We consider two aspects of the ground state of the $U=\ensuremath{\infty}$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\ensuremath{\infty}$ Hubbard ladder in the limit of the large interchain hopping ${(t}_{\ensuremath{\perp}}/t\ensuremath{\rightarrow}\ensuremath{\infty})$. In this limit, the total spin $S$ of the ground state is shown to be zero for the electron density $n<~0.5$ and its maximum ${(S=S}_{\mathrm{max}})$ for $n>0.5$ . The charge gap at quarter-filling is ${2t}_{\ensuremath{\perp}}.$ We extend these results to finite ${t}_{\ensuremath{\perp}}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite ${t}_{\ensuremath{\perp}}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio ${t}_{\ensuremath{\perp}}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the $t$ - $J$ ladder is briefly discussed.We consider two aspects of the ground state of the $U=\ensuremath{\infty}$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\ensuremath{\infty}$ Hubbard ladder in the limit of the large interchain hopping ${(t}_{\ensuremath{\perp}}/t\ensuremath{\rightarrow}\ensuremath{\infty})$. In this limit, the total spin $S$ of the ground state is shown to be zero for the electron density $n<~0.5$ and its maximum ${(S=S}_{\mathrm{max}})$ for $n>0.5$. The charge gap at quarter-filling is ${2t}_{\ensuremath{\perp}}.$ We extend these results to finite ${t}_{\ensuremath{\perp}}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite ${t}_{\ensuremath{\perp}}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio ${t}_{\ensuremath{\perp}}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the $t$-$J$ ladder is briefly discussed.

arXiv:cond-mat/9709170Physical review. B, Condensed matterDec 15, 199726 citations

Quantum Phases in the Extended Bose-Hubbard Ladder

Ji-Guo wang, Dong-Dong Pu, Ya-Fei Song +4 more

Jan 1, 20220 citations

Charge-order transition in the extended Hubbard model on a two-leg ladder

Matthias Vojta C, R. E. Hetzel, R. M. Noack

We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion $V$ using the density matrix renormalization group technique. We consider electron densities between quarter and half filling. For quarter filling and $U=8t,$ we find evidence for a continuous phase transition between a homogeneous state at small $V$ and a broken-symmetry state with ``checkerboard'' [wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$] charge order at large $V.$ This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of $U/t$ on the transition and estimate the position of the tricritical points.We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion $V$ using the density matrix renormalization group technique. We consider electron densities between quarter and half filling. For quarter filling and $U=8t,$ we find evidence for a continuous phase transition between a homogeneous state at small $V$ and a broken-symmetry state with ``checkerboard'' [wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$] charge order at large $V.$ This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of $U/t$ on the transition and estimate the position of the tricritical points.

arXiv:cond-mat/9906101Physical review. B, Condensed matterSep 15, 199934 citations

S

of the ground state is shown to be zero for the electron density

n<~0.5

and its maximum

{(S=S}_{\mathrm{max}})

for

n>0.5

. The charge gap at quarter-filling is ${2t}_{\ensuremath{\perp}}.$ We extend these results to finite ${t}_{\ensuremath{\perp}}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite ${t}_{\ensuremath{\perp}}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio ${t}_{\ensuremath{\perp}}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the

t

J

ladder is briefly discussed.

We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion

V

using the density matrix renormalization group technique. We consider electron densities between quarter and half filling. For quarter filling and

U=8t,

we find evidence for a continuous phase transition between a homogeneous state at small

V

and a broken-symmetry state with ``checkerboard'' [wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$] charge order at large

V.

This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of

U/t

on the transition and estimate the position of the tricritical points.