arXiv:cond-mat/0602310 · Journal of Physics A Mathematical and General

Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime

Satoshi Ejima, Fabian H. L. Eßler, Florian Gebhard

Published Apr 19, 2006• 7 citations

Abstract

We analyse the thermodynamic Bethe Ansatz equations of the one-dimensional half-filled Hubbard model in the ‘spin-disordered regime’, which is characterized by the temperature being much larger than the magnetic energy scale, but small compared to the Mott–Hubbard gap. In this regime the thermodynamics of the Hubbard model can be thought of in terms of gapped charged excitations with an effective dispersion and spin degrees of freedom that only contribute entropically. In particular, the internal energy and the effective dispersion become essentially independent of temperature. An interpretation of this regime in terms of a putative interacting-electron system at zero temperature leads to a metal–insulator transition at a finite interaction strength above which the gap opens linearly. We relate these observations to studies of the Mott–Hubbard transition in the limit of infinite dimensions.

DOI: 10.1088/0305-4470/39/18/005

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arXiv:cond-mat/0602310 · Journal of Physics A Mathematical and General

Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime

Satoshi Ejima, Fabian H. L. Eßler, Florian Gebhard

Published Apr 19, 2006• 7 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/39/18/005

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Analytic treatment of Mott-Hubbard transition in the half-filled Hubbard model and its thermodynamics

Jongbae Hong, Hae‐Young Kee

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arXiv:cond-mat/9501077Physical review. B, Condensed matterJul 15, 199520 citations

Δ_c \approx U/2

. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

{\mathit{U}}_{\mathit{c}}

of the Coulomb repulsion.

{\mathit{U}}_{\mathit{c}}

depends on N (

{\mathit{U}}_{\mathit{c}}

=0 for N=2). A qualitative change in the charge-rapidity distribution is found at

{\mathit{U}}_{\mathit{c}}

. The Fermi velocity is finite for U

{\mathit{U}}_{\mathit{c}}

, diverges as U\ensuremath{\rightarrow}

{\mathit{U}}_{\mathit{c}}

, and vanishes for U>

{\mathit{U}}_{\mathit{c}}

J

. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as

J

increases, the spin-charge couplings become important and the critical point

{U}_{c}

is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.

{\mathit{U}}_{\mathit{c}}

{\mathit{t}}_{\mathrm{*}}

and a sharp Lorentzian peak appearing at midgap at U

{\mathit{U}}_{\mathit{c}}

. For the N\'eel state, however, the system becomes an insulator for U>0. We also obtain the specific heat and entropy for both the metallic and insulating regimes. Our analytic work reproduces the key results obtained by numerical method in infinite dimensions.