One-particle versus two-particle crossover in weakly coupled Hubbard chains and ladders: perturbative renormalization group approach

Jun‐ichiro Kishine, Kenji Yonemitsu

Published Jan 1, 1998• 0 citations

Abstract

Physical nature of dimensional crossovers in weakly coupled Hubbard chains and ladders has been discussed within the framework of the perturbative renormalization-group approach. The difference between these two cases originates from different universality classes which the corresponding isolated systems belong to.

Related papers

One-Particle vs. Two-Particle Crossover in Weakly Coupled Hubbard Chains and Ladders: Perturbative Renormalization Group Approach

Jun‐ichiro Kishine, Kenji Yonemitsu

arXiv:cond-mat/9711085Nov 11, 19970 citations

Spin Gap and Superconductivity in Weakly Coupled Ladders: Interladder One-Particle vs. Two-Particle Crossover

Jun‐ichiro Kishine, Kenji Yonemitsu

arXiv:cond-mat/9709216Journal of the Physical Society of JapanDec 15, 199712 citations

Dimensional Crossovers in the Doped Ladder System: Spin Gap, Superconductivity and Interladder Coherent Band Motion

Jun‐ichiro Kishine, Kenji Yonemitsu

arXiv:cond-mat/9802185Journal of the Physical Society of JapanMay 15, 199818 citations

N -chain Hubbard model in weak coupling

Hsiu‐Hau Lin, Leon Balents, Matthew P. A. Fisher

arXiv:cond-mat/9703055Physical review. B, Condensed matterSep 15, 1997160 citations

Ground-state properties of the two-chain Hubbard ladder

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

New materials containing weakly coupled arrays of two-chain metal oxide ladders have recently been synthesized. The two-chain Hubbard ladder provides a possible theoretical model for these systems. Here we review results obtained from numerical renormalization group calculations for the two-chain Hubbard ladder and discuss some features of its ground-state phase diagram.

Philosophical Magazine BNov 1, 199611 citations

Renormalization group method for weakly coupled quantum chains: comparison with exact diagonalization

Jose Vicente Alvarez, S. Moukouri

arXiv:cond-mat/0402530Feb 20, 20040 citations

One-particle versus two-particle crossover in weakly coupled Hubbard chains and ladders: perturbative renormalization group approach

Jun‐ichiro Kishine, Kenji Yonemitsu

Published Jan 1, 1998• 0 citations

OpenAlex

Abstract

Related papers

One-Particle vs. Two-Particle Crossover in Weakly Coupled Hubbard Chains and Ladders: Perturbative Renormalization Group Approach

Jun‐ichiro Kishine, Kenji Yonemitsu

arXiv:cond-mat/9711085Nov 11, 19970 citations

Spin Gap and Superconductivity in Weakly Coupled Ladders: Interladder One-Particle vs. Two-Particle Crossover

Jun‐ichiro Kishine, Kenji Yonemitsu

Effects of the interladder one-particle hopping, $t_{\perp}$ , on the low-energy asymptotics of a weakly coupled Hubbard ladder system have been studied, based on the perturbative renormalization-group approach. We found that for finite intraladder Hubbard repulsion, $U$ , there exists a crossover value of the interladder one-particle hopping, $t_{\perp c}$ . For $0Effects of the interladder one-particle hopping, $t_{\perp}$, on the low-energy asymptotics of a weakly coupled Hubbard ladder system have been studied, based on the perturbative renormalization-group approach. We found that for finite intraladder Hubbard repulsion, $U$, there exists a crossover value of the interladder one-particle hopping, $t_{\perp c}$. For $0

arXiv:cond-mat/9709216Journal of the Physical Society of JapanDec 15, 199712 citations

Dimensional Crossovers in the Doped Ladder System: Spin Gap, Superconductivity and Interladder Coherent Band Motion

Jun‐ichiro Kishine, Kenji Yonemitsu

Based on the perturbative renormalization group (PRG) approach, we have studied dimensional crossovers in Hubbard ladders coupled via weak interladder one-particle hopping, $t_{\perp}$ . We found that the one-particle crossover is strongly suppressed through growth of the intraladder scattering processes which lead the isolated Hubbard ladder system toward the spin gap metal (SGM) phase. Consequently when $t_{\perp}$ sets in, there exists, for any finite intraladder Hubbard repulsion, $U>0$ , the region where the two-particle crossover dominates the one-particle crossover and consequently the d-wave superconducting transition, which is regarded as a bipolaron condensation, occurs. By solving the scaling equations for the interladder one-particle and two-particle hopping amplitudes, we give phase diagrams of the system with respect to $U$ , $t_{\perp0}$ (initial value of $t_{\perp}$ ) and the temperature, $T$ . We compared the above dimensional crossovers with those in a weakly coupled chain system, clarifying the difference between them.Based on the perturbative renormalization group (PRG) approach, we have studied dimensional crossovers in Hubbard ladders coupled via weak interladder one-particle hopping, $t_{\perp}$. We found that the one-particle crossover is strongly suppressed through growth of the intraladder scattering processes which lead the isolated Hubbard ladder system toward the spin gap metal (SGM) phase. Consequently when $t_{\perp}$ sets in, there exists, for any finite intraladder Hubbard repulsion, $U>0$, the region where the two-particle crossover dominates the one-particle crossover and consequently the d-wave superconducting transition, which is regarded as a bipolaron condensation, occurs. By solving the scaling equations for the interladder one-particle and two-particle hopping amplitudes, we give phase diagrams of the system with respect to $U$, $t_{\perp0}$ (initial value of $t_{\perp}$) and the temperature, $T$. We compared the above dimensional crossovers with those in a weakly coupled chain system, clarifying the difference between them.

arXiv:cond-mat/9802185Journal of the Physical Society of JapanMay 15, 199818 citations

N -chain Hubbard model in weak coupling

Hsiu‐Hau Lin, Leon Balents, Matthew P. A. Fisher

We present a systematic weak-coupling renormalization group (RG) technique for studying a collection of $N$ coupled one-dimensional interacting electron systems, focusing on the example of $N$ -leg Hubbard ladders. For $N=2,3,$ we recover previous results, and find that also more generally broad regions of the phase space of these models are unstable to pairing, usually with approximate $d$ -wave symmetry. We show how these instabilities can be understood in terms of a fairly conventional ``gap'' function \ensuremath{\Delta} at the discretized Fermi surface, and describe how this function is calculated. The dimensional crossovers as $N\ensuremath{\rightarrow}\ensuremath{\infty}$ and as many such ladders are weakly coupled together are also discussed.We present a systematic weak-coupling renormalization group (RG) technique for studying a collection of $N$ coupled one-dimensional interacting electron systems, focusing on the example of $N$-leg Hubbard ladders. For $N=2,3,$ we recover previous results, and find that also more generally broad regions of the phase space of these models are unstable to pairing, usually with approximate $d$-wave symmetry. We show how these instabilities can be understood in terms of a fairly conventional ``gap'' function \ensuremath{\Delta} at the discretized Fermi surface, and describe how this function is calculated. The dimensional crossovers as $N\ensuremath{\rightarrow}\ensuremath{\infty}$ and as many such ladders are weakly coupled together are also discussed.

arXiv:cond-mat/9703055Physical review. B, Condensed matterSep 15, 1997160 citations

Ground-state properties of the two-chain Hubbard ladder

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

Philosophical Magazine BNov 1, 199611 citations

Renormalization group method for weakly coupled quantum chains: comparison with exact diagonalization

Jose Vicente Alvarez, S. Moukouri

We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg spin ladders with a transverse Hamiltonian that can involve frustration. Due to the variational nature of the algorithm, the accuracy can be arbitrarily improved enlarging the basis of eigenstates of the density matrix defined in the transverse direction. We observe that the precision of the algorithm is directly correlated to the binding of the chains. We also show that the method performs especially well in frustrated systems.We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg spin ladders with a transverse Hamiltonian that can involve frustration. Due to the variational nature of the algorithm, the accuracy can be arbitrarily improved enlarging the basis of eigenstates of the density matrix defined in the transverse direction. We observe that the precision of the algorithm is directly correlated to the binding of the chains. We also show that the method performs especially well in frustrated systems.

arXiv:cond-mat/0402530Feb 20, 20040 citations

Effects of the interladder one-particle hopping,

t_{\perp}

, on the low-energy asymptotics of a weakly coupled Hubbard ladder system have been studied, based on the perturbative renormalization-group approach. We found that for finite intraladder Hubbard repulsion,

U

, there exists a crossover value of the interladder one-particle hopping,

t_{\perp c}

. For $0

Based on the perturbative renormalization group (PRG) approach, we have studied dimensional crossovers in Hubbard ladders coupled via weak interladder one-particle hopping,

t_{\perp}

. We found that the one-particle crossover is strongly suppressed through growth of the intraladder scattering processes which lead the isolated Hubbard ladder system toward the spin gap metal (SGM) phase. Consequently when

t_{\perp}

sets in, there exists, for any finite intraladder Hubbard repulsion,

U>0

, the region where the two-particle crossover dominates the one-particle crossover and consequently the d-wave superconducting transition, which is regarded as a bipolaron condensation, occurs. By solving the scaling equations for the interladder one-particle and two-particle hopping amplitudes, we give phase diagrams of the system with respect to

U

t_{\perp0}

(initial value of

t_{\perp}

) and the temperature,

T

. We compared the above dimensional crossovers with those in a weakly coupled chain system, clarifying the difference between them.

We present a systematic weak-coupling renormalization group (RG) technique for studying a collection of

N

coupled one-dimensional interacting electron systems, focusing on the example of

N

-leg Hubbard ladders. For

N=2,3,

we recover previous results, and find that also more generally broad regions of the phase space of these models are unstable to pairing, usually with approximate

d

-wave symmetry. We show how these instabilities can be understood in terms of a fairly conventional ``gap'' function \ensuremath{\Delta} at the discretized Fermi surface, and describe how this function is calculated. The dimensional crossovers as $N\ensuremath{\rightarrow}\ensuremath{\infty}$ and as many such ladders are weakly coupled together are also discussed.