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arXiv:1902.00466 · Physical review. B./Physical review. B

Ground state and low-energy excitations of the Kitaev-Heisenberg two-leg ladder

Cliò Efthimia Agrapidis, Jeroen van den Brink, Satoshi Nishimoto

Published Jun 13, 2019• 43 citations
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Abstract

We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a two-leg ladder geometry using the density-matrix renormalization-group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=sin\ensuremath{\phi}$ and $J=cos\ensuremath{\phi}$ with an angle parameter $\ensuremath{\phi}$. Based on the results for several types of order parameters, excitation gaps, string order parameter, and entanglement spectra, the $\ensuremath{\phi}$-dependent ground state phase diagram is determined. Remarkably, the phase diagram is quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice, exhibiting the same long-range-ordered states, namely rung singlet (analog to N\'eel in three dimensions), zigzag, ferromagnetic, and stripy, and the presence of gapped spin liquids around the exactly solvable Kitaev points $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. We also calculate the expectation value of a plaquette operator corresponding to a $\ensuremath{\pi}$-flux state in order to establish how the gapped Kitaev spin liquid extends away from the $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.

DOI
10.1103/physrevb.99.224418

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We study the spin-12\frac{1}{2}21​ Kitaev-Heisenberg (KJ) model in a two-leg ladder. Without a Heisenberg interaction, the Kitaev phase in the ladder model has Majorana fermions with local Z2{Z}_{2}Z2​ gauge fields, and is usually described as a disordered phase without any order parameter. Here we identify a long-range nonlocal string order parameter (SOP) in the Kitaev phase which survives with a finite Heisenberg interaction. The SOP is obtained by relating the Kitaev ladder, through a nonlocal unitary transformation, to a one-dimensional XYXYXY chain with an Ising coupling to a dangling spin at every site. This differentiates the Kitaev phases from other nearby phases including a rung singlet. Two phases with nonzero SOP corresponding to ferromagnetic and antiferromagnetic Kitaev interactions are identified. The full phase diagram of the KJ ladder is determined using exact diagonalization and density matrix renormalization group methods, which shows a striking similarity to the KJ model on a two-dimensional honeycomb lattice.
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