Off-shell self-energy for 1-D Fermi liquids

Dmitrii L. Maslov, Andrey V. Chubukov

Dermot Coffey, Kevin S. Bedell

Kyung-Soo Yi, J. J. Quinn

Klaus Morawetz, Vinod Ashokan, Kare Narain Pathak +2 more

Expanding the two-particle Green's functions determines the self-energy and the polarization as well as the response function on the same footing. The correlation energy is calculated with the help of the extended quasiparticle picture, which accounts for off-shell effects. The corresponding response function leads to the same correlation energy as the self-energy in agreement with perturbation theory, provided one works in the extended quasiparticle picture. A one-dimensional quantum wire of fermions is considered and ground-state properties are calculated in the high-density regime within the extended quasiparticle picture and Born approximation. While the on-shell selfenergies are strictly zero due to Pauli-blocking of elastic scattering, the off-shell behavior shows a rich structure of a gap in the damping of excitation, which is closed when the momentum approaches the Fermi one. The consistent spectral function is presented, completing the first two energy-weighted sum rules. The excitation spectrum shows a splitting due to holons and antiholons as non-Fermi liquid behavior. A renormalization procedure is proposed by subtracting an energy constant to render the Fock exchange energy finite. The effective mass derived from meanfield approximation shows a dip analogous to the onset of Peierls instability. The reduced density matrix or momentum distribution is calculated with the help of a Pad\'e regularization repairing deficiencies of the perturbation theory. A seemingly finite step at the Fermi energy indicating Fermi-liquid behavior is repaired in this way.

Sujay Ray, Tanmoy Das

Various angle-dependent measurements in hole-doped cuprates suggested that Non-Fermi liquid (NFL) and Fermi-liquid (FL) self-energies coexist in the Brillouin zone. Moreover, it is also found that NFL self-energies survive up to the overdoped region where the resistivity features a global FL-behavior. To address this problem, here we compute the momentum dependent self-energy from a single band Hubbard model. The self-energy is calculated self-consistently by using a momentum-dependent density-fluctuation (MRDF) method. One of our main result is that the computed self-energy exhibits a NFL-like frequency dependence only in the antinodal region, and FL-like behavior elsewhere, and retains its analytic form at all momenta and dopings. The dominant source of NFL self-energy in the antinodal region stems from the self-energy-dressed fluctuations between the itinerant and localized densities as self-consistency is invoked. We also calculate the DC conductivity by including the full momentum dependent self-energy. We find that the resistivity-temperature exponent n becomes 1 near the optimal doping, while the NFL self-energy occupies largest momentum-space volume. Surprisingly, even in the NFL state near the optimal doping, the nodal region contains FL-like self-energies; while in the under- and over-dopings (n ~ 2), the antinodal region remains NFL-like. These results highlight the non-local correlation physics in cuprates and in other similar intermediately correlated materials, where a direct link between the microscopic single-particle spectral properties and the macroscopic transport behavior can not be well established.