Presenting exact solutions for the two-dimensional periodic Anderson model with finite and nonzero on-site interactions $U>0,$ we describe a rigorous non-Fermi-liquid phase in normal phase and two dimensions. This new state emerges in multiband interacting Fermi systems above half filling, being generated by a flat-band effect. The momentum distribution function ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ together with its derivatives of any order is continuous. The state possesses a well-defined Fermi energy ${(e}_{F}),$ but the Fermi momentum concept is not definable, so the Fermi surface in $\stackrel{\ensuremath{\rightarrow}}{k}$ space is missing. The state emerges in the vicinity of a Mott insulating phase when lattice distortions are present and is highly degenerated and paramagnetic. A gap is present at high U in the density of low-lying excitations. During low-lying excitations, quasiparticles are not created above the Fermi level, only the number of particles at ${e}_{F}$ increases.Presenting exact solutions for the two-dimensional periodic Anderson model with finite and nonzero on-site interactions $U>0,$ we describe a rigorous non-Fermi-liquid phase in normal phase and two dimensions. This new state emerges in multiband interacting Fermi systems above half filling, being generated by a flat-band effect. The momentum distribution function ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ together with its derivatives of any order is continuous. The state possesses a well-defined Fermi energy ${(e}_{F}),$ but the Fermi momentum concept is not definable, so the Fermi surface in $\stackrel{\ensuremath{\rightarrow}}{k}$ space is missing. The state emerges in the vicinity of a Mott insulating phase when lattice distortions are present and is highly degenerated and paramagnetic. A gap is present at high U in the density of low-lying excitations. During low-lying excitations, quasiparticles are not created above the Fermi level, only the number of particles at ${e}_{F}$ increases.

arXiv:cond-mat/0104195Physical review. B, Condensed matterJul 9, 200134 citations

Binary distribution function of degenerate fermi systems

R. N. Petrashko, I. R. Yukhnovskii

Theoretical and Mathematical PhysicsOct 1, 19730 citations

Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems

Katharina Laubscher, Clara S. Weber, Dante Marvin Kennes +4 more

We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors $\ensuremath{\nu}=1/(2l+1)$, where $l$ is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has $2l+1$ different branches that cannot be connected adiabatically, reflecting the $(2l+1)$ -fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.We study fractional boundary charges (FBCs) for two classes of strongly interacting systems. First, we study strongly interacting nanowires subjected to a periodic potential with a period that is a rational fraction of the Fermi wavelength. For sufficiently strong interactions, the periodic potential leads to the opening of a charge density wave gap at the Fermi level. The FBC then depends linearly on the phase offset of the potential with a quantized slope determined by the period. Furthermore, different possible values for the FBC at a fixed phase offset label different degenerate ground states of the system that cannot be connected adiabatically. Next, we turn to the fractional quantum Hall effect (FQHE) at odd filling factors $\ensuremath{\nu}=1/(2l+1)$, where $l$ is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has $2l+1$ different branches that cannot be connected adiabatically, reflecting the $(2l+1)$-fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.

arXiv:2101.10301Physical review. B./Physical review. BJul 27, 20218 citations

Phase separation in the binary-alloy problem: The one-dimensional spinless Falicov-Kimball model

James K. Freericks, C. Gruber, Nicolas Macris

The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively, equal to p/q, ${\mathit{p}}_{\mathit{i}}$ /q, with p relatively prime to q and ${\mathit{p}}_{\mathit{i}}$ /q close enough to 1/2, we find that in the ground state the ion configuration has a period q. The situation is analogous to the Peierls instability, where the usual arguments predict a period-q state that produces a gap at the Fermi level and is insulating. However for ${\mathit{p}}_{\mathit{i}}$ /q far enough from 1/2, this phase becomes unstable against phase separation. The ground state is a mixture of a period-q ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from 1/2. \textcopyright{} 1996 The American Physical Society.The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively, equal to p/q, ${\mathit{p}}_{\mathit{i}}$/q, with p relatively prime to q and ${\mathit{p}}_{\mathit{i}}$/q close enough to 1/2, we find that in the ground state the ion configuration has a period q. The situation is analogous to the Peierls instability, where the usual arguments predict a period-q state that produces a gap at the Fermi level and is insulating. However for ${\mathit{p}}_{\mathit{i}}$/q far enough from 1/2, this phase becomes unstable against phase separation. The ground state is a mixture of a period-q ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from 1/2. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9602042Physical review. B, Condensed matterJun 15, 199622 citations

On Large Densities in Fermi Systems

A. A. Zamyatin, V. A. Malyshev

Mathematical NotesNov 1, 20050 citations

Presenting exact solutions for the two-dimensional periodic Anderson model with finite and nonzero on-site interactions

U>0,

we describe a rigorous non-Fermi-liquid phase in normal phase and two dimensions. This new state emerges in multiband interacting Fermi systems above half filling, being generated by a flat-band effect. The momentum distribution function ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ together with its derivatives of any order is continuous. The state possesses a well-defined Fermi energy

{(e}_{F}),

but the Fermi momentum concept is not definable, so the Fermi surface in $\stackrel{\ensuremath{\rightarrow}}{k}$ space is missing. The state emerges in the vicinity of a Mott insulating phase when lattice distortions are present and is highly degenerated and paramagnetic. A gap is present at high U in the density of low-lying excitations. During low-lying excitations, quasiparticles are not created above the Fermi level, only the number of particles at

{e}_{F}

increases.

l

is an integer. For a Corbino disk threaded by an external flux, we find that the FBC depends linearly on the flux with a quantized slope that is determined by the filling factor. Again, the FBC has

2l+1

different branches that cannot be connected adiabatically, reflecting the

(2l+1)

-fold degeneracy of the ground state. These results allow for several promising and strikingly simple ways to probe strongly interacting phases via boundary charge measurements.

{\mathit{p}}_{\mathit{i}}

/q, with p relatively prime to q and

{\mathit{p}}_{\mathit{i}}

/q close enough to 1/2, we find that in the ground state the ion configuration has a period q. The situation is analogous to the Peierls instability, where the usual arguments predict a period-q state that produces a gap at the Fermi level and is insulating. However for

{\mathit{p}}_{\mathit{i}}

/q far enough from 1/2, this phase becomes unstable against phase separation. The ground state is a mixture of a period-q ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from 1/2. \textcopyright{} 1996 The American Physical Society.