A Class of Fermi Liquids

Григорий Ефимович Воловик

Krzysztof Byczuk, Józef Spałek

We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi- or Luttinger-liquid states. In the statistical spin liquid the double occupancies are excluded from the physical space. Each of the above three cases (Fermi, Luttinger, and spin liquids) represents a universality class for the interacting many-particle fermion systems. The properties of the spin liquid such as the chemical potential, the entropy, and the magnetization curve, as well as the quasiparticle structure are briefly discussed.

Natan Andrei, Michael R. Douglas, Andrés Jerez

We identify a non-Fermi-liquid class of fixed points describing the infrared behavior of interacting chiral fermions in one dimension. The thermodynamic properties and asymptotic correlation functions are characterized by universal exponents, which we determine by means of conformal and Bethe Ansatz techniques. The mechanism leading to the breakdown of Fermi-liquid theory is quite general and can be expected to be realized in systems with broken T invariance. As an example we study the edge states of interacting quantum Hall effect systems, where we calculate the universal NMR response.

C. Di Castro, Roberto Raimondi

Sadao Nakajima, Yutaka Toyozawa, Ryuzo Abe

Ori Grossman, Erez Berg

Determinant quantum Monte Carlo (DQMC) is a powerful numerical technique to study many-body fermionic systems. In recent years, several classes of sign-free (SF) models have been discovered, where the notorious sign problem can be circumvented. However, it is not clear what the inherent physical characteristics and limitations of SF models are. In particular, which zero-temperature quantum phases of matter are accessible within such models, and which are fundamentally inaccessible? Here, we show that a model belonging to any of the known SF classes within DQMC cannot have a stable Fermi-liquid ground state in spatial dimension d≥2, unless the antiunitary symmetry that prevents the sign problem is spontaneously broken (for which there are currently no known examples in SF models). For SF models belonging to one of the symmetry classes (where the absence of the sign problem follows from a combination of nonunitary symmetries of the fermionic action), any putative Fermi liquid fixed point generically includes an attractive Cooper-like interaction that destabilizes it. In the recently discovered lower-symmetry classes of SF models, the Fermi surface (FS) is generically unstable even at the level of the quadratic action. Our results suggest a fundamental link between Fermi liquids and the fermion sign problem. Interestingly, our results do not rule out a non-Fermi-liquid ground state with a FS in a sign-free model.