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Physical review. B, Condensed matter

Specific heat of the half-filled Hubbard chain: A Feynman path-integral Monte Carlo investigation

Joachim Schulte, Michael C. Böhm

Published Jun 15, 1996• 20 citations
Publisher

Abstract

The specific heat C of the one-dimensional half-filled Hubbard model is studied by Feynman path-integral quantum Monte Carlo simulations as a function of temperature (T). The strength of the electronic correlations is modified by a variable intramolecular two-electron repulsion U. For weak correlations, C shows a single maximum. For intermediate correlations C has two maxima in the T interval studied. For strong correlations only one maximum and one minimum in C are found in the T interval considered. The influence of spin and electronic excitations on the T dependence of C are discussed. The C data are correlated with calculated probabilities of single occupancy, electronic charge fluctuations, and the electronic chemical potential. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.15385

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The specific heat C of the one-dimensional half-filled Hubbard model is studied by Feynman path-integral quantum Monte Carlo simulations as a function of temperature (T). The strength of the electronic correlations is modified by a variable intramolecular two-electron repulsion U. For weak correlations, C shows a single maximum. For intermediate correlations C has two maxima in the T interval studied. For strong correlations only one maximum and one minimum in C are found in the T interval considered. The influence of spin and electronic excitations on the T dependence of C are discussed. The C data are correlated with calculated probabilities of single occupancy, electronic charge fluctuations, and the electronic chemical potential. \textcopyright{} 1996 The American Physical Society.
The Feynman path-integral quantum Monte Carlo (PI QMC) approach has been employed to study the specific heat C of the one-dimensional (1D) half-filled Hubbard chain as a function of temperature. For not too strong many-body interactions C exhibits a single maximum only. With increasing correlation strength the C curve shows an intermediate minimum separating a sharp low-temperature maximum and a broad high-temperature profile. The first peak is caused by spin excitations and the high-temperature values of C are determined by charge degrees of freedom. The contribution of both quantities to the net specific heat curve has been quantified in the present theoretical setup. The specific heat data are interpreted with the aid of calculated charge fluctuations, probabilities Pi(n) to find n = 2, 1, 0 electrons at the respective lattice sites, a spin density wave (SDW) order parameter and the electronic chemical potential μ.
We have calculated the spin correlation length of the half-filled one-dimensional Hubbard model down to the temperature of T =0.01×(transfer integral) by the Bethe-Ansatz method for the quantum transfer matrix. Its temperature dependence shows the crossover from (2 log π T ) -1 at high temperatures to a T -1 with the log corrections at low temperatures, the low- T behavior being consistent with the prediction by the conformal field theory. When the Coulomb repulsion U is small, we have found at low temperatures another crossover in the proportional constant a from the value for the free electron system to that for the antiferromagnetic Heisenberg model. This crossover is due to the disappearance of charge fluctuation. A similar crossover has been observed for the linear coefficient of specific heat, C / T .
Local moment formation driven by the on-site repulsion U is one of the most fundamental features in the Hubbard model. At the simplest level, the temperature dependence of the local moment is expected to have a single structure at $T\ensuremath{\sim}U,$ reflecting the suppression of the double occupancy. In this paper we show low-temperature quantum Monte Carlo data for half-filling which emphasize that the local moment also has a signature at a lower energy scale which previously had been thought to characterize only the temperatures below which moments on different sites begin to correlate locally. We discuss implications of these results for the structure of the specific heat, and connections to quasiparticle resonance and pseudogap formation in the density of states.
We have calculated the spin correlation length of the half-filled one-dimensional Hubbard model down to the temperature of T =0.01×(transfer integral) by the Bethe-Ansatz method for the quantum transfer matrix. Its temperature dependence shows the crossover from (2 log π T ) -1 at high temperatures to a T -1 with the log corrections at low temperatures, the low- T behavior being consistent with the prediction by the conformal field theory. When the Coulomb repulsion U is small, we have found at low temperatures another crossover in the proportional constant a from the value for the free electron system to that for the antiferromagnetic Heisenberg model. This crossover is due to the disappearance of charge fluctuation. A similar crossover has been observed for the linear coefficient of specific heat, C / T .
Abstract The path‐integral formulation along with the quantum Monte Carlo method is used to study the physical properties of the one‐dimensional Hubbard model for various band fillings and values of interaction strength U. Results for singlet and triplet pairing correlations, local square magnetic moment, total energy, probability of double occupancy, and nearest‐neighbour charge‐density correlations are presented. These results are explored at β (inverse temperature) = 2.0, 1.0, and 0.5 for the linear chain N = 16. These results show that the effect of correlation on the physical quantities is small for low band‐filling and it becomes most evident for the half‐filled band at finite temperatures.
Using the quantum Monte Carlo simulation technique for the lattice fermion systems, we study the charge susceptibility of the two-dimensional Hubbard near the half-filled band. Lattice sizes up to 6×6 and inverse temperatures up to 6 t ( t : hopping parameter) are studied. We find that the behavior of the charge susceptibility is strongly dependent on the electron concentration at low temperature: the charge susceptibility is suppressed at the half-filled band, while it is considerably enhanced in non-half-filled band cases by the electron correlation. The above behavior of the charge susceptibility is quite similar to the recent Bethe-Ansatz result for the one-dimensional Hubbard model.