Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9802185 · Journal of the Physical Society of Japan

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

Jun‐ichiro Kishine, Kenji Yonemitsu

Published May 15, 1998• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1143/jpsj.67.1714

Related papers

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 $0

arXiv:cond-mat/9709216•Journal of the Physical Society of Japan•Dec 15, 1997•12 citations

Dimensional crossover in half-filled and lightly dopedN-leg Hubbard ladders

Urs Ledermann

We study the dimensional crossover from one to two dimensions in half-filled and lightly doped, weakly interacting N-leg Hubbard ladders. In this case, the Hubbard ladders are equivalent to an N-band model. Using renormalization-group techniques, we find that the half-filled ladders exhibit (in the spin sector) an odd-even effect only below a crossover energy ${E}_{c}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\ensuremath{\alpha}\mathrm{exp}(\ensuremath{\gamma}N)]$ $(\ensuremath{\alpha}\ensuremath{\ll}1$ and $\ensuremath{\gamma}\ensuremath{\sim}1$ depend on the interaction strength and on the hopping matrix elements): Below ${E}_{c},$ the dominant interactions take place within band pairs $(j,N+1\ensuremath{-}j)$ [and within the band $(N+1)/2$ for N odd], such that even-leg ladders are an insulating spin liquid, while odd-leg ladders have one gapless spinon mode. In contrast, above the energy scale ${E}_{c},$ all bands are interacting with each other and the system is a two-dimensional- (2D)-like (insulating) antiferromagnet; we obtain an analytical expression for the Hamiltonian which is similar to the 2D Heisenberg antiferromagnet. Bosonization techniques show that in the charge sector the Mott insulator is as well below and above ${E}_{c}$ of the same type as in $N/2$ half-filled two-leg ladders. Doping away from half-filling, we find that the effect of an increasing doping $\ensuremath{\delta}$ is very similar to decreasing the number of legs N: In both cases interactions between unpaired bands are suppressed and thereby the antiferromagnetic correlations reduced. The resulting band pairs form then insulating spin liquids and when doped, there is a spin gap, but phase coherence exists only within the band pairs. At higher doping levels ${\ensuremath{\delta}}_{c}={\ensuremath{\delta}}_{c}(N),$ phase coherence between all band pairs sets in and the system becomes a 2D-like d-wave superconductor $[{\ensuremath{\delta}}_{c}(N)\ensuremath{\rightarrow}0$ for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}].$

arXiv:cond-mat/0103159•Physical review. B, Condensed matter•Nov 8, 2001•7 citations

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

Jun‐ichiro Kishine, Kenji Yonemitsu

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.

•Jan 1, 1998•0 citations

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

Jun‐ichiro Kishine, Kenji Yonemitsu

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.

arXiv:cond-mat/9711085•Nov 11, 1997•0 citations

Phases of the two-band model of spinless fermions in one dimension

Urs Ledermann, Karyn Le Hur

We study the two-band model of spinless fermions in one dimension for weak repulsive interactions. In this case, the model is equivalent to the weakly interacting spinless two-leg ladder. We obtain nonuniversal analytic expressions for the power-law decays $\ensuremath{\propto}{x}^{\ensuremath{-}\ensuremath{\gamma}}$ of the charge-density and $\ensuremath{\propto}{x}^{\ensuremath{-}1/\ensuremath{\gamma}}$ of the superconducting pairing correlation functions. To leading order in the doping $\ensuremath{\delta}$ away from half filling and ${t}_{\ensuremath{\perp}}/t,$ we find $\ensuremath{\gamma}=1+({\ensuremath{\pi}}^{2}{/8)(t}_{\ensuremath{\perp}}{/t)}^{2}{\ensuremath{\delta}}^{2}$ $(t$ and ${t}_{\ensuremath{\perp}}$ are the hopping terms along and between the chains), such that superconducting pairing correlations dominate. We furthermore show that the transition from the superconducting phase to the usual one-dimensional (Luttinger) metal occurs via a mixed phase, where superconducting pairs are formed in the bonding band only. We give the phase diagram as a function of temperature and doping.

arXiv:cond-mat/9910187•Physical review. B, Condensed matter•Jan 15, 2000•47 citations

Weak-coupling phase diagram of the two-chain Hubbard model

Leon Balents, Matthew P. A. Fisher

We present a general method for determining the phase diagram of systems of a finite number of one-dimensional Hubbard-like systems coupled by single-particle hopping with weak interactions. The technique is illustrated by detailed calculations for the two-chain Hubbard model, providing controlled results for arbitrary doping and interchain hopping. Of nine possible states which could occur in such a spin-1/2 ladder, we find seven at weak coupling. We discuss the conditions under which the model can be regarded as a one-dimensional analog of a superconductor. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9503045•Physical review. B, Condensed matter•May 1, 1996•349 citations
Based on the perturbative renormalization group (PRG) approach, we have studied dimensional crossovers in Hubbard ladders coupled via weak interladder one-particle hopping, t⊥t_{\perp}t⊥​. 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⊥t_{\perp}t⊥​ sets in, there exists, for any finite intraladder Hubbard repulsion, U>0U>0U>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 UUU, t⊥0t_{\perp0}t⊥0​ (initial value of t⊥t_{\perp}t⊥​) and the temperature, TTT. We compared the above dimensional crossovers with those in a weakly coupled chain system, clarifying the difference between them.
Effects of the interladder one-particle hopping, t⊥t_{\perp}t⊥​, 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, UUU, there exists a crossover value of the interladder one-particle hopping, t⊥ct_{\perp c}t⊥c​. For $0
We study the dimensional crossover from one to two dimensions in half-filled and lightly doped, weakly interacting N-leg Hubbard ladders. In this case, the Hubbard ladders are equivalent to an N-band model. Using renormalization-group techniques, we find that the half-filled ladders exhibit (in the spin sector) an odd-even effect only below a crossover energy ${E}_{c}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\ensuremath{\alpha}\mathrm{exp}(\ensuremath{\gamma}N)]$ $(\ensuremath{\alpha}\ensuremath{\ll}1$ and $\ensuremath{\gamma}\ensuremath{\sim}1$ depend on the interaction strength and on the hopping matrix elements): Below Ec,{E}_{c},Ec​, the dominant interactions take place within band pairs $(j,N+1\ensuremath{-}j)$ [and within the band (N+1)/2(N+1)/2(N+1)/2 for N odd], such that even-leg ladders are an insulating spin liquid, while odd-leg ladders have one gapless spinon mode. In contrast, above the energy scale Ec,{E}_{c},Ec​, all bands are interacting with each other and the system is a two-dimensional- (2D)-like (insulating) antiferromagnet; we obtain an analytical expression for the Hamiltonian which is similar to the 2D Heisenberg antiferromagnet. Bosonization techniques show that in the charge sector the Mott insulator is as well below and above Ec{E}_{c}Ec​ of the same type as in N/2N/2N/2 half-filled two-leg ladders. Doping away from half-filling, we find that the effect of an increasing doping $\ensuremath{\delta}$ is very similar to decreasing the number of legs N: In both cases interactions between unpaired bands are suppressed and thereby the antiferromagnetic correlations reduced. The resulting band pairs form then insulating spin liquids and when doped, there is a spin gap, but phase coherence exists only within the band pairs. At higher doping levels ${\ensuremath{\delta}}_{c}={\ensuremath{\delta}}_{c}(N),$ phase coherence between all band pairs sets in and the system becomes a 2D-like d-wave superconductor $[{\ensuremath{\delta}}_{c}(N)\ensuremath{\rightarrow}0$ for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}].$
We study the two-band model of spinless fermions in one dimension for weak repulsive interactions. In this case, the model is equivalent to the weakly interacting spinless two-leg ladder. We obtain nonuniversal analytic expressions for the power-law decays $\ensuremath{\propto}{x}^{\ensuremath{-}\ensuremath{\gamma}}$ of the charge-density and $\ensuremath{\propto}{x}^{\ensuremath{-}1/\ensuremath{\gamma}}$ of the superconducting pairing correlation functions. To leading order in the doping $\ensuremath{\delta}$ away from half filling and ${t}_{\ensuremath{\perp}}/t,$ we find $\ensuremath{\gamma}=1+({\ensuremath{\pi}}^{2}{/8)(t}_{\ensuremath{\perp}}{/t)}^{2}{\ensuremath{\delta}}^{2}$ (t(t(t and ${t}_{\ensuremath{\perp}}$ are the hopping terms along and between the chains), such that superconducting pairing correlations dominate. We furthermore show that the transition from the superconducting phase to the usual one-dimensional (Luttinger) metal occurs via a mixed phase, where superconducting pairs are formed in the bonding band only. We give the phase diagram as a function of temperature and doping.
We present a general method for determining the phase diagram of systems of a finite number of one-dimensional Hubbard-like systems coupled by single-particle hopping with weak interactions. The technique is illustrated by detailed calculations for the two-chain Hubbard model, providing controlled results for arbitrary doping and interchain hopping. Of nine possible states which could occur in such a spin-1/2 ladder, we find seven at weak coupling. We discuss the conditions under which the model can be regarded as a one-dimensional analog of a superconductor. \textcopyright{} 1996 The American Physical Society.