We consider a one-dimensional system of electrons interacting via a short-range repulsion and coupled to phonons close to the metal-insulator transition at half-filling. We argue that the metal-insulator transition can be described as a standard one-dimensional incommensurate to commensurate transition, even if the electronic system is coupled to the lattice distortion. By making use of known results for this transition, we prove that low-momentum phonons, with the inclusion of the 4kF (≃2π near half-filling) scattering, do not play any relevant role close to the metal-insulator transition, unless their coupling to the electrons is large in comparison with the other energy scales present in the problem. In other words the effective strength of the low-momentum transferred electron-phonon coupling does not increase close to the metal-insulator transition, even though the effective velocity of the mobile carriers is strongly diminished.We consider a one-dimensional system of electrons interacting via a short-range repulsion and coupled to phonons close to the metal-insulator transition at half-filling. We argue that the metal-insulator transition can be described as a standard one-dimensional incommensurate to commensurate transition, even if the electronic system is coupled to the lattice distortion. By making use of known results for this transition, we prove that low-momentum phonons, with the inclusion of the 4kF (≃2π near half-filling) scattering, do not play any relevant role close to the metal-insulator transition, unless their coupling to the electrons is large in comparison with the other energy scales present in the problem. In other words the effective strength of the low-momentum transferred electron-phonon coupling does not increase close to the metal-insulator transition, even though the effective velocity of the mobile carriers is strongly diminished.

arXiv:cond-mat/9507070International Journal of Modern Physics BMay 30, 19963 citations

Quantum model for commensurate-incommensurate transitions

Steven F. Howes, Leo P. Kadanoff, Marcel den Nijs

Nuclear Physics BJan 1, 1983172 citations

Quantum critical behavior of antiferromagnetic itinerant systems with van Hove singularities

A. A. Katanin

The interplay of magnetic and superconducting fluctuations in two-dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization-group (fRG) approach. While the fRG flow has to be stopped at a certain minimal temperature ${T}_{\text{RG}}^{\text{min}}$ , we study temperature dependence of magnetic and superconducting susceptibilities below ${T}_{\text{RG}}^{\text{min}}$ to obtain the crossover temperatures to the regime with strong magnetic and superconducting fluctuations. Near half filling we obtain the largest crossover temperature, corresponding to a regime with strong commensurate magnetic fluctuations, which is replaced by a regime with strong incommensurate fluctuations further away from half filling. With further decreasing density the system undergoes quantum phase transition from incommensurate to paramagnetic phase. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the magnetic quantum-critical point is found almost linear in temperature.The interplay of magnetic and superconducting fluctuations in two-dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization-group (fRG) approach. While the fRG flow has to be stopped at a certain minimal temperature ${T}_{\text{RG}}^{\text{min}}$, we study temperature dependence of magnetic and superconducting susceptibilities below ${T}_{\text{RG}}^{\text{min}}$ to obtain the crossover temperatures to the regime with strong magnetic and superconducting fluctuations. Near half filling we obtain the largest crossover temperature, corresponding to a regime with strong commensurate magnetic fluctuations, which is replaced by a regime with strong incommensurate fluctuations further away from half filling. With further decreasing density the system undergoes quantum phase transition from incommensurate to paramagnetic phase. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the magnetic quantum-critical point is found almost linear in temperature.

arXiv:0906.4435Physical Review BApr 30, 20109 citations

Mott transitions in three-component Falicov-Kimball model

Duong-Bo Nguyen, Minh-Tien Tran

Metal-insulator transitions are studied within a three-component Falicov-Kimball model, which mimics a mixture of one-component and two-component fermionic particles with local repulsive interactions in optical lattices. Within the model, the two-component fermionic particles are able to hop in the lattice, while the one-component fermionic particles are localized. The model is studied by using the dynamical mean-field theory with exact diagonalization. Its homogeneous solutions establish Mott transitions for both commensurate and incommensurate fillings between one-third and two-thirds. At commensurate one-third and two-thirds fillings, the Mott transition occurs for any density of hopping particles, while at incommensurate fillings, the Mott transition can occur only for density one-half of hopping particles. At half-filling, depending on the repulsive interactions, the reentrant effect of the Mott insulator is observed. As increasing local interaction of hopping particles, the first insulator-metal transition is continuous, whereas the second metal-insulator transition is discontinuous. The second metal-insulator transition crosses a finite region where both metallic and insulating phase coexist. At third-filling, the Mott transition is established only for strong repulsive interactions. A phase separation occurs together with the phase transition.Metal-insulator transitions are studied within a three-component Falicov-Kimball model, which mimics a mixture of one-component and two-component fermionic particles with local repulsive interactions in optical lattices. Within the model, the two-component fermionic particles are able to hop in the lattice, while the one-component fermionic particles are localized. The model is studied by using the dynamical mean-field theory with exact diagonalization. Its homogeneous solutions establish Mott transitions for both commensurate and incommensurate fillings between one-third and two-thirds. At commensurate one-third and two-thirds fillings, the Mott transition occurs for any density of hopping particles, while at incommensurate fillings, the Mott transition can occur only for density one-half of hopping particles. At half-filling, depending on the repulsive interactions, the reentrant effect of the Mott insulator is observed. As increasing local interaction of hopping particles, the first insulator-metal transition is continuous, whereas the second metal-insulator transition is discontinuous. The second metal-insulator transition crosses a finite region where both metallic and insulating phase coexist. At third-filling, the Mott transition is established only for strong repulsive interactions. A phase separation occurs together with the phase transition.

arXiv:1308.6098Physical Review BJan 24, 20137 citations

Commensurate and Incommensurate Transitions for Interacting Particles

Cosima Schuster, Rudolf A. Römer, Michael Schreiber

Journal of the Physical Society of JapanJan 3, 20031 citation

{T}_{\text{RG}}^{\text{min}}

, we study temperature dependence of magnetic and superconducting susceptibilities below

{T}_{\text{RG}}^{\text{min}}

to obtain the crossover temperatures to the regime with strong magnetic and superconducting fluctuations. Near half filling we obtain the largest crossover temperature, corresponding to a regime with strong commensurate magnetic fluctuations, which is replaced by a regime with strong incommensurate fluctuations further away from half filling. With further decreasing density the system undergoes quantum phase transition from incommensurate to paramagnetic phase. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the magnetic quantum-critical point is found almost linear in temperature.