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/9911330

Non-Fermi Behavior of the Strongly Correlated Electron Systems

Cătălin Paşcu Moca

Published Nov 21, 1999• 0 citations
arXivHTMLPDF

Abstract

(1) The temperature dependence of the specific heat for a marginal Fermi liquid has been calculated. (2) We calculated the self-energy at T=0 for a two dimensional fermionic system with hyperbolic dispersion. The existence of the saddle points in the energy gives rise to a marginal behavior. (3) We showed that the two-dimensional fermionic system with the energy $ε_{\mathbf{k}}=k_xk_y$ has a non-Fermi behavior. (4) The electronic self-energy due to the electron-spin interaction is calculated for a two dimensional system. (5) We study the influence of the amplitude fluctuations of a non-Fermi superconductor on the energy spectrum of the two-dimensional Anderson non-Fermi system. (6) Using the field-theoretical methods we studied the evolution from BCS theory to Bose-Einstein condensation (BEC) for a non-Fermi system. (7) Using the renormalization group approach proposed by Millis we calculated the specific heat coefficient $γ(T)$ for the magnetic fluctuations with susceptibility $χ^{-1}\sim δ^α+| ω| ^α+f(q)$ near a Lifshitz point.

DOI
10.48550/arxiv.cond-mat/9911330

Related papers

Non-Fermi liquid properties of two-dimensional electron systems.

Yujong Bai

We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.

•Jan 1, 1995•0 citations

Electronic self-energy and triplet pairing fluctuations in the vicinity of a ferromagnetic instability in two-dimensional systems: Quasistatic approach

A. A. Katanin

The self-energy, spectral functions, and susceptibilities of two-dimensional systems with strong ferromagnetic fluctuations are considered within the quasistatic approach. The self-energy at low temperatures $T$ has a non-Fermi-liquid form in the energy window $\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}\ensuremath{\lesssim}{\ensuremath{\Delta}}_{0}$ near the Fermi level, where ${\ensuremath{\Delta}}_{0}$ is the ground-state spin splitting for magnetically ordered ground state, and ${\ensuremath{\Delta}}_{0}\ensuremath{\propto}{T}^{1∕2}\phantom{\rule{0.2em}{0ex}}{\mathrm{ln}}^{1∕2}({v}_{F}∕T)$ in the quantum critical regime (${v}_{F}$ is the Fermi velocity). Spectral functions have a two-peak structure at finite $T$ above the magnetically ordered ground state, which implies quasisplitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations. The triplet pairing amplitude in the quasistatic approximation increases with increasing correlation length; at low temperatures $T⪡{\ensuremath{\Delta}}_{0}$ the vertex corrections become important and the Eliashberg approach is not justified. The results for the spectral properties and susceptibilities in the quantum critical regime near charge (spin) instabilities with large enough correlation length $\ensuremath{\xi}⪢{(T∕{v}_{F})}^{\ensuremath{-}1∕3}$ are obtained.

arXiv:cond-mat/0501331•Physical Review B•Jul 8, 2005•15 citations

Fermi liquid theory of strongly correlated electron systems

K. Yamada

Heavy fermion systems are explained on the basis of the Fermi liquid theory. The specific heat, magnetic susceptibility and electrical resistivity are discussed. Using Anderson's orthogonality theorem, we show that the Fermi liquid is nothing but a local spin singlet state at every site. Heavy fermion systems The Fermi liquid theory is independent of a model Hamiltonian, and can be applied to any system as long as the system remains a Fermi liquid. The theory tells us that even if the electron interaction becomes strong, physical quantities behave as those of the non-interacting Fermi gas. The difference between them with and without interaction is not qualitative but quantitative. As seen at the Mott transition in Hubbard systems, the effective mass of the electron increases near the transition point. As a system realizing such a large effective mass, a Fermi liquid system called the heavy electron system or the heavy fermion system attracts general interest. The heavy fermion systems are composed of the rare earth metals such as Ce and Yb, and actinide atoms such as U. The heavy fermions are nothing but the quasi-particles in the Fermi liquid theory. As a quasi-particle in a strongly correlated electron system, the heavy fermion is an important issue to be studied in the development of the Fermi liquid theory. The heavy fermion realized in f -electron systems is one of the heavy quasi-particles appearing near the Mott transition.

Cambridge University Press eBooks•Sep 23, 2004•0 citations

Kinks in the periodic Anderson model

Andreas Kainz, A. Toschi, Robert Peters +1 more

Recently, dynamical mean-field-theory calculations have shown that kinks emerge in the real part of the self-energy of strongly correlated metals close to the Fermi level. This gives rise to a similar behavior in the quasiparticle dispersion relation as well as in the electronic specific heat. Since $f$-electron systems are even more strongly correlated than the hitherto studied $d$-electron systems, we apply the dynamical mean-field approach with the numerical renormalization group method as impurity solver to study whether there are kinks in the periodic Anderson model.

arXiv:1208.5349•Physical Review B•Nov 7, 2012•9 citations

Non-Fermi Liquid Behavior in the Three-Dimensional Hubbard Model

Samuel Kellar, Ka-Ming Tam, Juana Moreno

We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.

Crystals•Jan 6, 2023•2 citations

From the Bose-Einstein to fermion condensation

M. Ya. Amusia, ALFRED Z. MSEZANE, Vasily R. Shaginyan

The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M FC * and M L * and intersecting near the binding energy E 0, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E 0 persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as $$M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}$$ . The regime is restored at some temperature $$T^ * \propto \sqrt B $$ . The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.

arXiv:cond-mat/0301077•Physics of Atomic Nuclei•Oct 1, 2003•2 citations
(1) The temperature dependence of the specific heat for a marginal Fermi liquid has been calculated. (2) We calculated the self-energy at T=0 for a two dimensional fermionic system with hyperbolic dispersion. The existence of the saddle points in the energy gives rise to a marginal behavior. (3) We showed that the two-dimensional fermionic system with the energy εk=kxkyε_{\mathbf{k}}=k_xk_yεk​=kx​ky​ has a non-Fermi behavior. (4) The electronic self-energy due to the electron-spin interaction is calculated for a two dimensional system. (5) We study the influence of the amplitude fluctuations of a non-Fermi superconductor on the energy spectrum of the two-dimensional Anderson non-Fermi system. (6) Using the field-theoretical methods we studied the evolution from BCS theory to Bose-Einstein condensation (BEC) for a non-Fermi system. (7) Using the renormalization group approach proposed by Millis we calculated the specific heat coefficient γ(T)γ(T)γ(T) for the magnetic fluctuations with susceptibility χ−1∼δα+∣ω∣α+f(q)χ^{-1}\sim δ^α+| ω| ^α+f(q)χ−1∼δα+∣ω∣α+f(q) near a Lifshitz point.
We calculate the Green's function, particle-hole susceptibility and Cooper pair susceptibility of a 2D electron gas with long range current-current interactions, using Haldane bosonization scheme. We find Luttinger Liquid properties of weakly decaying power-law tails in the spectral function and a Kohn anomaly in the 2$k\sb{F}$ particle-hole susceptibility. At finite temperature, the system exhibits more radical departure from Fermi Liquid. The specific heat was determined being linearly proportional to temperature. The strong correlations of spins and holes are demonstrated in the 2D t-J model of spin-boson and hole-fermion, through the instability against charge ordering we find from our charge susceptibility calculation of bubble and ladder diagrams. We calculate the linear-T dependence of resistivity from the hole self-energy to the second order. The excitation spectra of holon and spinon found from the self-energy calculations agree with the mean-field results to that order.
The self-energy, spectral functions, and susceptibilities of two-dimensional systems with strong ferromagnetic fluctuations are considered within the quasistatic approach. The self-energy at low temperatures TTT has a non-Fermi-liquid form in the energy window $\ensuremath{\mid}\ensuremath{\omega}\ensuremath{\mid}\ensuremath{\lesssim}{\ensuremath{\Delta}}_{0}$ near the Fermi level, where ${\ensuremath{\Delta}}_{0}$ is the ground-state spin splitting for magnetically ordered ground state, and ${\ensuremath{\Delta}}_{0}\ensuremath{\propto}{T}^{1∕2}\phantom{\rule{0.2em}{0ex}}{\mathrm{ln}}^{1∕2}({v}_{F}∕T)$ in the quantum critical regime (vF{v}_{F}vF​ is the Fermi velocity). Spectral functions have a two-peak structure at finite TTT above the magnetically ordered ground state, which implies quasisplitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations. The triplet pairing amplitude in the quasistatic approximation increases with increasing correlation length; at low temperatures $T⪡{\ensuremath{\Delta}}_{0}$ the vertex corrections become important and the Eliashberg approach is not justified. The results for the spectral properties and susceptibilities in the quantum critical regime near charge (spin) instabilities with large enough correlation length $\ensuremath{\xi}⪢{(T∕{v}_{F})}^{\ensuremath{-}1∕3}$ are obtained.
Heavy fermion systems are explained on the basis of the Fermi liquid theory. The specific heat, magnetic susceptibility and electrical resistivity are discussed. Using Anderson's orthogonality theorem, we show that the Fermi liquid is nothing but a local spin singlet state at every site. Heavy fermion systems The Fermi liquid theory is independent of a model Hamiltonian, and can be applied to any system as long as the system remains a Fermi liquid. The theory tells us that even if the electron interaction becomes strong, physical quantities behave as those of the non-interacting Fermi gas. The difference between them with and without interaction is not qualitative but quantitative. As seen at the Mott transition in Hubbard systems, the effective mass of the electron increases near the transition point. As a system realizing such a large effective mass, a Fermi liquid system called the heavy electron system or the heavy fermion system attracts general interest. The heavy fermion systems are composed of the rare earth metals such as Ce and Yb, and actinide atoms such as U. The heavy fermions are nothing but the quasi-particles in the Fermi liquid theory. As a quasi-particle in a strongly correlated electron system, the heavy fermion is an important issue to be studied in the development of the Fermi liquid theory. The heavy fermion realized in f -electron systems is one of the heavy quasi-particles appearing near the Mott transition.
Recently, dynamical mean-field-theory calculations have shown that kinks emerge in the real part of the self-energy of strongly correlated metals close to the Fermi level. This gives rise to a similar behavior in the quasiparticle dispersion relation as well as in the electronic specific heat. Since fff-electron systems are even more strongly correlated than the hitherto studied ddd-electron systems, we apply the dynamical mean-field approach with the numerical renormalization group method as impurity solver to study whether there are kinks in the periodic Anderson model.
We present a numerical study on the non-Fermi liquid behavior of a three-dimensional strongly correlated system. The Hubbard model in a simple cubic lattice is simulated by the dynamical cluster approximation; in particular, the quasi-particle weight is calculated at finite dopings for a range of temperatures. By fitting the quasi-particle weight to the marginal Fermi liquid form at finite doping near the putative quantum critical point, we find evidence of a separatrix between Fermi liquid and non-Fermi liquid regions. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point exist in the non-symmetry broken solution of the three-dimensional interacting electron systems. We also calculate the spectral function, close to the half-filling, and we obtain evidence of pseudogap.
The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M FC * and M L * and intersecting near the binding energy E 0, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E 0 persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as $$M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}$$ . The regime is restored at some temperature T∗∝BT^ * \propto \sqrt B T∗∝B​ . The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.