arXiv:1207.0185 · Physical Review B

Universality class of the Mott transition in two dimensions

S. Moukouri, Eitan Eidelstein

Published Oct 8, 2012• 16 citations

Abstract

We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a nonperfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi-one-dimensional model displays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be $\ensuremath{\nu}\ensuremath{\approx}1.0$. This implies that the fermionic Mott transition belongs to the universality class of the 2D Ising model.

DOI: 10.1103/physrevb.86.155112

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arXiv:1207.0185 · Physical Review B

Universality class of the Mott transition in two dimensions

S. Moukouri, Eitan Eidelstein

Published Oct 8, 2012• 16 citations

arXiv HTML PDF

Abstract

\ensuremath{\nu}\ensuremath{\approx}1.0

. This implies that the fermionic Mott transition belongs to the universality class of the 2D Ising model.

DOI: 10.1103/physrevb.86.155112

Related papers

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\ensuremath{\nu}\ensuremath{\approx}1.0

. This implies that the fermionic Mott transition belongs to the universality class of the 2D Ising model.

{t}_{y}

from an insulator to a metal. Therefore, if

{t}_{y}

is fixed in the metallic phase, increasing the interaction

U

leads to a metal-to-insulator transition at a finite critical

U

. This is in contrast to the weak-coupling Hartree-Fock theory which predicts a nesting-induced antiferromagnetic insulator for any

U>0

The one-dimensional

\mathrm{SU}(n)

Hubbard model is investigated numerically for

n=2

, 3, 4, and 5 at half-filling and

1∕n

filling using the density-matrix renormalization-group method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive

U

n>2

. Furthermore, it is shown that the transition to the gapped phase at

{U}_{c}=0

is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd

n

. In the

1∕n

-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for

U>{U}_{c}=0

, the spin sector remains gapless, and the ground state is nondimerized.

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.

U

equals the bandwidth

{U}_{\mathrm{c}}=W

, where the single-particle gap opens linearly, $\mathrm{\ensuremath{\Delta}}(U\ensuremath{\ge}W)=U\ensuremath{-}W$. The simple nature of the elementary excitations permits us to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution

{n}_{k}

at the Fermi wave number

{k}_{\mathrm{F}}=0

cannot be used to locate accurately

{U}_{\mathrm{c}}

from finite-size systems. However, the slope of

{n}_{k}

at the band edges ${k}_{\mathrm{B}}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$, reveals the formation of a single-particle bound state which can be used to determine

{U}_{\mathrm{c}}

reliably from

{n}_{k}

using accurate finite-size data.

U

reaches a critical value

U_c

. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.