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arXiv:2604.17812

Pairing properties of correlated three-leg ladders with strong interchain couplings near 1/3 filling

Yushi Yamada, Tatsuya Kaneko, Masataka Kakoi, Ryota Ueda, Kazuhiko Kuroki

Published Apr 20, 2026• 0 citations
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Abstract

We investigate the ground-state properties of correlated three-leg ladders near 1/3 filling. We apply the density-matrix renormalization group method to the three-leg t-J ladder with strong interchain couplings and evaluate its pairing nature. When holes are doped into the spin-gapped state at 1/3 filling, we find that pair correlations develop with power-law decays while spin correlations decay exponentially. On the other hand, doping of electrons into the 1/3-filled state does not give rise to substantial pair correlations. We also discuss the hole-doped state in the three-leg Hubbard model to compare it with the pairing state in the t-J model. Our numerical demonstrations provide insights into the electronic properties of trilayer nickelate superconductors.

DOI
10.48550/arxiv.2604.17812

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We investigate the ground-state properties of correlated three-leg ladders near 1/3 filling. We apply the density-matrix renormalization group method to the three-leg t-J ladder with strong interchain couplings and evaluate its pairing nature. When holes are doped into the spin-gapped state at 1/3 filling, we find that pair correlations develop with power-law decays while spin correlations decay exponentially. On the other hand, doping of electrons into the 1/3-filled state does not give rise to substantial pair correlations. We also discuss the hole-doped state in the three-leg Hubbard model to compare it with the pairing state in the t-J model. Our numerical demonstrations provide insights into the electronic properties of trilayer nickelate superconductors.
Results for a doped three-leg ttt-JJJ ladder obtained using the density-matrix renormalization group are reported. At low hole doping, the holes form a dilute gas with a uniform density. The momentum occupation of the odd band shows a sharp decrease at a large value of kF{k}_{F}kF​ similar to the behavior of a lightly doped ttt-JJJ chain, while the even modes appear gapped. The spin-spin correlations decay as a power law consistent with the absence of a spin gap, but the pair-field correlations are negligible. At larger doping we find evidence for a spin gap and as xxx increases further we find three-hole diagonal domain walls. In this regime there are significant pair-field correlations and the internal pair orbital has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-like symmetry.
Motivated by high-temperature superconductivity in pressurized La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​, we investigate the pair correlations in the two-orbital Hubbard ladder, which consists of the nearly half-filled and nearly quarter-filled orbitals. By employing the density matrix renormalization group method, we demonstrate that the pair correlation exhibits a power-law decay against the distance while the spin correlation decays exponentially. The decay exponent of the pair correlation of the nearly half-filled orbital is comparable to the exponent of the quasi-long-range superconducting correlation in the doped single-orbital Hubbard ladder, which suggests the importance of the ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital in La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​.
Here we report results of a density-matrix-renormalization-group calculation of the charge, spin, and pairing properties of a two-leg CuO Hubbard ladder. The outer oxygen atoms as well as the rung and leg oxygen atoms are included along with near-neighbor and oxygen-hopping matrix elements. This model allows us to study the effects of hole and electron doping on a system that is a charge-transfer insulator at a filling of one hole per Cu and exhibits power law, d-wave-like pairing correlations when doped. In particular, we focus on the differences between doping with holes and with electrons.
We study current-current correlations in the three-band Hubbard model for two-leg CuO ladders using the density-matrix renormalization group method. We find that these correlations decrease exponentially with distance for low doping but as a power law for higher doping. Their pattern is compatible with the circulating current (CC) phase which Varma has proposed to explain the pseudogaped metallic phase in underdoped high-temperature superconductors. However, for model parameters leading to a realistic ground state in the undoped ladder, the current fluctuations decay faster than the ddd-wavelike pairing correlations in the hole-doped state, at least up to a doping of 10%. Thus we conclude that no phase with CC order or dominant CC fluctuations occur in the three-band model of two-leg CuO ladders at low doping.
We use the density-matrix renormalization group to study the single-particle and two-particle correlation functions of spinless fermions in the ground state of a quarter filled ladder. This ladder consists of two chains having an in-chain extended Coulomb interaction reaching to third neighbor and coupled by interchain hopping. Within our short numerical coherence lengths, typically reaching 10 to 20 sites, we find a strong renormalization of the interchain hopping and the existence of a dimensional crossover at smaller interactions. We also find power exponents for single-particle hopping and interchain polarization consistent with the single chain. The total occupation correlation function has a larger power exponent and shows signs of a crossover from incoherent fermion hopping to coherent particle-hole pair motion between chains. We believe the ladder is gapless.
Using density-matrix renormalization-group techniques, we have studied the ground states of the four-leg t-J ladder doped near half-filling. Depending upon J/t and the hole doping x, three characteristic types of ground states are found: (1) a state containing ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ pairs, (2) a striped charge-density wave (CDW) domain-wall state, and (3) a phase-separated regime. The CDW domain walls consist of fluctuating hole pairs and this state has significant ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ pair field correlations.