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

## TL;DR

This study explores the ground state and low-energy excitations of the Kitaev-Heisenberg ladder, revealing a phase diagram similar to the honeycomb lattice and identifying various ordered states and spin liquids.

## Contribution

It provides a detailed phase diagram of the Kitaev-Heisenberg ladder using DMRG and Lanczos methods, highlighting the similarity to the honeycomb lattice and characterizing spin liquid regions.

## Key findings

- Identified multiple long-range ordered states including rung-singlet, zigzag, ferromagnetic, and stripy phases.
- Discovered Kitaev spin liquids around exactly solvable points at =pi.
- Mapped the extension of the Kitaev spin liquid phase away from the =\u0012pi points.

## Abstract

We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a ladder geometry using the density matrix renormalization group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=\sin\phi$ and $J=\cos\phi$ with an angle parameter $\phi$. Based on the results for several types of order parameters, excitation gaps, and entanglement spectra, the $\phi$-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 3D), zigzag, ferromagnetic, and stripy; and the presence of Kitaev spin liquids around the exactly solvable Kitaev points $\phi=\pm\pi/2$. We also calculate the expectation value of a plaquette operator corresponding to a $\pi$-flux state in order to establish how the Kitaev spin liquid extends away from the $\phi=\pm\pi/2$. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.