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Philosophical Magazine B

Ground-state properties of the two-chain Hubbard ladder

R. M. Noack, Douglas J. Scalapino, Steven R. White

Published Nov 1, 1996• 11 citations
Publisher

Abstract

New materials containing weakly coupled arrays of two-chain metal oxide ladders have recently been synthesized. The two-chain Hubbard ladder provides a possible theoretical model for these systems. Here we review results obtained from numerical renormalization group calculations for the two-chain Hubbard ladder and discuss some features of its ground-state phase diagram.

DOI
10.1080/01418639608240351

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Phase diagram of the two-chain Hubbard model

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We have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.

arXiv:cond-mat/9811280•Physical review. B, Condensed matter•Jan 15, 1999•11 citations
New materials containing weakly coupled arrays of two-chain metal oxide ladders have recently been synthesized. The two-chain Hubbard ladder provides a possible theoretical model for these systems. Here we review results obtained from numerical renormalization group calculations for the two-chain Hubbard ladder and discuss some features of its ground-state phase diagram.
We present a general method for determining the phase diagram of systems of a finite number of one-dimensional Hubbard-like systems coupled by single-particle hopping with weak interactions. The technique is illustrated by detailed calculations for the two-chain Hubbard model, providing controlled results for arbitrary doping and interchain hopping. Of nine possible states which could occur in such a spin-1/2 ladder, we find seven at weak coupling. We discuss the conditions under which the model can be regarded as a one-dimensional analog of a superconductor. \textcopyright{} 1996 The American Physical Society.
Using a functional renormalization-group method, we obtain the phase diagram of the two-leg ladder system within the Holstein-Hubbard model, which includes both electron-electron and electron-phonon interactions. Our renormalization-group technique allows us to analyze the problem for both weak and strong electron-phonon couplings. We show that, in contrast to results from conventional weak-coupling studies, electron-phonon interactions can dominate electron-electron interactions, and retardation effects play an important role on the phase diagram.
The Hubbard model on a two-leg ladder structure has been studied by a combination of series expansions at T = 0 and the density-matrix renormalization group. We report results for the ground-state energy E 0 and spin gap Δ s at half-filling, as well as dispersion curves for one- and two-hole excitations. For small U both E 0 and Δ s show a dramatic drop near t / t ⊥ ~0.5, which becomes more gradual for larger U . This represents a crossover from a `band insulator' phase to a strongly correlated spin liquid. The various features are collected in a `phase diagram' for the model.
We have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.