arXiv:cond-mat/9711085

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

Jun‐ichiro Kishine, Kenji Yonemitsu

Published Nov 11, 1997• 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.

DOI: 10.48550/arxiv.cond-mat/9711085

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arXiv:cond-mat/9711085

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

Jun‐ichiro Kishine, Kenji Yonemitsu

Published Nov 11, 1997• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9711085

Related papers

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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 $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.