arXiv:cond-mat/9911290 · Physical review. B, Condensed matter

Effect of theWterm for at-U-WHubbard ladder

S. Daul, Douglas J. Scalapino, Steven R. White

Published Jun 15, 2000• 1 citation

Abstract

Antiferromagnetic and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-pairing correlations appear delicately balanced in the two-dimensional Hubbard model. Whether doping can tip the balance to pairing is unclear and models with additional interaction terms have been studied. In one of these, the square of a local hopping kinetic energy ${H}_{W}$ was found to favor pairing. However, such a term can be separated into a number of simpler processes and one would like to know which of these terms is responsible for enhancing the pairing. Here we analyze these processes for a two-leg Hubbard ladder.

DOI: 10.1103/physrevb.61.15526

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arXiv:cond-mat/9911290 · Physical review. B, Condensed matter

Effect of theWterm for at-U-WHubbard ladder

S. Daul, Douglas J. Scalapino, Steven R. White

Published Jun 15, 2000• 1 citation

arXiv HTML PDF

Abstract

Antiferromagnetic and

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}

-pairing correlations appear delicately balanced in the two-dimensional Hubbard model. Whether doping can tip the balance to pairing is unclear and models with additional interaction terms have been studied. In one of these, the square of a local hopping kinetic energy

{H}_{W}

was found to favor pairing. However, such a term can be separated into a number of simpler processes and one would like to know which of these terms is responsible for enhancing the pairing. Here we analyze these processes for a two-leg Hubbard ladder.

DOI: 10.1103/physrevb.61.15526

Related papers

Enhanced pairing in the checkerboard Hubbard ladder

George Karakonstantakis, Erez Berg, Steven R. White +1 more

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Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility $χ(q)$ and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have $d_{x^2-y^2}$ like symmetry. The single-particle spectral weight is also shown to peak near $(π,0)$ and $(0,π)$ when the ratio of the inter- to intra-chain hopping $t_{\perp}/t\simeq 1.5$ , leading to an increased tendency for pairing.Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility $χ(q)$ and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have $d_{x^2-y^2}$ like symmetry. The single-particle spectral weight is also shown to peak near $(π,0)$ and $(0,π)$ when the ratio of the inter- to intra-chain hopping $t_{\perp}/t\simeq 1.5$, leading to an increased tendency for pairing.

arXiv:cond-mat/9612166Dec 18, 19960 citations

Antiferromagnetic and

{d}_{{x}^{2}\ensuremath{-}{y}^{2}}

{H}_{W}

We study signatures of superconductivity in a two-leg ``checkerboard'' Hubbard ladder model, defined as a one-dimensional (period 2) array of square plaquettes with an intraplaquette hopping

t

and interplaquette hopping ${t}^{\ensuremath{'}}$, using the density-matrix renormalization-group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half-filling, $U\ensuremath{\approx}6t$ and ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.6$. Other forms of modulated hopping parameters, with periods of either one or three lattice constants, are also found to enhance pairing relative to the uniform two-leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.

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.

{E}_{c},

the dominant interactions take place within band pairs $(j,N+1\ensuremath{-}j)$ [and within the band

(N+1)/2

for N odd], such that even-leg ladders are an insulating spin liquid, while odd-leg ladders have one gapless spinon mode. In contrast, above the energy scale

{E}_{c},

all bands are interacting with each other and the system is a two-dimensional- (2D)-like (insulating) antiferromagnet; we obtain an analytical expression for the Hamiltonian which is similar to the 2D Heisenberg antiferromagnet. Bosonization techniques show that in the charge sector the Mott insulator is as well below and above

{E}_{c}

of the same type as in

N/2

half-filled two-leg ladders. Doping away from half-filling, we find that the effect of an increasing doping $\ensuremath{\delta}$ is very similar to decreasing the number of legs N: In both cases interactions between unpaired bands are suppressed and thereby the antiferromagnetic correlations reduced. The resulting band pairs form then insulating spin liquids and when doped, there is a spin gap, but phase coherence exists only within the band pairs. At higher doping levels ${\ensuremath{\delta}}_{c}={\ensuremath{\delta}}_{c}(N),$ phase coherence between all band pairs sets in and the system becomes a 2D-like d-wave superconductor $[{\ensuremath{\delta}}_{c}(N)\ensuremath{\rightarrow}0$ for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}].$

We analyze the influence of phonons on the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-pairing instability in the Hubbard model on the two-dimensional square lattice at weak to moderate interaction

U

, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the

{B}_{1g}

buckling mode enhances the pairing, while other phonon modes decrease the pairing. When various phonon modes are included together, the net effect on the scale is small. However, in situations where

d

-wave superconductivity and other tendencies, e.g., antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing.

The two-leg Hubbard ladder is characterized by the ratio of the inter- to intra-leg hopping ${t}_{\ensuremath{\perp}}/t$, the relative interaction strength

U/t,

and the electron filling. Here, using density matrix renormalization group and Monte Carlo simulations, we examine the dependence of the pairing correlations on these parameters. We find that the pairing correlations are enhanced when the top of the bonding quasiparticle band and the bottom of the antibonding band are near the Fermi level. We present results on the single-particle spectral weight and the antiferromagnetic correlations in order to explain this behavior.

χ(q)

and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of the leading singlet pair eigenvalue is found to have

d_{x^2-y^2}

like symmetry. The single-particle spectral weight is also shown to peak near

(π,0)

and

(0,π)

when the ratio of the inter- to intra-chain hopping

t_{\perp}/t\simeq 1.5

, leading to an increased tendency for pairing.