Jordan-Wigner Composite-fermion liquids in 2D quantum spin-ice

Inti Sodemann (University of Leipzig)

The Jordan-Wigner transformation and flux attachment are two celebrated statistical transmutation procedures that allow us to understand the emergence of fermions from microscopic models of bosons (or spin-1/2 degrees of freedom). In 2D these two duality maps are in fact equivalent, and the “Jordan-Wigner fermion” is a precise lattice regularization of the “composite fermion” that results from attaching a thin solenoid carrying 2\pi-flux to a hard-core boson. We will exploit this equivalence to introduce a procedure for constructing interesting spin liquid states in 2D quantum spin ice models. Our procedure is inspired by the parton construction of spin liquid states, but we find crucial differences that arise from the fact that the Jordan-Wigner/composite-fermions behave as extended dipolar partons (as opposed to the more traditional point-like Abrikosov-Schwinger fermions). We will illustrate this procedure by constructing a Dirac composite fermi liquid in the subspace corresponding to the six-vertex model and a state with a nested composite fermi surface in the quantum-dimer subspace. We will also discuss the peculiar pseudo-scalar transformations laws under certain microscopic symmetries of these states and their emergent gauge structure at low energies, which feature two U(1) gauge fields but with the Jordan-Wigner/composite-fermions carrying gauge charge under only one of them and behaving as gauge neutral dipoles under the other.