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arXiv:cond-mat/0104130 · Europhysics Letters (EPL)

Angle-resolved loss of Landau quasiparticles in 2D Hubbard model

Dražen Zanchi

Published Aug 1, 2001• 42 citations
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Abstract

The problem of weakly correlated electrons on a square lattice is studied theoretically. A simple renormalization group scheme for the angle-resolved weight Z of the quasiparticles at the Fermi surface is presented and applied to the Hubbard model. Upon reduction of the cutoff the Fermi surface is progressively destroyed from the van Hove points toward the zone diagonals. Due to the renormalized Z, divergences of both antiferromagnetic and superconducting correlation functions are suppressed at the critical scale, where the interactions diverge.

DOI
10.1209/epl/i2001-00413-7

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The problem of weakly correlated electrons on a square lattice is studied theoretically. A simple renormalization group scheme for the angle-resolved weight Z of the quasiparticles at the Fermi surface is presented and applied to the Hubbard model. Upon reduction of the cutoff the Fermi surface is progressively destroyed from the van Hove points toward the zone diagonals. Due to the renormalized Z, divergences of both antiferromagnetic and superconducting correlation functions are suppressed at the critical scale, where the interactions diverge.
We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in the form of the Polchinski equation. The advantage of this renormalization scheme is that the flow itself has a physical interpretation, i.e., the cutoff has the meaning of the temperature. We apply this method to the Hubbard model on a square lattice using both zero- and finite-temperature methods. Truncating the effective action at the sixth term in fermionic variables and neglecting self-energy renormalization, we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability TcRG{T}_{c}^{\mathrm{RG}}TcRG​ as a function of doping. Furthermore we calculate the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type ${d}_{{x}^{2}\ensuremath{-}{y}^{2}},$ while the AF fluctuations are of the type s. Following the strength of both SC and AF fluctuations along the instability line, we obtain the phase diagram. The temperature TcRG{T}_{c}^{\mathrm{RG}}TcRG​ can be identified with the crossover temperature Tco{T}_{\mathrm{co}}Tco​ found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime TcRG{T}_{c}^{\mathrm{RG}}TcRG​ corresponds to the superconducting critical temperature.
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 examine the quasiparticle lifetime and spectral weight near the Fermi surface in the two-dimensional Hubbard model. We use the FLEX approximation to self-consistently generate the Matsubara Green's functions and then we analytically continue to the real axis to obtain the quasiparticle spectral functions. We compare the spectral functions found in the nearest neighbor hopping only Hubbard model with those found when second neighbor hopping is included. This separates the effects of nesting, the Van Hove singularity and the short-ranged antiferromagnetic correlations. The quasiparticle scattering rate is enhanced along the (0,pi) to (pi,pi) Brillouin zone diagonal. When the density is close to half-filling these 'hot-spots' lie on the Fermi surface and the scattering rate increases with decreasing temperature. For the next-nearest neighbor hopping scenario we observe a large range of doping where there is no antiferromagnetism but the scattering rate has a linear temperature dependence. On decreasing the interaction this non-Fermi liquid behavior is confined to doping levels where the Fermi energy lies near to the Van Hove singularity. We conclude that the 'hot-spots' are associated with the antiferromagnetic phase transition while the linear temperature dependence of the scattering rate is associated with the Van Hove singularity.
We formulate the exact Wilsonian renormalization group for a system of interacting fermions on a lattice. The flow equations for all vertices of the Wilson effective action are expressed in form of the Polchinski equation. We apply this method to the Hubbard model on a square lattice using both zero- and finite- temperature methods. Truncating the effective action at the sixth term in fermionic variables we obtain the one-loop functional renormalization equations for the effective interaction. We find the temperature of the instability Tc^{RG} as function of doping. We calculate furthermore the renormalization of the angle-resolved correlation functions for the superconductivity (SC) and for the antiferromagnetism (AF). The dominant component of the SC correlations is of the type d while the AF fluctuations are of the type s Following the strength of both SC and AF fluctuation along the instability line we obtain the phase diagram. The temperature Tc^{RG} can be identified with the crossover temperature T{co} found in the underdoped regime of the high-temperature superconductors, while in the overdoped regime Tc^{RG} corresponds to the superconducting critical temperature.
The problem of weakly correlated electrons on a square lattice is formulated in terms of a one-loop renormalization group. Starting from the action for the entire Brillouin zone we reduce successively the cutoff \ensuremath{\Lambda} about the Fermi surface and follow the renormalization of the coupling U as a function of three energy-momenta. We calculate the intrinsic temperature scale Tco{\mathit{T}}_{\mathit{co}}Tco​ where the renormalization-group flow crosses over from the regime (\ensuremath{\Lambda}>Tco{\mathit{T}}_{\mathit{co}}Tco​) where the electron-electron (e-e) and electron-hole (e-h) terms are equally important to the regime (\ensuremath{\Lambda}Tco{\mathit{T}}_{\mathit{co}}Tco​) where only the e-e term plays a role. In the low-energy regime only the pairing interaction V is marginally relevant, containing contributions from all renormalization-group steps of the regime \ensuremath{\Lambda}>Tco{\mathit{T}}_{\mathit{co}}Tco​. We identify the most attractive eigenvalue ${\ensuremath{\lambda}}_{\mathrm{min}}$ of ${\mathit{V}}_{\mathrm{\ensuremath{\Lambda}}={\mathit{T}}_{\mathit{co}}}$. At low filling, ${\ensuremath{\lambda}}_{\mathrm{min}}$ corresponds to the B2{\mathit{B}}_{2}B2​ representation (dxy{\mathit{d}}_{\mathit{xy}}dxy​ symmetry), while near half filling the strongest attraction occurs in the B1{\mathit{B}}_{1}B1​ representation (${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$ symmetry). In the direction of the van Hove singularities, the order parameter shows peaks with increasing strength as one approaches half filling. We also give a possible interpretation of angle-resolved photoemission spectroscopy experiments trying to determine the symmetry of the order parameter in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ compound Bi2{\mathrm{Bi}}_{2}Bi2​Sr2{\mathrm{Sr}}_{2}Sr2​CaCu2{\mathrm{CaCu}}_{2}CaCu2​O8{\mathrm{O}}_{8}O8​. \textcopyright{} 1996 The American Physical Society.