scholarly journals First-Matsubara-frequency rule in a Fermi liquid. I. Fermionic self-energy

2012 ◽  
Vol 86 (15) ◽  
Author(s):  
Andrey V. Chubukov ◽  
Dmitrii L. Maslov
Keyword(s):  
Fermi Liquid ◽  
Matsubara Frequency ◽  
Self Energy

scholarly journals Self-Consistent Calculation of Particle-Hole Diagrams on the Matsubara Frequency: Flex Approximation

1997 ◽  
Vol 08 (05) ◽  
pp. 1145-1158
Author(s):  
J. J. Rodríguez-Núñez ◽  
S. Schafroth
Keyword(s):  
Hubbard Model ◽  
Imaginary Part ◽  
Chemical Potential ◽  
Order Approximation ◽  
The Self ◽  
Green Functions ◽  
Matsubara Frequency ◽  
Self Energy ◽  
Peak Structure ◽  
Self Consistent

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling (ρ =0.40), and for T/t = 0.03, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im Σ( k , ω) ≈ w2 around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully self-consistent and the non-self-consistent ones give different results for the parameters considered here. However, they have similar global results for small densities.

scholarly journals Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Xiao Yan Xu ◽  
Avraham Klein ◽  
Kai Sun ◽  
Andrey V. Chubukov ◽  
Zi Yang Meng
Keyword(s):  
Monte Carlo ◽  
Finite Temperature ◽  
Quantum Monte Carlo ◽  
Fermi Liquid ◽  
Quantum Critical Point ◽  
Critical Metals ◽  
Monte Carlo Data ◽  
Low Frequencies ◽  
Self Energy ◽  
Quantum Critical

Abstract Quantum Monte Carlo (QMC) simulations of correlated electron systems provide unbiased information about system behavior at a quantum critical point (QCP) and can verify or disprove the existing theories of non-Fermi liquid (NFL) behavior at a QCP. However, simulations are carried out at a finite temperature, where quantum critical features are masked by finite-temperature effects. Here, we present a theoretical framework within which it is possible to separate thermal and quantum effects and extract the information about NFL physics at T = 0. We demonstrate our method for a specific example of 2D fermions near an Ising ferromagnetic QCP. We show that one can extract from QMC data the zero-temperature form of fermionic self-energy Σ(ω) even though the leading contribution to the self-energy comes from thermal effects. We find that the frequency dependence of Σ(ω) agrees well with the analytic form obtained within the Eliashberg theory of dynamical quantum criticality, and obeys ω2/3 scaling at low frequencies. Our results open up an avenue for QMC studies of quantum critical metals.

Quasiparticle Self-Energy and Specific Heat of a Fermi Liquid: Application toHe3

1967 ◽  
Vol 19 (8) ◽  
pp. 425-428 ◽  
Author(s):  
D. J. Amit ◽  
J. W. Kane ◽  
H. Wagner
Keyword(s):  
Specific Heat ◽  
Fermi Liquid ◽  
Self Energy

A SELF-ENERGY FUNCTIONAL FOR THE INFINITE-DIMENSIONAL HUBBARD MODEL

1992 ◽  
Vol 06 (28) ◽  
pp. 1827-1833 ◽  
Author(s):  
Y.M. LI ◽  
N. d’AMBRUMENIL
Keyword(s):  
Hubbard Model ◽  
Specific Heat ◽  
Fermi Liquid ◽  
Natural Extension ◽  
Energy Functional ◽  
Symmetric Case ◽  
Kondo Temperature ◽  
Infinite Dimensional ◽  
Self Energy ◽  
Uncorrelated State

We present an approximate self-energy functional for the infinite-dimensional Hubbard model. This functional is a natural extension of the exact solution of the Falicov-Kimball model to the spin-symmetric case, and is exact in the uncorrelated and atomic limits. Using the functional we calculate the susceptibility and the specific heat for the Lorentzian density of states. We find that the susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations to a Fermi liquid state at low temperature via a Kondo-type anomaly. The specific heat shows a peak at the corresponding Kondo temperature.

scholarly journals Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures

2020 ◽  
Vol 9 (6) ◽  
Author(s):  
Daniel Rohe ◽  
Carsten Honerkamp
Keyword(s):  
Hubbard Model ◽  
Fermi Liquid ◽  
Renormalisation Group ◽  
Direct Access ◽  
Two Dimensional ◽  
Quasi Particle ◽  
Energy Data ◽  
Self Energy ◽  
Real Frequency

We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown.

scholarly journals Many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid theory

2015 ◽  
Vol 29 (15) ◽  
pp. 1530005 ◽  
Author(s):  
Naoya Arakawa
Keyword(s):  
Temperature Dependence ◽  
Fermi Liquid ◽  
Quantum Critical Point ◽  
Electron Systems ◽  
Many Body ◽  
Correlated Electron Systems ◽  
Orbital System ◽  
Self Energy ◽  
Correlated Electron ◽  
Many Body Effects

I review many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point (QCP). These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multi-orbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multi-orbital systems. To improve this situation, I formulate the resistivity of a multi-orbital Hubbard model using the extended Éliashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki–Thompson term. The results away from and near the antiferromagnetic QCP reproduce the temperature dependence observed in Sr 2 RuO 4 and Sr 2 Ru 0.075 Ti 0.025 O 4, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems.

scholarly journals COLOR SUPERFLUID AND TRIONIC STATE OF ATTRACTIVE THREE-COMPONENT LATTICE FERMIONIC ATOMS AT FINITE TEMPERATURES

2011 ◽  
Vol 25 (12n13) ◽  
pp. 987-994 ◽  
Author(s):  
KENSUKE INABA ◽  
SEI-ICHIRO SUGA
Keyword(s):  
Temperature Region ◽  
Fermi Liquid ◽  
Energy Functional ◽  
Order Transition ◽  
Attractive Interaction ◽  
Fixed Temperature ◽  
Self Energy ◽  
Fermionic Atoms ◽  
Second Order Transition ◽  
First Order Transition

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low temperature region, a second-order transition occurs from a Fermi liquid to a color superfluid (CSF). In the strong attractive region, a first-order transition occurs from a CSF to a trionic state. In the high temperature region, a cross-over between a Fermi liquid and a trionic state is observed with increasing the strength of the attractive interaction. The cross-over region for fixed temperature is almost independent of filling.

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