A Monte Carlo maximum-entropy calculation of the optical conductivity of the infinite-dimensional Hubbard model is presented. We show that the optical conductivity displays the anomalies found in the cuprate superconductors, including a Drude width which grows linearly with temperature, a Drude weight which grows linearly with doping, and a temperature and doping-dependent mid-IR peak. These anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the Fermi energy as T\ensuremath{\rightarrow}0, and are a generic property of the strongly correlated Hubbard model in all dimensions greater than one.A Monte Carlo maximum-entropy calculation of the optical conductivity of the infinite-dimensional Hubbard model is presented. We show that the optical conductivity displays the anomalies found in the cuprate superconductors, including a Drude width which grows linearly with temperature, a Drude weight which grows linearly with doping, and a temperature and doping-dependent mid-IR peak. These anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the Fermi energy as T\ensuremath{\rightarrow}0, and are a generic property of the strongly correlated Hubbard model in all dimensions greater than one.

arXiv:cond-mat/9412084Physical review. B, Condensed matterMay 1, 199561 citations

Magnetic and dynamic properties of the Hubbard model in infinite dimensions

Mark Jarrell, Thomas Pruschke

arXiv:cond-mat/9207012The European Physical Journal BJun 1, 1993119 citations

Hubbard Model in Infinite Dimensions

Florian Gebhard

Springer tracts in modern physicsJan 1, 19970 citations

Anomalous properties of the Hubbard model in infinite dimensions

Mark Jarrell, Thomas Pruschke

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.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.

Physical review. B, Condensed matterJan 1, 199454 citations

Partition functional and thermodynamic properties of the infinite-dimensional Hubbard model

Y. M. Li, N. d’Ambrumenil

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature ${\mathit{T}}^{\mathrm{*}}$ . 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 ${\mathit{T}}^{\mathrm{*}}$ .An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature ${\mathit{T}}^{\mathrm{*}}$. 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 ${\mathit{T}}^{\mathrm{*}}$.

arXiv:cond-mat/9401017Physical review. B, Condensed matterMar 1, 19944 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{*}}