Charge fluctuations and topological phases in Kitaev-Heisenberg ladders

TL;DR

This work examines how charge fluctuations and itinerant electrons influence topological phases in doped Kitaev-Heisenberg ladders described by a Hubbard generalization of the Kitaev-Heisenberg model. Using density matrix renormalization group calculations, the authors track a nonlocal string order parameter, spin correlations, and charge fluctuations across the phase diagram parameterized by $\theta$ and hopping $t$, with $J = A\cos\theta$ and $K = A\sin\theta$. They find that increasing bandwidth progressively suppresses string order and narrows the topological regions, with the antiferromagnetic Kitaev (AFK) phase being more fragile to charge dynamics than the ferromagnetic Kitaev (FK) phase; other phases such as stripy (ST) and rung-singlet (RS) also lose stability. The study highlights how local charge fluctuations and kinetic processes erode topological order, offering guidance for realizing Kitaev-like physics in real materials and engineered quantum devices where doping and hopping can be tuned. The results provide experimentally relevant signatures, such as diminished string order, enhanced charge fluctuations near phase boundaries, and directional charge mobility patterns, that inform the robustness of Kitaev-based topological phases under doping.

Abstract

We investigate the stability of topological phases in doped Kitaev-Heisenberg ladders by studying the competition with itinerant electrons and the associated charge fluctuations in a Hubbard model on a honeycomb ribbon geometry. We analyze the evolution of string order parameters, spin correlations, and charge fluctuations as functions of hopping amplitude and interaction strength in a half-filled band. Our results from density matrix renormalization group (DMRG) calculations show that increasing electron bandwidth progressively suppresses the topological phases, shifting and narrowing their stability regions in the phase diagram. We identify the critical values of hopping where string order vanishes and characterize the interplay between magnetic order and charge fluctuations. These findings provide insight into the robustness of topological phases against doping and charge dynamics, with implications for candidate Kitaev materials and engineered quantum systems.

Figures (7)

• Figure 1: (a) Schematic representation of the honeycomb ribbon with four rings, showing the bonds associated with the anisotropic Kitaev model with color-coded bonds. Dashed red lines indicate bonds across the two legs of the ladder. (b) Sketch of the phase diagram of the system governed by the extended Heisenberg-Kitaev model, t-HKM, for $t=0$ (top) and $t=0.3$ (bottom). The $\theta$ axis shows shifts in the phases as $t$ increases. The value of $\theta$ determines the exchange constants $J=A \cos \theta$ and $K=A \sin \theta$, where A is the total exchange coupling (see main text). The color bar regimes indicate different known phases. FM: ferromagnetic; FK: ferromagnetic Kitaev; ST: stripy or FM-rung Ising; RS: rung singlet; AFK: antiferromagnetic Kitaev; ZZ: FM-leg Ising, where rungs are vertical $z$-bonds and legs are $x,y$ bonds in (a).
• Figure 2: String order parameter ${\cal O}_0^z$ as function of $\theta$ near the FK phase for various values of $t$. Note the maximum value of ${\cal O}_0^z$ is attained at $\theta=3\pi/2$ for $t=0$ (black circles), as expected $(K=-1, J=0)$. Finite $t$ suppresses the maximum and shifts the region of nonzero SOP towards lower values of $\theta$. The SOP eventually vanishes for $t\ge0.4$.
• Figure 3: String order parameter ${\cal O}_0^z$ as function of $\theta$ near the AFK phase for various values of $t$. The maximum value of ${\cal O}_0^z=1$ at $\theta=\pi/2$ for $t=0$ (black circles), identifies the optimal AFK phase. Finite $t$ suppresses and shifts of SOP towards larger values of $\theta$, and eventually vanishes for $t \gtrsim 0.3$. Inset: Maximum value of $\mathcal{O}^z$ as a function of $t$ for the FK (open hexagons) and AFK (filled hexagon) phases. Maximum values of the SOP extracted from Fig. \ref{['fig2']} and Fig. \ref{['fig3']}. Notice that in both cases the $\theta$ for maxima depends on $t$.
• Figure 4: Local magnetic moments, $\mu^2$, (open symbols) and charge fluctuations, $\delta^2$, (filled symbols) as a function of $\theta$ for various values of the hopping $t$. For t = 0 there are no charge fluctuations while the magnetic moment is close to $3/4$, as expected for a full spin $1/2$ per site. As t increases, two charge fluctuations peaks emerge near the AFK and FK phases. These peaks are accompanied by dips in the magnetic moment in the same positions
• Figure 5: Stripy rotated order parameter, $\langle \tilde{S}_{\text{tot}}^2 \rangle$, as a function of $\theta$. Filled blue circles correspond to $t=0$, indicating the presence of the stripy phase in the range $\theta/\pi \in [1.56, 1.71]$. Open circles correspond to $t=0.3$, indicating that the ST phase has shifted to the range $\theta/\pi \in [1.43, 1.54]$. The inset shows a schematic representation of the spin arrangements in the ladder in the stripy phase.