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arXiv:1905.02929 · Physica Scripta

Negative electron compressibility in the Hubbard model

A Sherman

Published Aug 30, 2019• 6 citations
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Abstract

Abstract Using the strong coupling diagram technique, we study the one-band repulsive Hubbard model on a two-dimensional square lattice in a wide range of chemical potentials μ . Infinite sequences of diagrams describing interactions of electrons with spin and charge fluctuations are taken into account. At low temperatures, regions of the negative electron compressibility are found for μ ≈ 0 and μ ≈ U , where U is the Hubbard repulsion. They are manifestations of non-rigid electron bands, which change drastically in the mentioned regions of chemical potentials due to the level crossing in the Hubbard atom.

DOI
10.1088/1402-4896/ab401a

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Abstract Using the strong coupling diagram technique, we study the one-band repulsive Hubbard model on a two-dimensional square lattice in a wide range of chemical potentials μ . Infinite sequences of diagrams describing interactions of electrons with spin and charge fluctuations are taken into account. At low temperatures, regions of the negative electron compressibility are found for μ ≈ 0 and μ ≈ U , where U is the Hubbard repulsion. They are manifestations of non-rigid electron bands, which change drastically in the mentioned regions of chemical potentials due to the level crossing in the Hubbard atom.
Abstract The two-orbital Hubbard-Kanamori model is studied using the strong coupling diagram technique. This approach allows one to take into account the interactions of electrons with spin, charge, and orbital fluctuations of all ranges. It was found that, at low temperatures, the model has four regions of the negative electron compressibility, which can lead to charge inhomogeneities with the assistance of phonons. For half-filling, the phase diagram of the model contains regions of the Mott and Slater insulators, bad-metal, and states with spin-polaron peaks. These sharp peaks at the Fermi level are seen in doped states also. A finite Hund coupling leads to a large increase of antiferromagnetic spin correlations with strong suppression of charge and orbital fluctuations near half-filling. For moderate doping, all types of correlations become comparable. They peak at the antiferromagnetic wave vector except for a narrow region with an incommensurate response. Stronger doping destroys all correlations.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
The phase diagram, the Bethe-ansatz ground-state properties, including the chemical potential μ, the spin (magnetic) and charge susceptibilities, are calculated within the one-dimensional Hubbard model in entire range of interaction strength (-∞< U/t<+∞), magnetic field (h≥ 0) and all electron concentrations (0≤n≤1). The continuous and smooth variation of μ with n and h in the vicinity of n=1 points on the gapless character of charge excitations at U<0 and provides rigorous upper and lower bounds for μ. The spin (magnetic) susceptability χ at half-filling changes discontinuously as U→0 and is strongly enhanced by electron repulsion, comparing with that of the non-interactig case. The compressibility κ ch increases with n at U<0 and shows non-monotonous behavior with a dramatic increase at U>0. Variations of κ ch -1 in both repulsive and attractive cases qualitatively well reproduces corresponding behavior of charge stiffness.
[[abstract]]Cited: 0 References: 20 Citation Map Abstract: The phase diagram, the Bethe-ansatz ground-state properties, including the chemical potential mu, the spin (magnetic) and charge susceptibilities, are calculated within the one-dimensional Hubbard model in entire range of interaction strength (-infinity < U/t < + infinity), magnetic field (h greater than or equal to 0) and all electron concentrations (0 less than or equal to n less than or equal to 1). The continuous and smooth variation of mu with n and h in the vicinity of n = 1 points on the gapless character of charge excitations at U < <0 and provides rigorous upper and lower bounds for <mu>. The spin (magnetic) susceptibility chi at half-filling changes discontinuously as U --> 0 and is strongly enhanced by electron repulsion, comparing with that of the non-interacting case. The compressibility rc,h increases with n at U < 0 and shows non-monotonous behavior with a dramatic increase at U > 0. Variation of k(ch)(-1) in both repulsive and attractive cases qulitatively well reproduces corresponding behavior of charge stiffness.
Abstract The possibility of the superconducting transition in the repulsive Hubbard model on a square lattice is studied using the ladder approximation of the strong coupling diagram technique. The t – U and t – t ′– t ″– U models are considered in the regime of strong correlations, for the on-site Coulomb repulsion U = 8 t , in the range of temperatures 0.02 t ≲ T ≲ 0.3 t . To avoid the influence of the phase separation and size effects the calculations are performed in an infinite crystal, in the part of the phase diagram without inhomogeneities, for the electron concentration n ¯ = 0.92 . Solutions of the Eliashberg equation for singlet and triplet pairing, which are transformed according to one-dimensional representations of the lattice point group D 4 , are considered. For both models and all considered symmetries, eigenvalues of the Eliashberg equation are less than unity and demonstrate no upward trend with decreasing temperature. This result points to the absence of superconductivity in the Hubbard model in the strong-coupling regime. We discuss the reason for the small eigenvalue of the Eliashberg equation in the case of the singlet d x 2 − y 2 pairing.
Abstract We consider the extended Hubbard model on a two-dimensional square lattice at half-filling. The model is investigated using the strong coupling diagram technique. We sum infinite series of ladder diagrams allowing for full-scale charge and spin fluctuations and the actual short-range antiferromagnetic order for nonzero temperatures. In agreement with earlier results, we find the first-order phase transition in the charge subsystem occurring at v = v c ≳ U/4 with v and U the intersite and on-site Coulomb repulsion constants. The transition reveals itself in an abrupt sign change of a sharp maximum in the zero-frequency charge susceptibility at the corner of the Brillouin. States arising at the transition have alternating deviations of electron occupations from the mean value on neighboring sites. Due to fluctuations, these alternating occupation deviations have short-range order. For the considered parameters, such behavior is found for U ≲ 5t with t the hopping constant. For the insulating case U ≳ 6t, in which the transition is not observed, we find a continuous growth of the Mott gap with v. The evolution of the electron density of states with increasing v is also considered.