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arXiv:2603.12198

Kinetic obstruction to pairing in the doped Kitaev-Heisenberg ladder

Bradraj Pandey, Bo Xiao, Satoshi Okamoto, Gonzalo Álvarez, Gábor B. Halász, Elbio R. Dagotto, Pontus Laurell

Published Mar 12, 2026• 0 citations
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Abstract

We investigate the hole-doped Kitaev-Heisenberg ($t$-$J$-$K$) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We first consider the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength $t$ and doping level. This reveals intriguing pairing tendencies only for $\frac{t}{K} \lesssim 0.65$, consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between the spatial profiles of the plaquette operator and the charge density. We construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping $t=1$. Upon doping, the rung-singlet region develops dominant superconducting correlations. Charge-density-wave correlations dominate at weak doping near the transition to the stripy phase. Spin-density wave-like behavior is found in the AFK and ferromagnetic Kitaev limits, and in the stripy phase.

DOI
10.48550/arxiv.2603.12198

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We investigate the hole-doped Kitaev-Heisenberg (ttt-JJJ-KKK) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We first consider the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength ttt and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K} \lesssim 0.65Kt​≲0.65, consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between the spatial profiles of the plaquette operator and the charge density. We construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t=1t=1t=1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Charge-density-wave correlations dominate at weak doping near the transition to the stripy phase. Spin-density wave-like behavior is found in the AFK and ferromagnetic Kitaev limits, and in the stripy phase.
Abstract Doped quantum magnets, especially spin liquids with fractionalized excitations, have long attracted attention as a promising path towards unconventional superconductivity. We investigate the hole-doped Kitaev-Heisenberg ( t – J – K ) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We consider the behavior of the antiferromagnetic Kitaev spin-liquid phase as a function of hopping strength t and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K}\lesssim 0.65Kt​≲0.65 t K ≲ 0.65 , consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between spatial profiles of the plaquette operator and the charge density. We also construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t = 1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Spin-density wave-like behavior is found in the Kitaev limits, and in the stripy phase.
We study the impact of hole doping on the Kitaev-Heisenberg model on the honeycomb lattice. We investigate the pairing tendencies and correlation functions in the framework of a $t\ensuremath{-}J\ensuremath{-}K$ model using density matrix renormalization group calculations on three-leg cylinders. In the case of the pure Kitaev model, which realizes a quantum spin-liquid phase at half-filling, we find that binding of two holes only occurs at low values of the hopping, where the holes are slow. We have theoretically verified that pair formation occurs in the limit of immobile holes, where the pure Kitaev model remains exactly solvable. When we instead fix the hopping at an intermediate, more realistic, value, and vary the Heisenberg and Kitaev interaction strengths, we find pairing tendencies only in the N\'eel phase. This is in contrast to prior mean-field calculations, highlighting the importance of accounting for the kinetic energy of dopants in generalized Kitaev models. Interestingly, we also find signatures of pair-density wave formation over the studied range of model parameters, namely, a periodic modulation of the charge density as well as the spin-spin and pair-pair correlations in real space. Moreover, we present a comparative study of the different correlations as a function of doping. We finally discuss the potential for experimentally observing the studied physics in quantum materials and heterostructures.
Inspired by the observation of a robust ddd-wave superconducting phase driven by tuning the next-nearest-neighbor (NNN) electron hopping in recent density matrix renormalization group (DMRG) studies of six- and eight-leg $t\text{\ensuremath{-}}J$ model, we systematically study the phase diagram of the two-leg $t\text{\ensuremath{-}}J$ ladder with the NNN couplings (including NNN hopping and spin interaction) in a large region of doping level, by means of the DMRG calculations. Upon doping from half filling, we identify the Luther-Emery liquid (LEL) phase, which can be distinguished as the pairing-dominant and charge density-dominant regime by comparing the Luttinger parameter ${K}_{\ensuremath{\rho}}$. With the growing NNN couplings, pairing correlations are enhanced and correspondingly ${K}_{\ensuremath{\rho}}$ increases, driving the system from the density-dominant to the pairing-dominant regime. In the Tomonaga-Luttinger liquid (TLL) phase in the larger doping region, we identify two TLL regimes with different features of charge density correlation. At the quarter filling (1/21/21/2 doping level), we find that the strong dimer orders of bond energy in the open system actually decay algebraically and thus do not indicate a spontaneous translational symmetry breaking. Our results show that in the LEL phase of the two-leg ladder, the NNN couplings seem to play the similar role as that on the wider $t\text{\ensuremath{-}}J$ cylinder, and studies on this more accessible system can be helpful toward understanding the emergence of the remarkable ddd-wave superconducting phase on the wider system.
We study the hole-doped Kitaev-Heisenberg chain using the density-matrix renormalization group. In the Kitaev-only limit, the bond-directional exchange itself promotes pairing, favoring spin-singlet and spin-triplet superconducting tendencies for antiferromagnetic and ferromagnetic Kitaev couplings, respectively, together with finite-size Majorana edge correlations suggestive of topological superconductivity. In the full Kitaev-Heisenberg chain, cooperative J - and K exchanges broadly stabilize superconductivity, while competition between J and K induces a strong filling dependence and enables superconductivity even when both J and K are weak. At quarter filling, this competition produces a Mott insulator with spontaneous hopping dimerization. These results identify magnetic frustration as a common mechanism underlying superconducting and interaction-driven insulating phases in doped Kitaev systems.
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.
The two-leg $t\ensuremath{-}J$ ladder forms a spin liquid at half filling that evolves to a Luther-Emery liquid upon doping. Our aim is to obtain a complete phase diagram for isotropic coupling (i.e., rungs and legs equal) as a function of electron density n and the ratio J/t.J/t.J/t. Two known limiting cases are n<12,n<\frac{1}{2},n<21​, which is a single band Luttinger liquid, and small hole doping $\ensuremath{\delta}\ensuremath{\ll}1$ for $J/\stackrel{\ensuremath{\rightarrow}}{t}0,$ which is a Nagaoka ferromagnet. Using Lanczos techniques we examine the region between the Nagaoka and Luther-Emery phases for 1>n>12.1>n>\frac{1}{2}.1>n>21​. We find evidences for gapless behavior in both spin and charge channels for J/t<0.3,J/t<0.3,J/t<0.3, consistent with Luttinger liquids in both bonding and antibonding bands (i.e., C2S2).C2S2).C2S2). This proposal is based on the behavior of spin and charge correlation functions. For example, the hole-hole correlation function that displays hole pairing at larger J/tJ/tJ/t shows hole-hole repulsion in this region. As a further test, we examined the dependence of the energy on a relative phase shift between bonding and antibonding bands. For J/t<0.3J/t<0.3J/t<0.3 this is very weak, indicating a lack of pairing between these channels.