arXiv:cond-mat/0107094 · Physical review. B, Condensed matter

Staggered orbital currents in the half-filled two-leg ladder

John Ove Fjærestad, John Bradley Marston

Published Mar 13, 2002• 49 citations

Abstract

Using Abelian bosonization with a careful treatment of the Klein factors, we show that a certain phase of the half-filled two-leg ladder, previously identified as having spin-Peierls order, instead exhibits staggered orbital currents with no dimerization.

DOI: 10.1103/physrevb.65.125106

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arXiv:cond-mat/0107094 · Physical review. B, Condensed matter

Staggered orbital currents in the half-filled two-leg ladder

John Ove Fjærestad, John Bradley Marston

Published Mar 13, 2002• 49 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.65.125106

Related papers

Absence of true long-range orbital order in a two-leg Kondo ladder

J. C. Xavier, André Luiz Malvezzi

arXiv:cond-mat/0608100Physical Review BJul 16, 200712 citations

Staggered Orbital Currents in a Model of Strongly Correlated Electrons

John Bradley Marston, Asle Sudbø

This preprint has been withdrawn, as the evidence for persistent currents found with the "infinite-size" DMRG algorithm has not been reproduced with the (presumably more accurate) "finite-size" version of the algorithm (M. Troyer and U. Schollwoeck, private communiation). A much clearer example of long-range order in orbital currents is presented in: J. O. Fjaerestad and J. B. Marston, ``Staggered Orbital Currents in the Half-Filled Two-Leg Ladder,'' cond-mat/0107094.This preprint has been withdrawn, as the evidence for persistent currents found with the "infinite-size" DMRG algorithm has not been reproduced with the (presumably more accurate) "finite-size" version of the algorithm (M. Troyer and U. Schollwoeck, private communiation). A much clearer example of long-range order in orbital currents is presented in: J. O. Fjaerestad and J. B. Marston, ``Staggered Orbital Currents in the Half-Filled Two-Leg Ladder,'' cond-mat/0107094.

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Phase diagram of the three-band half-filled Cu-O two-leg ladder

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The ground state of the $S=1/2$ two-leg ladder with the staggered bond alternations is investigated. We have determined the precise phase diagram on the $\ensuremath{\delta}\ensuremath{-}{J}^{\ensuremath{'}}$ plane $(\ensuremath{\delta}$ and ${J}^{\ensuremath{'}}$ are the magnitudes of the bond alternation and the rung interaction, respectively), employing the level spectroscopic analysis of the numerical diagonalization data obtained by the Lanczos algorithm with the twisted boundary condition. The phase boundary between the leg-dimer state and the rung-dimer state near $(\ensuremath{\delta}{,J}^{\ensuremath{'}})=(0,0)$ is of the form ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{0.69},$ which is consistent with the prediction ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2/3}$ by Mart\'{\i}n-Delgado, Duleksky, and Sierra, and also by Wang and Nersesyan, but not with ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2}$ by Cabra and Grynberg.The ground state of the $S=1/2$ two-leg ladder with the staggered bond alternations is investigated. We have determined the precise phase diagram on the $\ensuremath{\delta}\ensuremath{-}{J}^{\ensuremath{'}}$ plane $(\ensuremath{\delta}$ and ${J}^{\ensuremath{'}}$ are the magnitudes of the bond alternation and the rung interaction, respectively), employing the level spectroscopic analysis of the numerical diagonalization data obtained by the Lanczos algorithm with the twisted boundary condition. The phase boundary between the leg-dimer state and the rung-dimer state near $(\ensuremath{\delta}{,J}^{\ensuremath{'}})=(0,0)$ is of the form ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{0.69},$ which is consistent with the prediction ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2/3}$ by Mart\'{\i}n-Delgado, Duleksky, and Sierra, and also by Wang and Nersesyan, but not with ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2}$ by Cabra and Grynberg.

Physical review. B, Condensed matterJun 24, 200317 citations

We determine the phase diagram of the half-filled two-leg ladder both at weak and strong coupling, taking into account the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and the O

{p}_{x}

and

{p}_{y}

orbitals. At weak coupling, renormalization group flows are interpreted with the use of bosonization. Two different models with and without outer oxygen orbitals are examined. For physical parameters, and in the absence of the outer oxygen orbitals, the D-Mott phase arises; a dimerized phase appears when the outer oxygen atoms are included. We show that the circulating current phase that preserves translational symmetry does not appear at weak coupling. In the opposite strong-coupling atomic limit the model is purely electrostatic and the ground states may be found by simple energy minimization. The phase diagram so obtained is compared to the weak-coupling one.

The ground state of the

S=1/2

two-leg ladder with the staggered bond alternations is investigated. We have determined the precise phase diagram on the $\ensuremath{\delta}\ensuremath{-}{J}^{\ensuremath{'}}$ plane $(\ensuremath{\delta}$ and ${J}^{\ensuremath{'}}$ are the magnitudes of the bond alternation and the rung interaction, respectively), employing the level spectroscopic analysis of the numerical diagonalization data obtained by the Lanczos algorithm with the twisted boundary condition. The phase boundary between the leg-dimer state and the rung-dimer state near $(\ensuremath{\delta}{,J}^{\ensuremath{'}})=(0,0)$ is of the form ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{0.69},$ which is consistent with the prediction ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2/3}$ by Mart\'{\i}n-Delgado, Duleksky, and Sierra, and also by Wang and Nersesyan, but not with ${J}^{\ensuremath{'}}\ensuremath{\propto}{\ensuremath{\delta}}^{2}$ by Cabra and Grynberg.