Exact thermodynamics of pairing and charge–spin separation crossovers in small Hubbard nanoclusters

Abstract

The exact numerical diagonalization and thermodynamics in an ensemble of small Hubbard clusters in the ground state and finite temperatures reveal intriguing insights into the nascent charge and spin pairings, Bose condensation and ferromagnetism in nanoclusters. The phase diagram off half filling strongly suggests the existence of subsequent transitions from electron pairing into unsaturated and saturated ferromagnetic Mott-Hubbard like insulators, driven by electron repulsion. Rigorous criteria for the existence of quantum critical points in the ground state and corresponding crossovers at finite temperatures are formulated. The phase diagram for 2 × 4-site clusters illustrates how these features are scaled with cluster size. The phase separation and electron pairing, monitored by a magnetic field and electron doping, surprisingly resemble phase diagrams in the family of doped high Tc cuprates.

Antiferromagnetic model and magnetization plateaus on the zigzag ladder with two- and three-site exchanges

“…The thermodynamic properties of a physical system like a free energy, magnetization, magnetic susceptibility, heat capacity, entropy can be derived from the partition function. The partition function can be calculated using dynamic technique [1], transfer matrix [2], Monte Carlo simulation [3], path integral [4], exact diagonalization in clusters [5], etc. Phase transition behavior of the system can be studied by the transfer matrix method (TMM) [6].…”

Magnetization and Lyapunov exponents on a kagome chain with multi-site exchange interaction

“…To obtain the recursion relation for the partition function that is related to s 2 site one can separate the kagome chain into two identical parts as shown in Fig. 3: 24) and the contribution of each branch is denoted by g n (s 1 , s 2 ). The recursion relations for g n can be obtained by performing eleven (s 3 , .…”

“…(H (2,3) (s0,s1,s2)+H (2,3) (s0,p1,p2))− J 6 2T H (6) } (24) and the contribution of each branch is denoted by g n (s 1 , s 2 ). The recursion relations for g n can be obtained by performing eleven (s 3 .…”

“…Magnetization plateaus appear in a wide range of models on chains, ladders, hierarchical lattices, theoretically analyzed by dynamical, transfer matrix approaches and exact diagonalization in clusters (see Refs. [14][15][16][17][18][19][20][21][22][23][24][25][26]). The experimental evidence for the appearance of magnetization plateaus has also been found for two-dimensional systems [27][28][29][30].…”

Geometrical frustration of an extended Hubbard diamond chain in the quasiatomic limit

“…For small nanoclusters by the exact numerical diagonalization the average electron density, magnetization plateaus via chemical potential or magnetic field have been studied in Hubbard model 12,13 .…”