quantum transition point at U/t = 11.1 must not be a Mott metal-insulator transition because L 0 is continuous [9]. For U/t >> 1, L 0 is approximately equal to 1/4 and we can conclude that each site is occupied by just one electron.…”

“…For small and intermediary U/t the curves present a peak. The temperature associated with the peak of χ corresponds approximately to the rapid decay of L 1 and L 2 , and is a consequence of the collective excitations that lead to the destruction of the antiferromagetic order [9]. Here the ground state has spin S = 1/2 and χ must go to infinity at temperature T = 0.…”

Phase separation and electron pairing in repulsive Hubbard clusters

“…Hence, it is important to conduct theoretical studies of such clusters, and this work reports a number of surprising results based on the methodology discussed in our previous work. 1,2 The significance of the present study is twofold: First, although numerous properties, including eigenvalues and susceptibilities, of Hubbard clusters have been calculated [3][4][5][6][7][8][9][10][11] previously, many open questions remain with regard to microscopic origins of charge-spin separation, pseudogap behavior, and various scenarios of possible pairings at low temperature. Apparently, the above studies did not search for transitions, as we have done here, over an extended parameter space that includes variations in chemical potential, magnetic field, Coulomb repulsion, and temperature.…”

Magnetism and the electronic correlations in Mn clusters

“…In this many-body scheme, the correlated ground-state energy is obtained exactly within a controlled numerical accuracy. Throughout this work the term "exact" should be understood as exact within 10 −10 in the ground-state energy [19].…”