Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high- $T_{\rm c}$ cuprates.Single-particle excitation spectra of the two-dimensional Hubbard model on the square lattice near half filling and at zero temperature are investigated on the basis of the self-consistent projection operator method. The method guarantees a high accuracy of the spectra with high energy and high momentum resolutions. It takes into account long-range intersite correlations as well as the strong on-site correlations. Effects of nonlocal excitations are clarified by comparing the results with those of the single-site approximation. The calculated spectra verify the quantum Monte-Carlo results for finite temperatures. The spectra at the Fermi level yield a hole-like Fermi surface in the underdoped region and an electron-like Fermi surface in the overdoped region. From a numerical analysis of the momentum dependent effective mass and self-energy, it is concluded that a marginal Fermi-liquid like state persists even at finite doping concentrations in the strongly correlated region because a van Hove singularity is pinned to the Fermi surface. It is also found that a kink structure appears in the quasiparticle energy band in the same region. The kink is shown to be caused by a mixing between the quasiparticle band and an excitation band with strong short-range antiferromagnetic correlations. These results suggest an explanation for some of the unusual properties of the normal state in high-$T_{\rm c}$ cuprates.

arXiv:0705.0581Journal of the Physical Society of JapanJun 25, 20074 citations

Nonequilibrium transport in the strange metal and pseudogap phases of the cuprates

Ka Wai Lo, Seungmin Hong, Philip Phillips

We propose that the nonequilibrium current measured in the $a$ - $b$ plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used to diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively, one expects the strange metal to be more different from a Fermi liquid than the pseudogap is. We compute the expected nonequilibrium transport signal with the three Green's functions that are available in the literature: (1) marginal Fermi-liquid theory, (2) the phenomenological ansatz for the pseudogap regime, and (3) the Wilsonian reduction of the Hubbard model which contains both the strange metal and pseudogap. All three give linear $I$ - $V$ curves at low bias voltages. Significant deviations from linearity at higher voltages obtain only in the marginal Fermi-liquid approach. The key finding, however, is that $I$ - $V$ curves for the strange metal/Fermi-liquid contact exceed that of the pseudogap/Fermi-liquid system. If this is borne out experimentally, this implies that the strange metal is less orthogonal to a Fermi liquid than the pseudogap is. Within the Wilsonian reduction of the Hubbard model, this result is explained in terms of a composite-particle picture. Namely, the pseudogap corresponds to a confinement transition of the charge degrees of freedom present in the strange metal. In the strange metal the composite excitations break up and electron quasiparticles scatter off bosons. The bosons here, however, do not arise from phonons but from the charge degrees of freedom responsible for dynamical spectral weight transfer.We propose that the nonequilibrium current measured in the $a$-$b$ plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used to diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively, one expects the strange metal to be more different from a Fermi liquid than the pseudogap is. We compute the expected nonequilibrium transport signal with the three Green's functions that are available in the literature: (1) marginal Fermi-liquid theory, (2) the phenomenological ansatz for the pseudogap regime, and (3) the Wilsonian reduction of the Hubbard model which contains both the strange metal and pseudogap. All three give linear $I$-$V$ curves at low bias voltages. Significant deviations from linearity at higher voltages obtain only in the marginal Fermi-liquid approach. The key finding, however, is that $I$-$V$ curves for the strange metal/Fermi-liquid contact exceed that of the pseudogap/Fermi-liquid system. If this is borne out experimentally, this implies that the strange metal is less orthogonal to a Fermi liquid than the pseudogap is. Within the Wilsonian reduction of the Hubbard model, this result is explained in terms of a composite-particle picture. Namely, the pseudogap corresponds to a confinement transition of the charge degrees of freedom present in the strange metal. In the strange metal the composite excitations break up and electron quasiparticles scatter off bosons. The bosons here, however, do not arise from phonons but from the charge degrees of freedom responsible for dynamical spectral weight transfer.

arXiv:1308.4691Physical Review BDec 13, 20131 citation

Quasiparticle scattering in Fermi fluids

Franz Mohling, James C. Rainwater

Journal of Low Temperature PhysicsAug 1, 19758 citations

Long-wavelength correlations and transport in a marginal Fermi liquid

Arkady Shekhter, Chandra Mohan Varma

Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due to the form of the assumed fluctuation spectra is that the large inelastic quasiparticle relaxation rate near the Fermi surface is proportional to the energy measured from the chemical potential, ${\ensuremath{\tau}}_{i}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\epsilon}$. We present a microscopic long-wavelength derivation of the hydrodynamic properties in such a situation by an extension of the procedure that Eliashberg used for the derivation of the hydrodynamic properties of a Landau-Fermi liquid. In particular, the density-density and the current-current correlations and the relation between the two are derived, and the connection to microscopic calculations of the frequency dependence of the optical conductivity with an additional Fermi-liquid correction factor shown to follow. The method used here may be necessary, quite generally, for the correct hydrodynamic theory for any problem of quantum-critical fluctuations in fermions.Marginal Fermi liquid was originally introduced as a phenomenological description of the cuprates in a part of the metallic doping range which appears to be governed by fluctuations due to a quantum-critical point. An essential result due to the form of the assumed fluctuation spectra is that the large inelastic quasiparticle relaxation rate near the Fermi surface is proportional to the energy measured from the chemical potential, ${\ensuremath{\tau}}_{i}^{\ensuremath{-}1}\ensuremath{\propto}\ensuremath{\epsilon}$. We present a microscopic long-wavelength derivation of the hydrodynamic properties in such a situation by an extension of the procedure that Eliashberg used for the derivation of the hydrodynamic properties of a Landau-Fermi liquid. In particular, the density-density and the current-current correlations and the relation between the two are derived, and the connection to microscopic calculations of the frequency dependence of the optical conductivity with an additional Fermi-liquid correction factor shown to follow. The method used here may be necessary, quite generally, for the correct hydrodynamic theory for any problem of quantum-critical fluctuations in fermions.

arXiv:0809.1104Physical Review BJan 23, 200920 citations

T_{\rm c}

cuprates.

We propose that the nonequilibrium current measured in the

a

b

plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used to diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively, one expects the strange metal to be more different from a Fermi liquid than the pseudogap is. We compute the expected nonequilibrium transport signal with the three Green's functions that are available in the literature: (1) marginal Fermi-liquid theory, (2) the phenomenological ansatz for the pseudogap regime, and (3) the Wilsonian reduction of the Hubbard model which contains both the strange metal and pseudogap. All three give linear

I

V

curves at low bias voltages. Significant deviations from linearity at higher voltages obtain only in the marginal Fermi-liquid approach. The key finding, however, is that

I

V

curves for the strange metal/Fermi-liquid contact exceed that of the pseudogap/Fermi-liquid system. If this is borne out experimentally, this implies that the strange metal is less orthogonal to a Fermi liquid than the pseudogap is. Within the Wilsonian reduction of the Hubbard model, this result is explained in terms of a composite-particle picture. Namely, the pseudogap corresponds to a confinement transition of the charge degrees of freedom present in the strange metal. In the strange metal the composite excitations break up and electron quasiparticles scatter off bosons. The bosons here, however, do not arise from phonons but from the charge degrees of freedom responsible for dynamical spectral weight transfer.