arXiv:1311.4796 · Physical Review B

Mechanism of hole propagation in the orbital compass models

Wojciech Brzezicki, Maria Daghofer, Andrzej M. Oleś

Published Jan 27, 2014• 10 citations

Abstract

We explore the propagation of a single hole in the quantum compass model, whose nematic ground state is given by mutually decoupled antiferromagnetic chains. The compass model can be seen as the strong-coupling limit of a spinless two-band Hubbard model, which we study here using mean-field theory and the variational cluster approach. Due to the symmetries of the compass model, the inherent disorder along one lattice direction turns out not to affect hole motion, and doping a hole consequently does not lift the subextensive degeneracy of the nematic phase. To broaden and deepen understanding, we derive a generalized itinerant model and address the transition to two-dimensional Ising order. We observe coherent hole motion in both the nematic and the antiferromagnetic phases, also in the presence of quantum fluctuations away from pure Ising exchange. In addition to quantum fluctuations and interorbital hopping, three-site hopping is found to play an important role and to dominate propagation in the two-dimensional Ising limit as well as along the antiferromagnetic chains in the nematic order which forms in the compass model.

DOI: 10.1103/physrevb.89.024417

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arXiv:1311.4796 · Physical Review B

Mechanism of hole propagation in the orbital compass models

Wojciech Brzezicki, Maria Daghofer, Andrzej M. Oleś

Published Jan 27, 2014• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.89.024417

Related papers

Hole Propagation in the Orbital Compass Models

Wojciech Brzezicki, Maria Daghofer, Andrzej M. Oleś

arXiv:1405.5322Acta Physica Polonica AFeb 1, 20154 citations

Stripping the planar quantum compass model to its basics

Soumya Sur, M. S. Laad, Syed R. Hassan

We introduce a novel mean-field theory (MFT) around the exactly soluble two-leg ladder limit for the planar quantum compass model (QCM). In contrast to usual MFT, our construction respects the stringent constraints imposed by emergent, lower (here $d=1$ ) dimensional symmetries of the QCM. Specializing our construction to the QCM on a periodic four-leg ladder, we find that a first-order transition separates two mutually dual Ising nematic phases, in good accord with state-of-the-art numerics for the planar QCM. One pseudo-spin-flip excitation in the ordered phase turns out to be two (Jordan-Wigner) fermion bound states, reminiscent of spin waves in spin- $1/2$ Heisenberg chains. We discuss the novel implications of our work on (1) the emergence of coupled orbital and magnetic ordered and liquidlike disordered phases and (2) a rare instance of orbital-spin separation in $d>1$ , in the context of a Kugel-Khomskii view of multiorbital Mott insulators.We introduce a novel mean-field theory (MFT) around the exactly soluble two-leg ladder limit for the planar quantum compass model (QCM). In contrast to usual MFT, our construction respects the stringent constraints imposed by emergent, lower (here $d=1$) dimensional symmetries of the QCM. Specializing our construction to the QCM on a periodic four-leg ladder, we find that a first-order transition separates two mutually dual Ising nematic phases, in good accord with state-of-the-art numerics for the planar QCM. One pseudo-spin-flip excitation in the ordered phase turns out to be two (Jordan-Wigner) fermion bound states, reminiscent of spin waves in spin-$1/2$ Heisenberg chains. We discuss the novel implications of our work on (1) the emergence of coupled orbital and magnetic ordered and liquidlike disordered phases and (2) a rare instance of orbital-spin separation in $d>1$, in the context of a Kugel-Khomskii view of multiorbital Mott insulators.

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Exact ground states and phase diagram of the quantum compass model under an in-plane field

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We investigate the effect of hole doping on the strong-coupling Hubbard model at half filling in spatial dimensions D\ensuremath{\ge}1. We start with an antiferromagnetic mean-field description of the insulating state, and show that doping creates solitons in the antiferromagnetic background. In one dimension, the soliton is topological, spinless, and decoupled from the background antiferromagnetic fluctuations at low energies. In two dimensions and above, the soliton is nontopological, has spin quantum number 1/2, and is strongly coupled to the antiferromagnetic fluctuations. We derive the effective action governing the quasiparticle motion, study the properties of a single carrier, and comment on a possible description at finite concentration. \textcopyright{} 1996 The American Physical Society.We investigate the effect of hole doping on the strong-coupling Hubbard model at half filling in spatial dimensions D\ensuremath{\ge}1. We start with an antiferromagnetic mean-field description of the insulating state, and show that doping creates solitons in the antiferromagnetic background. In one dimension, the soliton is topological, spinless, and decoupled from the background antiferromagnetic fluctuations at low energies. In two dimensions and above, the soliton is nontopological, has spin quantum number 1/2, and is strongly coupled to the antiferromagnetic fluctuations. We derive the effective action governing the quasiparticle motion, study the properties of a single carrier, and comment on a possible description at finite concentration. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9512090Physical review. B, Condensed matterSep 15, 19960 citations

d=1

) dimensional symmetries of the QCM. Specializing our construction to the QCM on a periodic four-leg ladder, we find that a first-order transition separates two mutually dual Ising nematic phases, in good accord with state-of-the-art numerics for the planar QCM. One pseudo-spin-flip excitation in the ordered phase turns out to be two (Jordan-Wigner) fermion bound states, reminiscent of spin waves in spin-

1/2

Heisenberg chains. We discuss the novel implications of our work on (1) the emergence of coupled orbital and magnetic ordered and liquidlike disordered phases and (2) a rare instance of orbital-spin separation in

d>1

, in the context of a Kugel-Khomskii view of multiorbital Mott insulators.

We consider the square lattice

S=1/2

quantum compass model (QCM) parametrized by

{J}_{x},{J}_{z}

, under a field,

\mathbf{h}

, in the $x\text{\ensuremath{-}}z$ plane. At the special field value

({h}_{x}^{★},{h}_{z}^{★})=2S({J}_{x},{J}_{z})

, we show that the QCM Hamiltonian may be written in a form such that two simple product states can be identified as exact ground states, below a gap. Exact excited states can also be found. We use the staggered vector chirality to characterize the exact ground states at

({h}_{x}^{★},{h}_{z}^{★})

and states obtained for fields within the vicinity of

({h}_{x}^{★},{h}_{z}^{★})

. This gapped phase occupies most of the in-plane field phase diagram. For some values of

{h}_{x}>{h}_{z}

and

{h}_{z}>{h}_{x}

at the edges of the phase diagram, we have found transitions between this gapped phase and phases of weakly coupled Ising-chain states. In zero field, the QCM is known to have an emergent subextensive ground-state degeneracy. As the field is increased from zero, we find that this degeneracy is partially lifted, resulting in bond-oriented spin-stripe states, which are each separated from one another and the gapped phase by first-order transitions. Our findings are important for understanding the field dependent phase diagram of materials with predominantly directionally dependent Ising interactions.