arXiv:0808.1116 · Journal of the Physical Society of Japan

Mott Transition in the Hubbard Model on Checkerboard Lattice

Takuya Yoshioka, Akihisa Koga, Norio Kawakami

Published Sep 25, 2008• 18 citations

Abstract

We investigate the bandwidth-controlled Mott transition in the Hubbard model on the checkerboard lattice at half filling using the path-integral renormalization group (PIRG) method. It is demonstrated that the system undergoes a first-order phase transition to the plaquette-singlet insulating phase at a finite Hubbard interaction. This conclusion is drawn via a detailed analysis of the spin and charge correlations around the phase transition point by means of the PIRG method aided with a new iteration scheme introduced in this paper.

DOI: 10.1143/jpsj.77.104702

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arXiv:0808.1116 · Journal of the Physical Society of Japan

Mott Transition in the Hubbard Model on Checkerboard Lattice

Takuya Yoshioka, Akihisa Koga, Norio Kawakami

Published Sep 25, 2008• 18 citations

arXiv HTML PDF

Abstract

DOI: 10.1143/jpsj.77.104702

Related papers

Mott transition in the Hubbard model on the triangular lattice

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Abstract We investigate a metal–insulator Mott transition in the half‐filled Hubbard model on the triangular lattice. In this study, we make use of the path‐integral renormalization group method with an iteration and truncation scheme proposed recently, which allows us to access the competing ground states around the transition point. We find for a cluster with 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic (PM) state undergoes a metal–insulator phase transition to a nonmagnetic insulating (NMI) state at $U_{\rm c} \sim 7.4t$ , where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.Abstract We investigate a metal–insulator Mott transition in the half‐filled Hubbard model on the triangular lattice. In this study, we make use of the path‐integral renormalization group method with an iteration and truncation scheme proposed recently, which allows us to access the competing ground states around the transition point. We find for a cluster with 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic (PM) state undergoes a metal–insulator phase transition to a nonmagnetic insulating (NMI) state at $U_{\rm c} \sim 7.4t$ , where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.

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Jaichul Yi, Lizeng Zhang, Geoffrey Canright

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U_{\rm c} \sim 7.4t

, where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.

U

increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at

U_{c1}\sim 7.7t

, which is followed by another first-order transition to a

120^\circ

Néel ordered state at

U_{c2}\sim 10t

, where

t

is the transfer integral. Our results ensure the existence of the intermediate NMI phase, and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions. We find that

κ

-(BEDT-TTF)

_2

_2

(CN)

_3

is located in the NMI phase close to the metal-insulator transition point.

Numerical studies on Mott transitions caused by the control of the ratio between bandwidth and electron-electron interaction (

U

) are reported. By using the recently proposed path-integral renormalization group(PIRG) algorithm, physical properties near the transitions in the ground state of two-dimensional half-filled models with the nearest and the next-nearest neighbor transfers (

-t

and

t'

, respectively) are studied as a prototype of geometrically frustrated system. The nature of the bandwidth-control transitions shows sharp contrast with that of the filling-control transitions: First, the metal-insulator and magnetic transitions are separated each other and the metal-insulator (MI) transition occurs at smaller

U

, although the both transition interactions

U

increase with increasing

t'

. Both transitions do not contradict the first-order transitions for smaller

t'/t

while the MI transitions become continuous type accompanied by emergence of {\it unusual metallic phase} near the transition for large

t'/t

. A nonmagnetic insulator phase is stabilized between MI and AF transitions. The region of the nonmagnetic insulator becomes wider with increasing

t'/t

. The phase diagram naturally connects two qualitatively different limits, namely the Hartree-Fock results at small

t'/t

and speculations in the strong coupling Heisenberg limit.

{U=U}_{c}

and

{U=U}_{s}

that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase

(U<{U}_{c})

and drops below the band gap when U exceeds a special point

{U}_{e}.

The exciton gap closes at the first critical point

{U}_{c}

while the charge and spin gaps persist and coincide between

{U}_{c}<U<{U}_{s}

where the system is dimerized. Both the charge and spin gaps collapse at

{U=U}_{s}

when the transition to the MI phase occurs. In the MI phase

(U>{U}_{s})

the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.

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.

{\mathit{U}}_{\mathit{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.