Sea-boson theory of Landau-Fermi liquids, Luttinger liquids and Wigner crystals

Reinhold Egger, Hermann Grabert

Girish S. Setlur

We apply the sea-boson method to compute the momentum distribution of a spinless continuum Fermi gas in two space dimensions with short-range repulsive interactions. We find that the ground state of the system is a Landau Fermi liquid($ 0 < Z_{F} < 1 $). We also apply this method to study the one-dimensional system when the interactions are long-ranged gauge interactions. We map the Wigner crystal phase of this system.

Ajit Coimbatore Balram, Csaba Tőke, Jainendra K. Jain

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.

Heinz J. Schulz, Gianaurelio Cuniberti, P. Pieri

Emil J. Bergholtz, A. Karlhede

We consider the lowest Landau level on a torus as a function of its circumference L 1 . When L 1 → 0, the ground state at general rational filling fraction is a crystal with a gap—a Tao–Thouless state. For filling fractions ν = p /(2 pm + 1), these states are the limits of Laughlin's or Jain's wavefunctions describing the gapped quantum Hall states when L 1 → ∞ . For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral fermions (dipoles), or rather to a Luttinger liquid modification thereof, at L 1 ∼ 5 magnetic lengths. Using exact diagonalization we identify this state as a version of the Rezayi–Read state, and find that it develops continuously into the state that is believed to describe the observed metallic phase as L 1 → ∞ . Furthermore, the effective Landau level structure that emerges within the lowest Landau level is found to be a consequence of the magnetic symmetries.

Лев П. Питаевский