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arXiv:1702.02796 · Physical review. B./Physical review. B

Low quasiparticle coherence temperature in the one-band Hubbard model: A slave-boson approach

Alejandro Mezio, Ross H. McKenzie

Published Jul 13, 2017• 12 citations
arXivHTMLPDF

Abstract

We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight $Z$ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature ${T}_{\mathrm{coh}}$ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.

DOI
10.1103/physrevb.96.035121

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We use the Kotliar-Ruckenstein slave-boson formalism to study the temperature dependence of paramagnetic phases of the one-band Hubbard model for a variety of band structures. We calculate the Fermi liquid quasiparticle spectral weight ZZZ and identify the temperature at which it decreases significantly to a crossover to a bad metal region. Near the Mott metal-insulator transition, this coherence temperature Tcoh{T}_{\mathrm{coh}}Tcoh​ is much lower than the Fermi temperature of the uncorrelated Fermi gas, as is observed in a broad range of strongly correlated electron materials. After a proper rescaling of temperature and interaction, we find a universal behavior that is independent of the band structure of the system. We obtain the temperature-interaction phase diagram as function of doping, and we compare the temperature dependence of the double occupancy, entropy, and charge compressibility with previous results obtained with dynamical mean-field theory. We analyze the stability of the method by calculating the charge compressibility.
We use the Kotliar-Ruckenstein slave boson formalism to study the phase diagram of the doped antiferromagnetic Mott insulator at zero and finite temperatures. We obtain the commensurate magnetic phase diagram as a function of doping and temperature. At higher doping and temperatures we find a paramagnetic metallic phase. Reducing doping and temperature, we find antiferromagnetic phases with both metallic and insulating solutions. We calculate the electronic density of states in various regions of the phase diagram. We use our results for the electronic compressibility and magnetic susceptibility to analyze the stability of the various phases obtained within this mean field formalism. We find various parameter regimes where the method fails to provide physical solutions. We argue that those regions correspond to more exotic phases that cannot be described within the current mean field theory.
We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors Q=(π,π),(0,π), and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q), and (Q,π) vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q) and (Q,π) phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.
We present a comprehensive study of the two-dimensional one-band Hubbard model applying the spin-rotation-invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$, $(0,\ensuremath{\pi})$, and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q)\mathbf{Q}=(Q,Q)Q=(Q,Q) and $(Q,\ensuremath{\pi})$ vary continuously with filling, interaction strength, or temperature. The mean-field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q)(Q,Q)(Q,Q) and $(Q,\ensuremath{\pi})$ phases, indicating a first-order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength, and temperature. Finally, a temperature-interaction strength phase diagram is established.
We study the finite-temperature properties of the half-filled two-band Hubbard model in the presence of Hund's rule coupling and orbital anisotropy. We use the mean-field treatment of the Z2{Z}_{2}Z2​ slave-spin theory with a finite-temperature extension of the zero-temperature gauge variable previously developed by Hassan and de' Medici [Phys. Rev. B 81, 035106 (2010)]. We consider the instability of the Fermi-liquid phases and how it is enhanced by the Hund's rule. We identify paramagnetic solutions that have zero quasiparticle weight with a bad metal, and the first-order transition temperature between the bad metal and the Fermi-liquid phase as a coherence temperature that signals the crossover to the bad metallic state. When orbital anisotropy is present, we found an intermediate transition to an orbital-selective bad metal (OSBM), where the narrow band becomes a bad metal while the wide band remains a renormalized Fermi liquid. The temperatures Tcoh{T}_{\text{coh}}Tcoh​ and TOSBM{T}_{\text{OSBM}}TOSBM​ at which the system transitions to the bad metal phases can be orders of magnitude less than the Fermi temperature associated with the noninteracting band. The parameter dependence of the temperature at which the OSBM is destroyed can be understood in terms of a ferromagnetic Kondo-Hubbard lattice model. In general, Hund's rule coupling enhances the bad metallic phases, reduces interorbital charge fluctuations, and increases spin fluctuations. The qualitative difference found in the ground state whether the Hund's rule is present or not, related to the degeneracy of the low-energy manifold, is also maintained for finite temperatures.
We study the electronic state of the doped Mott-Hubbard insulator within the dynamical mean field theory. The evolution of the finite temperature spectral functions as a function of doping show large redistributions of spectral weight in both antiferromagnetic and paramagnetic phases. In particular, a metallic antiferromagnetic state is obtained with a low frequency Slater-splitted quasiparticle peak coexisting with Hubbard bands. In the high temperature paramagnetic metallic phase, upon reducing doping, the system has a crossover through a ``bad metal'' state characterized by an anomalous shift of the quasiparticle peak away from the Fermi energy. We find that the charge compressibility of the antiferromagnetic metal is dramatically enhanced upon approaching the second order N\'eel line.
We study the two-dimensional one-band Hubbard model on the square lattice through the spin rotation invariant Kotliar-Ruckenstein slave-boson method, with an emphasis on the electron-doped regime. The phase diagram determined within mean field approximation reveals three different magnetically ordered phases separated by first-order transitions, and a wide instability region as indicated by a negative compressibility. We show that this conundrum of the unstable mean field domain is resolved by spatially mixed phases of neighboring stable states. We also find charge density wave type instabilities in the antiferromagnetically ordered (AFM) state at wave vectors commensurate with the doping. The corresponding charge and spin density response functions are calculated from a Gaussian fluctuations formalism about a magnetic saddle point, for which we provide a detailed derivation. Further, we present density and spin excitation spectra in the AFM phase, allowing for a quantitative calculation of the spin wave parameters, the gap in the longitudinal spin excitation spectrum, and the density excitations in the upper Hubbard band.