arXiv:cond-mat/0206037 · Physical review. B, Condensed matter

Thermodynamics of the planar Hubbard model

J. Bonča, Peter Prelovšek

Published Feb 7, 2003• 57 citations

Abstract

The thermodynamic properties of specific heat, entropy, chemical potential, spin susceptibility ${\ensuremath{\chi}}_{s},$ and charge susceptibility ${\ensuremath{\chi}}_{c}$ are studied as functions of temperature and doping within the two-dimensional Hubbard model with various $U/t=4--12.$ Quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of $4\ifmmode\times\else\texttimes\fi{}4$ sites. Results show that the entropy at low T reaches a maximum near half-filling at the electron density $n\ensuremath{\sim}1\ifmmode\pm\else\textpm\fi{}0.15$ in the whole regime of studied $U/t.$ The pseudogap in ${\ensuremath{\chi}}_{s}(T)$ becomes clearly pronounced for $U/t>~8$ while ${\ensuremath{\chi}}_{c}$ shows a maximum close to half-filling. The relation of results to those within the $t\ensuremath{-}J$ model and to experiments is discussed.

DOI: 10.1103/physrevb.67.085103

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Thermodynamics of the Planar Hubbard Model

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arXiv:cond-mat/0206037 · Physical review. B, Condensed matter

Thermodynamics of the planar Hubbard model

J. Bonča, Peter Prelovšek

Published Feb 7, 2003• 57 citations

arXiv HTML PDF

Abstract

The thermodynamic properties of specific heat, entropy, chemical potential, spin susceptibility

{\ensuremath{\chi}}_{s},

and charge susceptibility

{\ensuremath{\chi}}_{c}

are studied as functions of temperature and doping within the two-dimensional Hubbard model with various

U/t=4--12.

Quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of

4\ifmmode\times\else\texttimes\fi{}4

sites. Results show that the entropy at low T reaches a maximum near half-filling at the electron density

n\ensuremath{\sim}1\ifmmode\pm\else\textpm\fi{}0.15

in the whole regime of studied

U/t.

The pseudogap in

{\ensuremath{\chi}}_{s}(T)

becomes clearly pronounced for

U/t>~8

while

{\ensuremath{\chi}}_{c}

shows a maximum close to half-filling. The relation of results to those within the

t\ensuremath{-}J

model and to experiments is discussed.

DOI: 10.1103/physrevb.67.085103

Related papers

Thermodynamics of the Planar Hubbard Model

J. Bonča, Peter Prelovšek

International Journal of Modern Physics BAug 10, 20033 citations

Thermodynamic Properties of the Planar t − J Model

Janez Jaklič, Peter Prelovšek

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Recent experiments on cuprates show that as a function of doping, the normal-state specific heat sharply peaks at the doping ${\ensuremath{\delta}}^{*}$, where the pseudogap ends at low temperature. This finding is taken as the thermodynamic signature of a quantum critical point, whose nature has not yet been identified. Here we present calculations for the two-dimensional Hubbard model in the doped Mott insulator regime, which indicate that the specific heat anomaly can arise from the finite-temperature critical end point of a first-order transition between a pseudogap phase with dominant singlet correlations and a metal. As a function of doping at the temperature of the end point, the specific heat diverges. Upon increasing temperature, the peak becomes broader. The diverging correlation length is associated with uniform density fluctuations. No broken symmetries are needed. These anomalies also occur at half-filling as a function of interaction strength, and are relevant for organic superconductors and ultracold atoms.Recent experiments on cuprates show that as a function of doping, the normal-state specific heat sharply peaks at the doping ${\ensuremath{\delta}}^{*}$, where the pseudogap ends at low temperature. This finding is taken as the thermodynamic signature of a quantum critical point, whose nature has not yet been identified. Here we present calculations for the two-dimensional Hubbard model in the doped Mott insulator regime, which indicate that the specific heat anomaly can arise from the finite-temperature critical end point of a first-order transition between a pseudogap phase with dominant singlet correlations and a metal. As a function of doping at the temperature of the end point, the specific heat diverges. Upon increasing temperature, the peak becomes broader. The diverging correlation length is associated with uniform density fluctuations. No broken symmetries are needed. These anomalies also occur at half-filling as a function of interaction strength, and are relevant for organic superconductors and ultracold atoms.

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arXiv:1305.6798Physical Review BOct 7, 201355 citations

The thermodynamic properties of specific heat, entropy, chemical potential, spin susceptibility

{\ensuremath{\chi}}_{s},

and charge susceptibility

{\ensuremath{\chi}}_{c}

are studied as functions of temperature and doping within the two-dimensional Hubbard model with various

U/t=4--12.

Quantities are calculated using the finite-temperature Lanczos method with additional phase averaging for a system of

4\ifmmode\times\else\texttimes\fi{}4

sites. Results show that the entropy at low T reaches a maximum near half-filling at the electron density

n\ensuremath{\sim}1\ifmmode\pm\else\textpm\fi{}0.15

in the whole regime of studied

U/t.

The pseudogap in

{\ensuremath{\chi}}_{s}(T)

becomes clearly pronounced for

U/t>~8

while

{\ensuremath{\chi}}_{c}

shows a maximum close to half-filling. The relation of results to those within the

t\ensuremath{-}J

model and to experiments is discussed.

Several thermodynamic quantities within the planar $t\ensuremath{-}J$ model are calculated using the

T>0

Lanczos method on clusters of up to 26 sites. The hole density ${c}_{h}(\ensuremath{\mu},T)$ shows a non-Fermi-liquid behavior as a function of

T

and suggests a transition from small to large Fermi surfaces at ${c}_{h}\ensuremath{\sim}0.15$. The specific heat reveals a maximum at the exchange energy scale up to

{c}_{h}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.2

, where it becomes almost

T

independent for $T\ensuremath{\gtrsim}0.15t$. At constant

T

the entropy has maximum for ${c}_{h}\ensuremath{\sim}0.15$ with large values at low

T

, consistent with experiments on cuprates. In the underdoped regime the spin susceptibility ${\ensuremath{\chi}}_{0}(T)$ exhibits a maximum at finite

{T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T}^{*}

, with

{T}^{*}

decreasing with doping and disappearing for

{c}_{h}>0.15

{T}^{*}

which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold-atom experiments.