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/9906379 · Molecular crystals and liquid crystals science technology. Section A, Molecular crystals and liquid crystals/Molecular crystals and liquid crystals science and technology. Section A, Molecular crystals and liquid crystals

Interplay of Correlation, Randomness and Dimensionality Effects in Weakly-Coupled Half-Filled Random Hubbard Chains

Jun‐ichiro Kishine, Kenji Yonemitsu

Published Apr 1, 2000• 1 citation
arXivHTMLPDF

Abstract

We study interplay of electronic correlation, randomness and dimensionality effects in half-filled random Hubbard chains weakly coupled via an interchain one-particle hopping. Based on the two-loop renormalization-group approach, phase diagrams are given in terms of temperature vs. strengths of the intrachain electron-electron umklapp scattering, the random scattering and the interchain one-particle hopping.

DOI
10.1080/10587250008026198

Related papers

Interplay of randomness, electron correlation, and dimensionality effects in quasi-one-dimensional conductors

Jun‐ichiro Kishine, Kenji Yonemitsu

We study the interplay of randomness, electron correlation, and dimensionality effects in weakly coupled half-filled Hubbard chains with weak quenched random potentials, based on the renormalization-group (RG) approach. We perform a two-loop RG analysis of an effective action derived by using the replica trick, and examine the following crossovers and phase transitions from an incoherent metal regime: (1) a crossover to the Anderson localization regime, (2) an antiferromagnetic phase transition, and (3) a crossover to the quasi-one-dimensional weak-localization regime. The case of $d=1+\ensuremath{\epsilon}$ $(\ensuremath{\epsilon}\ensuremath{\ll}1)$ dimensions is also mentioned.

Physical review. B, Condensed matter•Nov 15, 2000•2 citations

Antiferromagnetic Phase Transition and Crossover to Fermi Liquid Phase in a Weakly Coupled Half-Filled Chain System

Jun‐ichiro Kishine, Kenji Yonemitsu

Effects of the intrachain electron-electron umklapp process and the interchain one-particle hopping, t ⊥ , in a weakly coupled half-filled chain system have been studied, based on the perturbative renormalization-group approach. By solving the scaling equations, we found that the intrachain umklapp process strongly suppresses an interchain one-particle process and causes a finite critical value for t ⊥ , t ⊥ c . For t ⊥ < t ⊥ c , as the temperature decreases, the system undergoes a phase transition into an antiferromagnetic long-range-ordered phase at a transition temperature T N which increases with the increasing t ⊥ . On the other hand, for t ⊥ > t ⊥ c , the system undergoes a crossover to the Fermi liquid phase where the interchain coherent propagation of quasi-particles occurs.

Journal of the Physical Society of Japan•Aug 15, 1998•23 citations

Two-loop renormalization group theory for the quasi-one-dimensional Hubbard model at half filling

Masahisa Tsuchiizu

We derive two-loop renormalization group equations for the half filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the $g$-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half filled Hubbard model and obtain constraints on the $g$-ological coupling constants by which resultant renormalization equations are given in a compact form. By solving the renormalization group equations numerically, we estimate the magnitude of excitation gaps and clarify that the charge gap is suppressed due to the interchain hopping but is always finite even for the relevant interchain hopping. To show the validity of the present analysis, we also apply this to the two-leg ladder system. By utilizing the field-theoretical Bosonization and Fermionization method, we derive low-energy effective theory and analyze the magnitude of all the excitation gaps in detail. It is shown that the low-energy excitations in the two-leg Hubbard ladder have $\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry when the interchain hopping exceeds the magnitude of the charge gap.

arXiv:cond-mat/0603644•Physical Review B•Oct 13, 2006•9 citations

Strong-coupling phases of two Hubbard chains with interchain hopping

Michele Fabrizio, Alberto Parola, Erio Tosatti

The T=0 phase diagram for two Hubbard chains with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and on-site repulsion U is derived within a renormalization-group (RG) approach. We explicitly allow for renormalization of the Fermi momenta. A nonzero ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ drives the chains towards strong coupling, and only for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ is a Luttinger liquid recovered. By use of weak-coupling RG, a qualitative picture of the phase diagram can be obtained. Our calculations show two different strong-coupling regimes: one with nonvanishing effective interchain hopping (〈${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$〉\ensuremath{\ne}0), not confining, for small U, and another with 〈${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$〉=0, confining, for large U. Numerical diagonalizations for a small cluster support the RG results.

Physical review. B, Condensed matter•Aug 1, 1992•89 citations

Strong correlations and formation of "hot spots" in the quasi-one-dimensional Hubbard model at weak coupling

Rohe, D., Antoine Georges

We study the anisotropic two-dimensional Hubbard model at and near half filling within a functional renormalization group method, focusing on the structure of momentum-dependent correlations which grow strongly upon approaching a critical temperature from above. We find that a finite nearest-neighbor interchain hopping is not sufficient to introduce a substantial momentum dependence of single-particle properties along the Fermi surface. However, when a sufficiently large second-nearest neighbor inter-chain hopping is introduced, the system is frustrated and we observe the appearance of so-called "hot spots", specific points on the Fermi surface around which scattering becomes particularly strong. We compare our results with other studies on quasi-one-dimensional systems.

arXiv:cond-mat/0608032•Aug 1, 2006•0 citations

Spinless fermion chains with weak interchain hopping

J. Szṅajd, K. W. Becker

The linear renormalization-group transformation is used to study the thermodynamics of weakly coupled spinless fermion chains at half-filling. The model consists of a competing nearest-neighbour Coulomb repulsion and kinetic energy terms. The specific heat and the nearest-neighbour correlation function are studied as functions of temperature by varying the ratio of Coulomb repulsion to kinetic energy. The role of an interchain hopping is studied and the metal–insulator phase transition temperature as a function of hopping parameters is discussed.

Journal of Physics Condensed Matter•Nov 1, 2005•5 citations
We study interplay of electronic correlation, randomness and dimensionality effects in half-filled random Hubbard chains weakly coupled via an interchain one-particle hopping. Based on the two-loop renormalization-group approach, phase diagrams are given in terms of temperature vs. strengths of the intrachain electron-electron umklapp scattering, the random scattering and the interchain one-particle hopping.
We study the interplay of randomness, electron correlation, and dimensionality effects in weakly coupled half-filled Hubbard chains with weak quenched random potentials, based on the renormalization-group (RG) approach. We perform a two-loop RG analysis of an effective action derived by using the replica trick, and examine the following crossovers and phase transitions from an incoherent metal regime: (1) a crossover to the Anderson localization regime, (2) an antiferromagnetic phase transition, and (3) a crossover to the quasi-one-dimensional weak-localization regime. The case of $d=1+\ensuremath{\epsilon}$ $(\ensuremath{\epsilon}\ensuremath{\ll}1)$ dimensions is also mentioned.
Effects of the intrachain electron-electron umklapp process and the interchain one-particle hopping, t ⊥ , in a weakly coupled half-filled chain system have been studied, based on the perturbative renormalization-group approach. By solving the scaling equations, we found that the intrachain umklapp process strongly suppresses an interchain one-particle process and causes a finite critical value for t ⊥ , t ⊥ c . For t ⊥ < t ⊥ c , as the temperature decreases, the system undergoes a phase transition into an antiferromagnetic long-range-ordered phase at a transition temperature T N which increases with the increasing t ⊥ . On the other hand, for t ⊥ > t ⊥ c , the system undergoes a crossover to the Fermi liquid phase where the interchain coherent propagation of quasi-particles occurs.
We derive two-loop renormalization group equations for the half filled one-dimensional Hubbard chains coupled by the interchain hopping. Our renormalization group scheme for the quasi-one-dimensional electron system is a natural extension of that for the purely one-dimensional systems in the sense that transverse-momentum dependences are introduced in the ggg-ological coupling constants and we regard the transverse momentum as a patch index. We develop symmetry arguments for the particle-hole symmetric half filled Hubbard model and obtain constraints on the ggg-ological coupling constants by which resultant renormalization equations are given in a compact form. By solving the renormalization group equations numerically, we estimate the magnitude of excitation gaps and clarify that the charge gap is suppressed due to the interchain hopping but is always finite even for the relevant interchain hopping. To show the validity of the present analysis, we also apply this to the two-leg ladder system. By utilizing the field-theoretical Bosonization and Fermionization method, we derive low-energy effective theory and analyze the magnitude of all the excitation gaps in detail. It is shown that the low-energy excitations in the two-leg Hubbard ladder have $\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry when the interchain hopping exceeds the magnitude of the charge gap.
The T=0 phase diagram for two Hubbard chains with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and on-site repulsion U is derived within a renormalization-group (RG) approach. We explicitly allow for renormalization of the Fermi momenta. A nonzero ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ drives the chains towards strong coupling, and only for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ is a Luttinger liquid recovered. By use of weak-coupling RG, a qualitative picture of the phase diagram can be obtained. Our calculations show two different strong-coupling regimes: one with nonvanishing effective interchain hopping (〈${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$〉\ensuremath{\ne}0), not confining, for small U, and another with 〈${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$〉=0, confining, for large U. Numerical diagonalizations for a small cluster support the RG results.
We study the anisotropic two-dimensional Hubbard model at and near half filling within a functional renormalization group method, focusing on the structure of momentum-dependent correlations which grow strongly upon approaching a critical temperature from above. We find that a finite nearest-neighbor interchain hopping is not sufficient to introduce a substantial momentum dependence of single-particle properties along the Fermi surface. However, when a sufficiently large second-nearest neighbor inter-chain hopping is introduced, the system is frustrated and we observe the appearance of so-called "hot spots", specific points on the Fermi surface around which scattering becomes particularly strong. We compare our results with other studies on quasi-one-dimensional systems.
The linear renormalization-group transformation is used to study the thermodynamics of weakly coupled spinless fermion chains at half-filling. The model consists of a competing nearest-neighbour Coulomb repulsion and kinetic energy terms. The specific heat and the nearest-neighbour correlation function are studied as functions of temperature by varying the ratio of Coulomb repulsion to kinetic energy. The role of an interchain hopping is studied and the metal–insulator phase transition temperature as a function of hopping parameters is discussed.