A simple model of spinless fermions with nested Fermi surface leading to a charge density wave is considered. A quantum critical point (QCP) is obtained by tuning the nesting mismatch of the Fermi surface so that the critical temperature is zero. The amplitudes of de Haas-van Alphen oscillations are calculated using a Lifshitz-Kosevich expression modified by the quasi-particle selfenergy. The amplitudes are considerably reduced by the interaction. The effects of the QCP extend over a large temperature interval.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with
f-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.
Recently, the statistical effect of fermionic superradiance has been verified by a series of experiments both in free space and in a cavity. The Pauli blocking effect can be visualized by a 1/2 scaling of the Dicke transition critical pumping strength against the particle number
Nat for fermions in a trap. However, the evidence for the Fermi surface (FS) nesting effect, which manifests the enhancement of superradiance by Fermi statistics, is still missing. Here we report a scheme for detecting FS nesting with the help of the trap-induced localization on the trap edge. We find two scalings of the critical pumping strength as ${N}_{\mathrm{at}}^{\ensuremath{-}1.33}$ and ${N}_{\mathrm{at}}^{\ensuremath{-}0.67}$ for a moderate particle number when localization enters and the Pauli blocking scaling
1/3 (two-dimensional case) in the ${N}_{\mathrm{at}}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit is unaffected. Further, we find the scaling of the critical pumping strength against the particle number increases with the ratio between the recoil energy and the trap frequency in the direction orthogonal to the pumping direction ${E}_{R}/{\ensuremath{\omega}}_{z}$. The scaling larger than 1 can be identified as a result of the Fermi surface nesting effect. Thus, we find a practical experimental scheme for visualizing the long-desired Fermi surface nesting effect with the help of trap-induced localization in a two-dimensional Fermi gas in a cavity.