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/0406164 · Physical Review B

Pseudogap at hot spots in the two-dimensional Hubbard model at weak coupling

Daniel Rohe, Walter Metzner

Published Mar 30, 2005• 72 citations
arXivHTMLPDF

Abstract

We analyze the interaction-induced renormalization of single-particle excitations in the two-dimensional Hubbard model at weak coupling using the Wick-ordered version of the functional renormalization group. The self-energy is computed for real frequencies by integrating a flow equation with renormalized two-particle interactions. In the vicinity of hot spots, that is, points where the Fermi surface intersects the umklapp surface, self-energy effects beyond the usual quasiparticle renormalizations and damping occur near instabilities of the normal, metallic phase. Strongly enhanced renormalized interactions between particles at different hot spots generate a pronounced low-energy peak in the imaginary part of the self-energy, leading to a pseudogaplike double-peak structure in the spectral function for single-particle excitations.

DOI
10.1103/physrevb.71.115116

Related papers

Quasiparticle Anisotropy and Pseudogap Formation from the Weak-Coupling Renormalization Group Point of View

A. A. Katanin, A. P. Kampf

Using the one-loop functional renormalization group technique, we evaluate the self-energy in the weak-coupling regime of the 2D t-t(') Hubbard model. At van Hove (vH) band fillings and at low temperatures, the quasiparticle weight along the Fermi surface (FS) continuously vanishes on approaching the (pi,0) point where the quasiparticle concept is invalid. Away from vH band fillings the quasiparticle peak is formed inside an anisotropic pseudogap and the self-energy has the conventional Fermi-liquid characteristics near the Fermi level. The spectral weight of the quasiparticle features is reduced on parts of the FS between the near vicinity of hot spots and the FS points closest to (pi,0) and (0,pi).

arXiv:cond-mat/0310112•Physical Review Letters•Sep 3, 2004•80 citations

Anisotropic pseudogap in the half-filling 2-d Hubbard model at finite T

Taiichirou Saikawa, Ferraz, A.

We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the $(\pm π,0)$, $(0,\pm π)$ regions as the normal state pseudogap observed in the high-$T_c$ superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around ${\bf Q}=(π,π)$ and the flatness of the band dispersion around the saddle point.

arXiv:cond-mat/9810393•Oct 29, 1998•0 citations

Renormierungsgruppenanalyse des Hubbard-Modells in zwei Dimensionen

Rohe, Daniel

In this thesis we apply the functional renormalisation group (fRG) to the two-dimensional Hubbard model (2D-HM). We do this by solving approximate renormalisation group equations for the self energy and the two-particle interaction numerically. The purpose of these calculations is two-fold in the sense that we want to learn about the reliability of the method on the one hand, and about the physics of the 2D-HM on the other. We find that different fRG schemes agree in describing the mutual interplay and the resulting competition between different correlations, but also that the results sometimes differ quantitatively. This sharpens our perception when it comes to interpreting fRG results, and tells us that we have to separate the indicative character from the quantitative aspects of the results. The main line of arguments presented in previous fRG studies is confirmed, that in the weak-coupling region particle-hole correlations feed back into the particle-particle channel, triggering strong superconducting correlations in a non-zero parameter range. Concerning the physics of the 2D-HM show new results for the single-particle spectral functions for the case of a Fermi surface which is not perfectly nested and intersects the Umklapp surface at so-called hot spots. These results are obtained from the Wick-ordered fRG scheme, and the calculations are done directly on the real frequency axis. We find that close to a critical temperature $T_c$ where correlations become strong, a dip appears in the single-particle spectral functions for momenta close to and at the hot spots. Away from the van Hove scale, this is traced back to strong correlations in the particle-hole channel and attributed to antiferromagnetic fluctuations, in agreement with numerous previous studies. For a Fermi surface at or very close to the van Hove scale, there exists a degeneracy in the sense that the strongest correlations are found around a point in coupling space which is relevant for both superconductivity and antiferromagnetism, and we can thus not distinguish between the importance of the respective fluctuations.

•Jan 1, 2005•0 citations

Spectral properties of the two-dimensional Hubbard model

V. Zlatić, K. D. Schotte, Gudrun Schliecker

The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.

Physical review. B, Condensed matter•Aug 1, 1995•25 citations

ANISOTROPIC PSEUDOGAP IN THE HALF-FILLING TWO-DIMENSIONAL HUBBARD MODEL AT FINITE TEMPERATURE

Taiichiro Saikawa, Álvaro Antônio Bandeira Ferraz

We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperatures. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.

International Journal of Modern Physics B•Aug 20, 2000•0 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
We analyze the interaction-induced renormalization of single-particle excitations in the two-dimensional Hubbard model at weak coupling using the Wick-ordered version of the functional renormalization group. The self-energy is computed for real frequencies by integrating a flow equation with renormalized two-particle interactions. In the vicinity of hot spots, that is, points where the Fermi surface intersects the umklapp surface, self-energy effects beyond the usual quasiparticle renormalizations and damping occur near instabilities of the normal, metallic phase. Strongly enhanced renormalized interactions between particles at different hot spots generate a pronounced low-energy peak in the imaginary part of the self-energy, leading to a pseudogaplike double-peak structure in the spectral function for single-particle excitations.
Using the one-loop functional renormalization group technique, we evaluate the self-energy in the weak-coupling regime of the 2D t-t(') Hubbard model. At van Hove (vH) band fillings and at low temperatures, the quasiparticle weight along the Fermi surface (FS) continuously vanishes on approaching the (pi,0) point where the quasiparticle concept is invalid. Away from vH band fillings the quasiparticle peak is formed inside an anisotropic pseudogap and the self-energy has the conventional Fermi-liquid characteristics near the Fermi level. The spectral weight of the quasiparticle features is reduced on parts of the FS between the near vicinity of hot spots and the FS points closest to (pi,0) and (0,pi).
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the (±π,0)(\pm π,0)(±π,0), (0,±π)(0,\pm π)(0,±π) regions as the normal state pseudogap observed in the high-TcT_cTc​ superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around Q=(π,π){\bf Q}=(π,π)Q=(π,π) and the flatness of the band dispersion around the saddle point.
In this thesis we apply the functional renormalisation group (fRG) to the two-dimensional Hubbard model (2D-HM). We do this by solving approximate renormalisation group equations for the self energy and the two-particle interaction numerically. The purpose of these calculations is two-fold in the sense that we want to learn about the reliability of the method on the one hand, and about the physics of the 2D-HM on the other. We find that different fRG schemes agree in describing the mutual interplay and the resulting competition between different correlations, but also that the results sometimes differ quantitatively. This sharpens our perception when it comes to interpreting fRG results, and tells us that we have to separate the indicative character from the quantitative aspects of the results. The main line of arguments presented in previous fRG studies is confirmed, that in the weak-coupling region particle-hole correlations feed back into the particle-particle channel, triggering strong superconducting correlations in a non-zero parameter range. Concerning the physics of the 2D-HM show new results for the single-particle spectral functions for the case of a Fermi surface which is not perfectly nested and intersects the Umklapp surface at so-called hot spots. These results are obtained from the Wick-ordered fRG scheme, and the calculations are done directly on the real frequency axis. We find that close to a critical temperature TcT_cTc​ where correlations become strong, a dip appears in the single-particle spectral functions for momenta close to and at the hot spots. Away from the van Hove scale, this is traced back to strong correlations in the particle-hole channel and attributed to antiferromagnetic fluctuations, in agreement with numerous previous studies. For a Fermi surface at or very close to the van Hove scale, there exists a degeneracy in the sense that the strongest correlations are found around a point in coupling space which is relevant for both superconductivity and antiferromagnetism, and we can thus not distinguish between the importance of the respective fluctuations.
The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) is momentum dependent. Using Ap{\mathit{A}}_{\mathbf{p}}Ap​(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.
We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperatures. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the self-energy imaginary part. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. This anisotropy of the pseudogap is produced by the flatness of the band dispersion around the saddle point rather than the nesting condition on the Fermi level.
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.