Exact diagonalization of Hubbard clusters at finite temperatures

• Published in: The European physical journal. D, Atomic, molecular and optical physics (Print) Atomic, molecular and optical physics (Print), 2009-04, Vol.52 (1-3), p.159-162
• Main Authors: López-Urías, F., Pastor, G. M.
• Format: Article
• Language: English
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Atomic and molecular clusters; Atomic and molecular physics; Band and itinerant models; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electronic and magnetic properties of clusters; Exact sciences and technology; General theory and models of magnetic ordering; ISSPIC’14 - 14th International Symposium on Small Particles and Inorganic Cluster; Magnetic properties and materials; Molecular; Optical and Plasma Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Spectroscopy/Spectrometry; Spintronics; Studies of special atoms, molecules and their ions; clusters
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2009-00009-9

Finite temperature electronic and magnetic properties of small clusters are investigated in the framework of the Hubbard model by using exact diagonalization methods and by sampling the different cluster topologies exhaustively. Results are discussed for the specific heat C(T), magnetic susceptibility χ(T), local magnetic moments μ i (T), average magnetic moments and spin-correlation functions γ ij (T). Representative cluster sizes and band-fillings are considered showing antiferromagnetic-like (AF) and ferromagnetic-like (FM) behaviors. For half-band filling ν= N the susceptibility shows an AF high-temperature behavior of the form χ≈1/(T + T N ) from which the cluster `Néel’ temperature T N is derived. In contrast, for ν= N + 1 a FM high-temperature behavior of the form χ≈1/(T - T C ) is found, where T C can be interpreted as the cluster `Curie’ temperature. In both cases one also observes peaks in C(T), either at T≃T N or T≃T C , which reflect the development of spin fluctuationsand the breakdown of the low-temperature short-range magnetic order. The dependence of T N and T C on cluster size N and interaction strength U/t is analyzed in terms of effective Heisenberg spin interactions. Finally, the effects of temperature-induced structural fluctuations are discussed.