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arXiv:cond-mat/9706250 · Physical review. B, Condensed matter

Ground-state properties of the doped three-leg t - J ladder

Steven R. White, Douglas J. Scalapino

Published Feb 1, 1998• 56 citations
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Abstract

Results for a doped three-leg $t$-$J$ 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 ${k}_{F}$ similar to the behavior of a lightly doped $t$-$J$ 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 $x$ 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.

DOI
10.1103/physrevb.57.3031

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We have numerically investigated the doped t-J ladder using exact diagonalization. We have studied both the limit of strong interchain coupling and isotropic coupling. The ladder scales to the Luther-Emery liquid regime in the strong interchain coupling limit. In this strong coupling limit there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling. At J=0 we have indications of a ferromagnetic ground state. At a large J/t the ladder is phase separated into holes and a Heisenberg ladder. At intermediate coupling the ground state shows hole pairing with a modified d-wave symmetry. The excitation spectrum separates into a limited number of quasiparticles which carry charge +\ensuremath{\Vert}e\ensuremath{\Vert} and spin 1/2 and a triplet magnon mode. At half filling the former vanish but the latter evolves continuously into the magnon band of the spin liquid. At low doping the quasiparticles form a dilute Fermi gas with a strong attraction but simultaneously the Fermi wave vector, as would be measured in photoemission, is large. The dynamical structure factors are calculated and are found to be very similar to calculations on two-dimensional clusters. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9510150•Physical review. B, Condensed matter•Jan 1, 1996•173 citations
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 dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​-like symmetry.
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.
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.
We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.
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.
In this paper, we have systematically studied the single-hole problem in two-leg Hubbard and $t\ensuremath{-}J$ ladders by large-scale density-matrix renormalization-group calculations. We found that the doped holes in both models behave similarly, while the three-site correlated hopping term is not important in determining the ground-state properties. For more insights, we have also calculated the elementary excitations, i.e., the energy gaps to the excited states of the system. In the strong-rung limit, we found that the doped hole behaves as a Bloch quasiparticle in both systems where the spin and charge of the doped hole are tightly bound together. In the isotropic limit, while the hole still behaves like a quasiparticle in the long-wavelength limit, our results show that its spin and charge components are only loosely bound together inside the quasiparticle, whose internal structure can lead to a visible residual effect which dramatically changes the local structure of the ground-state wave function.
We have numerically investigated the doped t-J ladder using exact diagonalization. We have studied both the limit of strong interchain coupling and isotropic coupling. The ladder scales to the Luther-Emery liquid regime in the strong interchain coupling limit. In this strong coupling limit there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling. At J=0 we have indications of a ferromagnetic ground state. At a large J/t the ladder is phase separated into holes and a Heisenberg ladder. At intermediate coupling the ground state shows hole pairing with a modified d-wave symmetry. The excitation spectrum separates into a limited number of quasiparticles which carry charge +\ensuremath{\Vert}e\ensuremath{\Vert} and spin 1/2 and a triplet magnon mode. At half filling the former vanish but the latter evolves continuously into the magnon band of the spin liquid. At low doping the quasiparticles form a dilute Fermi gas with a strong attraction but simultaneously the Fermi wave vector, as would be measured in photoemission, is large. The dynamical structure factors are calculated and are found to be very similar to calculations on two-dimensional clusters. \textcopyright{} 1996 The American Physical Society.