Motivated by the presence of different orders in multilayered high-temperature superconductors, we examine a model consisting of nonequivalent two Hubbard chains coupled by interchain hopping by using the density-matrix renormalization group (DMRG) and a mean-field theory. As an example, we consider a system with noninteracting chain without order and a Hubbard chain with strong antiferromagnetic (AF) spin-density-wave correlation. We find that the magnitude of the interchain hopping controls the strength of induced AF correlation as well as that of original one. It is also found that the induced AF correlation decreases with increasing the magnitude of the original correlation. Implications to the multilayered system are discussed. Recently the coexistence of antiferromagnetism and superconductivity has been reported in multilayered high-Tc cuprate superconductors from nuclear magnetic resonance experiments. 1),2) In the superconductors, there are different layers whose carrier concentrations are unequal. When the concentration is small (large), antiferromagneticMotivated by the presence of different orders in multilayered high-temperature superconductors, we examine a model consisting of nonequivalent two Hubbard chains coupled by interchain hopping by using the density-matrix renormalization group (DMRG) and a mean-field theory. As an example, we consider a system with noninteracting chain without order and a Hubbard chain with strong antiferromagnetic (AF) spin-density-wave correlation. We find that the magnitude of the interchain hopping controls the strength of induced AF correlation as well as that of original one. It is also found that the induced AF correlation decreases with increasing the magnitude of the original correlation. Implications to the multilayered system are discussed. Recently the coexistence of antiferromagnetism and superconductivity has been reported in multilayered high-Tc cuprate superconductors from nuclear magnetic resonance experiments. 1),2) In the superconductors, there are different layers whose carrier concentrations are unequal. When the concentration is small (large), antiferromagnetic

Nov 20, 20122 citations

Antiferromagnetically coupled alternating spin chains

A. E. Trumper, C. J. Gazza

The effect of antiferromagnetic interchain coupling in alternating spin-(1,1/2) chains is studied by means of spin-wave theory and density-matrix renormalization group (DMRG). In particular, two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. Results of the ground-state properties like energy, spin gap, magnetizations, and correlation functions are reported for the whole range of the interchain coupling ${J}_{\ensuremath{\perp}}.$ For the 2D case the spin-wave results predict a smooth dimensional crossover from 1D to 2D keeping the ground state always ordered. For the ladder system, the DMRG results show that any ${J}_{\ensuremath{\perp}}>0$ drives the system to a gapped ground state. Furthermore the behavior of the correlation functions closely resemble the uniform spin-1/2 ladder. For ${J}_{\ensuremath{\perp}}$ lower than 0.3, however, the gap behaves quadratically as $\ensuremath{\Delta}\ensuremath{\sim}{0.6J}_{\ensuremath{\perp}}^{2}.$ Finally, it is argued that the behavior of the spin gap for an arbitrary number of mixed coupled spin chains is analogous to that of the uniform spin-1/2 chains.The effect of antiferromagnetic interchain coupling in alternating spin-(1,1/2) chains is studied by means of spin-wave theory and density-matrix renormalization group (DMRG). In particular, two limiting cases are investigated, the two-leg ladder and its two-dimensional (2D) generalization. Results of the ground-state properties like energy, spin gap, magnetizations, and correlation functions are reported for the whole range of the interchain coupling ${J}_{\ensuremath{\perp}}.$ For the 2D case the spin-wave results predict a smooth dimensional crossover from 1D to 2D keeping the ground state always ordered. For the ladder system, the DMRG results show that any ${J}_{\ensuremath{\perp}}>0$ drives the system to a gapped ground state. Furthermore the behavior of the correlation functions closely resemble the uniform spin-1/2 ladder. For ${J}_{\ensuremath{\perp}}$ lower than 0.3, however, the gap behaves quadratically as $\ensuremath{\Delta}\ensuremath{\sim}{0.6J}_{\ensuremath{\perp}}^{2}.$ Finally, it is argued that the behavior of the spin gap for an arbitrary number of mixed coupled spin chains is analogous to that of the uniform spin-1/2 chains.

arXiv:cond-mat/0103424Physical review. B, Condensed matterSep 4, 200128 citations

Emergence of dxy -wave superconductivity in a doped two-leg diagonal ladder

Jie Hou, Ting-Kuo Lee, Jie Lou +1 more

We propose a doped two-leg spin- $1/2$ diagonal ladder model (or a composite spin model) to simulate a doped spin-1 chain. By using the density matrix renormalization group method for an open chain, we find that the ground state hosts a dominant singlet ${d}_{xy}$ -wave superconducting correlation with features similar to those of the spin-1 Haldane phase. Meanwhile, we apply the renormalized mean-field theory to the model and obtain a ${d}_{xy}$ -wave superconducting state. The superconducting order exhibits a domelike shape as a function of hole concentration $\ensuremath{\delta}$. Our work provides a physical understanding of the origin of ${d}_{xy}$ pairing symmetry, which originates from antiferromagnetic Heisenberg interaction in the diagonal direction, and the intrachain hopping term makes it stable.We propose a doped two-leg spin-$1/2$ diagonal ladder model (or a composite spin model) to simulate a doped spin-1 chain. By using the density matrix renormalization group method for an open chain, we find that the ground state hosts a dominant singlet ${d}_{xy}$-wave superconducting correlation with features similar to those of the spin-1 Haldane phase. Meanwhile, we apply the renormalized mean-field theory to the model and obtain a ${d}_{xy}$-wave superconducting state. The superconducting order exhibits a domelike shape as a function of hole concentration $\ensuremath{\delta}$. Our work provides a physical understanding of the origin of ${d}_{xy}$ pairing symmetry, which originates from antiferromagnetic Heisenberg interaction in the diagonal direction, and the intrachain hopping term makes it stable.

Physical review. B./Physical review. BMar 12, 20196 citations

Enhanced dx2−y2 pairing correlations in the two-leg Hubbard ladder

R. M. Noack, N. Bulut, Douglas J. Scalapino +1 more

The two-leg Hubbard ladder is characterized by the ratio of the inter- to intra-leg hopping ${t}_{\ensuremath{\perp}}/t$, the relative interaction strength $U/t,$ and the electron filling. Here, using density matrix renormalization group and Monte Carlo simulations, we examine the dependence of the pairing correlations on these parameters. We find that the pairing correlations are enhanced when the top of the bonding quasiparticle band and the bottom of the antibonding band are near the Fermi level. We present results on the single-particle spectral weight and the antiferromagnetic correlations in order to explain this behavior.The two-leg Hubbard ladder is characterized by the ratio of the inter- to intra-leg hopping ${t}_{\ensuremath{\perp}}/t$, the relative interaction strength $U/t,$ and the electron filling. Here, using density matrix renormalization group and Monte Carlo simulations, we examine the dependence of the pairing correlations on these parameters. We find that the pairing correlations are enhanced when the top of the bonding quasiparticle band and the bottom of the antibonding band are near the Fermi level. We present results on the single-particle spectral weight and the antiferromagnetic correlations in order to explain this behavior.

arXiv:cond-mat/9612165Physical review. B, Condensed matterSep 15, 199794 citations

Renormalization-group calculations with k‖ -dependent couplings in a ladder

G. Abramovici, J. C. Nickel, M. Héritier

We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling ${t}_{\ensuremath{\perp}}$. We use a renormalization-group method, in a one loop expansion, introducing an original method to include ${k}_{\ensuremath{\Vert}}$ dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include ${k}_{\ensuremath{\Vert}}$ dependence or not. When we do so, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small ${t}_{\ensuremath{\perp}}$, followed by a superconducting region with a simultaneous divergence of the spin density waves channel. We also investigate the effect of a nonlocal backward interchain scattering: we observe, on one hand, the suppression of singlet superconductivity and of spin density waves, and, on the other hand, the increase of charge density waves and, for some values of ${t}_{\ensuremath{\perp}}$, of triplet superconductivity. Our results eventually show that ${k}_{\ensuremath{\Vert}}$ is an influential variable in the renormalization-group flow, for this kind of system.We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling ${t}_{\ensuremath{\perp}}$. We use a renormalization-group method, in a one loop expansion, introducing an original method to include ${k}_{\ensuremath{\Vert}}$ dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include ${k}_{\ensuremath{\Vert}}$ dependence or not. When we do so, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small ${t}_{\ensuremath{\perp}}$, followed by a superconducting region with a simultaneous divergence of the spin density waves channel. We also investigate the effect of a nonlocal backward interchain scattering: we observe, on one hand, the suppression of singlet superconductivity and of spin density waves, and, on the other hand, the increase of charge density waves and, for some values of ${t}_{\ensuremath{\perp}}$, of triplet superconductivity. Our results eventually show that ${k}_{\ensuremath{\Vert}}$ is an influential variable in the renormalization-group flow, for this kind of system.

arXiv:cond-mat/0505385Physical Review BJul 14, 200511 citations

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

Yushi Yamada, Tatsuya Kaneko, Masataka Kakoi +2 more

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 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.

arXiv:2604.17812Apr 20, 20260 citations

We propose a doped two-leg spin-

1/2

diagonal ladder model (or a composite spin model) to simulate a doped spin-1 chain. By using the density matrix renormalization group method for an open chain, we find that the ground state hosts a dominant singlet

{d}_{xy}

-wave superconducting correlation with features similar to those of the spin-1 Haldane phase. Meanwhile, we apply the renormalized mean-field theory to the model and obtain a

{d}_{xy}

-wave superconducting state. The superconducting order exhibits a domelike shape as a function of hole concentration $\ensuremath{\delta}$. Our work provides a physical understanding of the origin of

{d}_{xy}

pairing symmetry, which originates from antiferromagnetic Heisenberg interaction in the diagonal direction, and the intrachain hopping term makes it stable.

The two-leg Hubbard ladder is characterized by the ratio of the inter- to intra-leg hopping ${t}_{\ensuremath{\perp}}/t$, the relative interaction strength

U/t,

and the electron filling. Here, using density matrix renormalization group and Monte Carlo simulations, we examine the dependence of the pairing correlations on these parameters. We find that the pairing correlations are enhanced when the top of the bonding quasiparticle band and the bottom of the antibonding band are near the Fermi level. We present results on the single-particle spectral weight and the antiferromagnetic correlations in order to explain this behavior.