Fermi Operators

Kang-Le Cai, Meng Cheng

Disorder operators are a type of non-local observables for quantum many-body systems, measuring the fluctuations of symmetry charges inside a region. It has been shown that disorder operators can reveal global aspects of many-body states that are otherwise difficult to access through local measurements. We study the disorder operator for U(1) (charge or spin) symmetry in two-dimensional Fermi and non-Fermi liquid states, using the multidimensional bosonization formalism. For a region $A$, the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asymptotically as $l_A\ln l_A$, with $l_A$ being the linear size of the region $A$. We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of the Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point the scaling behavior of the charge disorder operators is drastically modified to $l_A \ln^2 l_A$. We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as $l_A$.

Hong-Yi Fan

The mapping of the SUn group transformation in Grassmann number space into unitary normally ordered and antinormally ordered Fermi operator realizations in Hilbert space are investigated. The unitary Fermi operators are evaluated in fermion coherent state representation using the ‘‘integration within ordered product’’ technique for a fermionic system. Some new Fermi operator identities are thus obtained.

Zsolt Gulácsi

Abstract Recently, it has been shown that the quantum spin–1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [1] and 2D [2] as well. In this paper, using the same technique based on an extended Jordan–Wigner transformation, we show in 1D that the quantum spin-1/2 operators can be exactly transformed also in spinful canonical Fermi operators of spin-1/2 fermions that are belong to two bands.

Michael Stone