Pair binding and enhancement of pairing correlations in asymmetric Hubbard ladders

Asymmetric two-leg Hubbard ladders with different on-site interactions $U_y$ and hoppings $t_y$ on each leg are investigated using the density-matrix renormalization group method and exact diagonalizations. The pairing found in symmetric ladders is robust against the introduction of the leg asymmetry. When studying pairing, one-band Hubbard ladder models are better described as one-dimensional correlated two-band models than as sublattices of higher-dimensional systems. The asymmetric Hubbard ladder provides us with a simple model for studying pairing in the crossover regime between charge-transfer and Mott insulators.

Figure 1

Sketch of the asymmetric Hubbard ladder described by the Hamiltonian (1) with different on-site repulsions $U_y$ and hoppings $t_y$ on each leg ($y=1,2$) and interchain hopping $t_{\perp }$.

Figure 2

Pair binding energy $E_{pb}^{-}$ as function of $t_{\perp }$ for ladders with length $L=128$ and average density $n=1.125$. (a) Ladders with $u_1=u_2=20/3$ and various $\mathrm{\Delta }t\ge 0$ (see Table 1). (b) Ladders with $\mathrm{\Delta }t=1, u_1=20/3$, and various couplings $U_2=u_2{t}_2=u_2/2>0$ (see Table 2). (c) Ladders with $\mathrm{\Delta }U=0$ and various $\mathrm{\Delta }t$ (see Table 3). Error bars show the size of DMRG truncation errors.

Figure 3

Pair binding energy $E_{pb}^{-}$ as function of $u_1=U_1/t_1$ and $u_2=U_2/t_2$ for two electrons added to a half-filled $2\times 6$ ladder with $t_1=4/3, t_2=2/3$ ($\Rightarrow \mathrm{\Delta }t=2/3$), and $t_{\perp }=4/3$.

Figure 4

Pair binding energy $E_{pb}^{-}$ as a function of the average density $n$ for ladders with $L=128$ rungs. The model parameters are listed in Table 1. Error bars show the size of DMRG truncation errors.

Figure 5

Pair binding energy $E_{pb}^{-}$ as a function of the inverse ladder length for an average density $n=1.125$. The model parameters are listed in Table 1. Error bars show the size of DMRG truncation errors.

Figure 6

(a) Single-particle gap $E_p$, (b) spin gap $E_s$, and (c) charge gap $E_c$ as a function of the inverse ladder length for an average density $n=1.125$. The model parameters are listed in Table 1. Error bars show the size of DMRG truncation errors.

Figure 7

Absolute value of the pair correlation function (8) for ladders with $L=128$ rungs and a density $n=1.125$. The dashed lines are $\sim |x_0{-x|}^{-1}$ and $\sim |x_0{-x|}^{-2}$. The model parameters are listed in Table 1.

Figure 8

Absolute value of pair correlation functions for ladders with $L=128$ rungs and a density $n=1.125$. (a) For the leg-leg pair correlation function (10) and (b) for the rung-rung pair correlation function (9). The dashed lines are $\sim |x_0{-x|}^{-1}$ and $\sim |x_0{-x|}^{-2}$. The model parameters are listed in Table 1.

Figure 9

Exponent $\alpha$ of pairing rung-leg correlations (8) as function of $t_{\perp }$ for ladders with $L=128$ rungs and a density $n=1.125$. The model parameters are listed in Table 1.