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arXiv:cond-mat/0005403 · Physical review. B, Condensed matter

Evolution of the spin gap upon doping a 2-leg ladder

Didier Poilblanc, O. Chiappa, José A. Riera, Steven R. White, Douglas J. Scalapino

Published Dec 1, 2000• 31 citations
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Abstract

The evolution of the spin gap of a 2-leg ladder upon doping depends upon the nature of the lowest triplet excitations in a ladder with two holes. Here we study this evolution using various numerical techniques for a $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}J$ ladder as the next-near-neighbor hopping ${t}^{\ensuremath{'}}$ is varied. We find that depending on the value of ${t}^{\ensuremath{'}},$ the spin gap can evolve continuously or discontinuously and the lowest triplet state can correspond to a magnon, a bound magnon-hole-pair, or two separate quasiparticles. Previous experimental results on the superconducting two-leg ladder ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ are discussed.

DOI
10.1103/physrevb.62.r14633

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The evolution of the spin gap of a 2-leg ladder upon doping depends upon the nature of the lowest triplet excitations in a ladder with two holes. Here we study this evolution using various numerical techniques for a t\ensuremath−t\ensuremath′\ensuremath−Jt\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}Jt\ensuremath−t\ensuremath′\ensuremath−J ladder as the next-near-neighbor hopping t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ is varied. We find that depending on the value of t\ensuremath′,{t}^{\ensuremath{'}},t\ensuremath′, the spin gap can evolve continuously or discontinuously and the lowest triplet state can correspond to a magnon, a bound magnon-hole-pair, or two separate quasiparticles. Previous experimental results on the superconducting two-leg ladder Sr14\ensuremath−xCaxCu24O41{\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14\ensuremath−x​Cax​Cu24​O41​ are discussed.
The spin dynamics of a doped two-leg spin ladder is investigated by numerical techniques. We show that a hole pair-magnon boundstate evolves at finite hole doping into a sharp magnetic excitation below the two-particle continuum. This is supported by a field theory argument based on a SO(6)\mathrm{SO}(6)SO(6)-symmetric ladder. Similarities and differences with the resonant mode of the high-TC{T}_{C}TC​ cuprates are discussed.
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.
The effect of a ring exchange on doped two-leg ladders is investigated combining exact diagonalization (ED) and density matrix renormalization group (DMRG) computations. We focus on the nature and weights of the low-energy magnetic excitations and on superconducting pairing. The stability with respect to this cyclic term of a remarkable resonant mode originating from a hole pair-magnon bound state is examined. We also find that, near the zero-doping critical point separating rung-singlet and dimerized phases, doping reopens a spin gap.
We present an analytic theory for the energy spectrum of a two-leg spin ladder doped with two holes. Starting from a pseudo-fermion-bond-boson representation of the corresponding t1,2−J1,2t_{1,2}-J_{1,2}t1,2​−J1,2​ Hamiltonian we apply a diagrammatic approach adapted to the limit of strong rung coupling, which includes both, the coupling of holes to the spin background as well as the two-hole interactions. The two-hole spectrum is calculated and the formation of bound states is discussed. Additionally the evolution of the spin gap of the ladder upon doping is analyzed. A comparison with existing exact diagonalization data is presented and good agreement is found.
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.
The gap function $\ensuremath{\phi}(k,\ensuremath{\omega})$, determined from a Lanczos calculation for a doped 2-leg $t\text{\ensuremath{-}}J$ ladder, is used to provide insight into the spatial and temporal structure of the pairing interaction. It implies that this interaction is a local near-neighbor coupling which is retarded. The onset frequency of the interaction is set by the energy of an S=1S=1S=1 magnon-hole pair and it is spread out over a frequency region of the order of the bandwidth.