New numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton's method. Thermodynamic quantities of one-dimensional Hubbard model is numerically calculated and compared with high temperature expansion and numerical results of quantum transfer matrix method by Jüttner, Klümper and Suzuki. The coincidence is surprisingly good. We get high-temperature expansion of grand potential up to $β^6$ .New numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton's method. Thermodynamic quantities of one-dimensional Hubbard model is numerically calculated and compared with high temperature expansion and numerical results of quantum transfer matrix method by Jüttner, Klümper and Suzuki. The coincidence is surprisingly good. We get high-temperature expansion of grand potential up to $β^6$.

arXiv:cond-mat/0110645Oct 31, 20012 citations

High-temperature transport in the Hubbard Model

B. Sriram Shastry, Edward Perepelitsky, Andrew Galatas +3 more

Bulletin of the American Physical SocietyMar 17, 20160 citations

Thermodynamics of the strongly correlated Hubbard model

Sam Y. S. Yang, Colin J. Thompson

High-temperature expansions for the specific heat and susceptibility of the strongly correlated Hubbard model are compared with corresponding quantities for spinless free fermions and free spins. It is found numerically that, when the temperature is high, the ratio of the specific heat of the strongly correlated Hubbard model to that of spinless free fermions approaches a particle-density-dependent constant. For fixed temperature, the susceptibility of the Hubbard model is less (greater) than that of free spins when the particle density is below (above) a certain threshold density of approximately 0.7. The ratio of the susceptibilities for the two systems, however, appears to be finite for any value of the particle density. Given that the free spin system does not have a ferromagnetic state at any finite temperature, it is concluded that the strongly correlated Hubbard model does not have a finite phase transition temperature. This conclusion is consistent with recent high-temperature expansion studies.High-temperature expansions for the specific heat and susceptibility of the strongly correlated Hubbard model are compared with corresponding quantities for spinless free fermions and free spins. It is found numerically that, when the temperature is high, the ratio of the specific heat of the strongly correlated Hubbard model to that of spinless free fermions approaches a particle-density-dependent constant. For fixed temperature, the susceptibility of the Hubbard model is less (greater) than that of free spins when the particle density is below (above) a certain threshold density of approximately 0.7. The ratio of the susceptibilities for the two systems, however, appears to be finite for any value of the particle density. Given that the free spin system does not have a ferromagnetic state at any finite temperature, it is concluded that the strongly correlated Hubbard model does not have a finite phase transition temperature. This conclusion is consistent with recent high-temperature expansion studies.

Journal of Physics A Mathematical and GeneralMar 21, 199110 citations

β^6