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arXiv:cond-mat/9401013 · Physical Review Letters

Correlations in a Two-Chain Hubbard Model

R. M. Noack, Steven R. White, Douglas J. Scalapino

Published Aug 8, 1994• 257 citations
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Abstract

Equal-time spin-spin and pair-field correlation functions are calculated for a two-chain Hubbard model using a density-matrix numerical renormalization group approach. At half filling, the antiferromagnetic and pair-field correlations both decay exponentially with the pair field having a much shorter correlation length. This is consistent with a gapped spin-liquid ground state. Below half filling, the antiferromagnetic correlations become incommensurate and the spin gap persists. The pair-field correlations appear to follow a power law decay which is similar to their noninteracting $U=0$ behavior.

DOI
10.1103/physrevlett.73.882

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Equal-time spin-spin and pair-field correlation functions are calculated for a two-chain Hubbard model using a density-matrix numerical renormalization group approach. At half filling, the antiferromagnetic and pair-field correlations both decay exponentially with the pair field having a much shorter correlation length. This is consistent with a gapped spin-liquid ground state. Below half filling, the antiferromagnetic correlations become incommensurate and the spin gap persists. The pair-field correlations appear to follow a power law decay which is similar to their noninteracting U=0U=0U=0 behavior.
The properties of the two-chain Hubbard model doped away from half-filling are investigated with the density matrix renormalization group. The charge gap is found to vanish, but a finite spin gap phase exists over a range of interchain hopping strength t ⊥ . In this phase, there are modified d x 2 - y 2 pairing correlations which exhibit a power law decay while both the 2 k F spin and charge correlations are short range. Above a critical value of t ⊥ , the system behaves as a Luttinger liquid.
We investigate the ground-state properties of a correlated model for the double-chain structure in cuprates. We consider the ttt-JJJ model, in which the nearest-neighbor spin interaction J1J_1J1​ is smaller than the next-nearest-neighbor interaction J2J_2J2​ corresponding to the CuO double-chain structure. We vary J1J_1J1​ from antiferromagnetic to ferromagnetic values and calculate the correlation functions including the superconducting pair correlation function. Employing the density-matrix renormalization group method, we show that the ground state for antiferromagnetic J1J_1J1​ exhibits the hallmarks of the Luther-Emery liquid phase, in which the spin-singlet pair and charge-density-wave correlations exhibit power-law decays against distance, and the spin correlation function decays exponentially. Its signatures are gradually dismissed as J1J_1J1​ approaches the ferromagnetic regime. Our findings suggest that the antiferromagnetic double-chain structure without ferromagnetic bonds is favorable for superconductivity.
In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we reexamine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling JJJ, the Hubbard interaction UUU, and the distance RRR between the impurities. The exponents for finite systems obtained in this work deviate from previously published DMRG calculations. We furthermore show that the long-distance behavior of the exponents is the same for impurities coupled to the bulk or to both ends of the chain. We note that a universal exponent for the asymptotic behavior can not be extracted from these finite-size systems with open boundary conditions.
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Abstract We study the ground state properties of the Hubbard model on three-leg triangular cylinders using large-scale density-matrix renormalization group simulations. At half-filling, we identify an intermediate gapless spin liquid phase, which has one gapless spin mode and algebraic spin–spin correlations but exponential decay scalar chiral–chiral correlations, between a metallic phase at weak coupling and Mott insulating dimer phase at strong interaction. Upon light doping the gapless spin liquid, the system exhibits power-law charge-density-wave (CDW) correlations but short-range single-particle, spin–spin, and chiral–chiral correlations. Similar to CDW correlations, the superconducting correlations also decay in power-law but oscillate in sign as a function of distance, which is consistent with the striped pair-density wave. When further doping the gapless spin liquid phase or doping the dimer order phase, another phase takes over, which has similar CDW correlations but all other correlations decay exponentially.