Physical review. B, Condensed matter

Anomalous properties of the Hubbard model in infinite dimensions

Mark Jarrell, Thomas Pruschke

Published Jan 1, 1994• 54 citations

Abstract

Anomalies are found in the resistivity \ensuremath{\rho} and NMR rate 1/${\mathit{T}}_{1}$ of the infinite-dimensional Hubbard model using quantum Monte Carlo calculations and the noncrossing approximation. For temperatures greater than the ``Kondo scale'' ${\mathit{T}}_{0}$, we obtain 1/${\mathit{T}}_{1}$\ensuremath{\sim}a+bT and \ensuremath{\rho}\ensuremath{\sim}c+dT (a, b, c, d constants). For temperatures T\ensuremath{\ll}${\mathit{T}}_{0}$ we infer from a saturation of the effective mass of the carriers that the ground state of the system is a Fermi liquid.

DOI: 10.1103/physrevb.49.1458

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Transport Properties of the Infinite-Dimensional Hubbard Model

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Physical review. B, Condensed matter

Anomalous properties of the Hubbard model in infinite dimensions

Mark Jarrell, Thomas Pruschke

Published Jan 1, 1994• 54 citations

Publisher

Abstract

Anomalies are found in the resistivity \ensuremath{\rho} and NMR rate 1/

{\mathit{T}}_{1}

of the infinite-dimensional Hubbard model using quantum Monte Carlo calculations and the noncrossing approximation. For temperatures greater than the ``Kondo scale''

{\mathit{T}}_{0}

, we obtain 1/

{\mathit{T}}_{1}

\ensuremath{\sim}a+bT and \ensuremath{\rho}\ensuremath{\sim}c+dT (a, b, c, d constants). For temperatures T\ensuremath{\ll}

{\mathit{T}}_{0}

we infer from a saturation of the effective mass of the carriers that the ground state of the system is a Fermi liquid.

DOI: 10.1103/physrevb.49.1458

Related papers

Transport Properties of the Infinite-Dimensional Hubbard Model

Thomas Pruschke, Daniel Lee Cox, Mark Jarrell

Results for the optical conductivity and resistivity of the Hubbard model in infinite spatial dimensions are presented. At half-filling we observe a gradual crossover from a metal with a Drude peak at ω = 0 in the optical conductivity to an insulator as a function of U for temperatures above the antiferromagnetic phase transition. When doped, the "insulator" becomes a Fermi liquid with a corresponding temperature dependence of the optical conductivity and resistivity. We find a T 2 -coefficient in the low-temperature resistivity which suggests that the carriers in the system acquire a considerable mass-enhancement due to the strong local correlations. At high temperatures, a crossover into a semi-metallic regime takes place.Results for the optical conductivity and resistivity of the Hubbard model in infinite spatial dimensions are presented. At half-filling we observe a gradual crossover from a metal with a Drude peak at ω = 0 in the optical conductivity to an insulator as a function of U for temperatures above the antiferromagnetic phase transition. When doped, the "insulator" becomes a Fermi liquid with a corresponding temperature dependence of the optical conductivity and resistivity. We find a T 2 -coefficient in the low-temperature resistivity which suggests that the carriers in the system acquire a considerable mass-enhancement due to the strong local correlations. At high temperatures, a crossover into a semi-metallic regime takes place.

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Quantum Monte Carlo study of spin correlations in the one-dimensional Hubbard model

Anders W. Sandvik, Douglas J. Scalapino, C. Singh

The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding T=0 correlation function of the infinite system. For the T\ensuremath{\rightarrow}0 divergence of the q=2 ${\mathit{k}}_{\mathit{F}}$ spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2 ${\mathit{k}}_{\mathit{F}}$ )\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding T=0 correlation function of the infinite system. For the T\ensuremath{\rightarrow}0 divergence of the q=2${\mathit{k}}_{\mathit{F}}$ spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2${\mathit{k}}_{\mathit{F}}$)\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.

Physical review. B, Condensed matterJul 15, 199315 citations

Anomalous normal-state properties of high- T c superconductors: intrinsic properties of strongly correlated electron systems?

Thomas Pruschke, M. Jarrell, James K. Freericks

A systematic study of optical and transport properties of the Hubbard model, based on the Metzner-Vollhardt dynamical mean-field approximation, is reviewed. This model shows interesting anomalous properties that are, in our opinion, ubiquitous to single-band strongly correlated systems (for all spatial dimensions greater than one) and also compare qualitatively with many anomalous transport features of the high-T c cuprates. This anomalous behaviour of the normal-state properties is traced to a ‘collective single-band Kondo effect’, in which a quasiparticle resonance forms at the Fermi level as the temperature is lowered, ultimately yielding a strongly renormalized Fermi liquid at zero temperature.A systematic study of optical and transport properties of the Hubbard model, based on the Metzner-Vollhardt dynamical mean-field approximation, is reviewed. This model shows interesting anomalous properties that are, in our opinion, ubiquitous to single-band strongly correlated systems (for all spatial dimensions greater than one) and also compare qualitatively with many anomalous transport features of the high-T c cuprates. This anomalous behaviour of the normal-state properties is traced to a ‘collective single-band Kondo effect’, in which a quasiparticle resonance forms at the Fermi level as the temperature is lowered, ultimately yielding a strongly renormalized Fermi liquid at zero temperature.

arXiv:supr-con/9502001Advances In PhysicsJan 1, 1995441 citations

Anomalies are found in the resistivity \ensuremath{\rho} and NMR rate 1/

{\mathit{T}}_{1}

of the infinite-dimensional Hubbard model using quantum Monte Carlo calculations and the noncrossing approximation. For temperatures greater than the ``Kondo scale''

{\mathit{T}}_{0}

, we obtain 1/

{\mathit{T}}_{1}

\ensuremath{\sim}a+bT and \ensuremath{\rho}\ensuremath{\sim}c+dT (a, b, c, d constants). For temperatures T\ensuremath{\ll}

{\mathit{T}}_{0}

we infer from a saturation of the effective mass of the carriers that the ground state of the system is a Fermi liquid.

{\mathit{T}}^{\mathrm{*}}

. We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near

{\mathit{T}}^{\mathrm{*}}

. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around

{\mathit{T}}^{\mathrm{*}}

, and has a rough linear temperature dependence above

{\mathit{T}}^{\mathrm{*}}

The nature of the Mott-Hubbard metal-insulator transition in the infinite-dimensional Hubbard model is investigated by quantum Monte Carlo simulations down to temperature

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}W/140

(

W\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{bandwidth}

). Calculating with significantly higher precision than in previous work, we show that the hysteresis below ${T}_{\mathrm{IPT}}\ensuremath{\simeq}0.022W$, reported in earlier studies, disappears. Hence the transition is found to be continuous rather than discontinuous down to at least

{T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.325T}_{\mathrm{IPT}}

. We also study the changes in the density of states across the transition, which illustrate that the Fermi liquid breaks down before the gap opens.

{\mathit{k}}_{\mathit{F}}

spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2

{\mathit{k}}_{\mathit{F}}

)\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.