Spin chains and chiral lattice fermions

H. B. Thacker

The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter’s corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by fermionized nearest-neighbor Heisenberg spin chain operators. The transformation properties of the local lattice fermion operators under a boost provide a natural and precise way of generalizing the chiral structure of a continuum Dirac field to the lattice. The resulting formulation differs from both the Wilson and staggered (Kogut-Susskind) prescriptions. In particular, an axial Q5 rotation is sitewise local, while the vector charge rotation mixes nearest neighbors on even and odd sublattices. One of the most interesting developments in the theory of solvable two-dimensional lattice statistics models is Baxter’s invention of the “corner transfer matrix ” (CTM)[[1]]. In the same sense that an ordinary (row-to-row) transfer matrix can be viewed as an operator which translates by one row of sites on a lattice, the CTM may be defined as an operator which rotates around a central

Rodrigo G. Pereira

Manuel Valiente

We consider one-dimensional theories of chiral fermions and bosons on a lattice, which arise as edge states of two-dimensional topological matter breaking time-reversal invariance. We show that hard core bosons or their spin chain equivalent exhibit properties that are similar to free fermions, solving the many-body problem exactly. For fermions, we study the effect of a static impurity exactly and show the orthogonality catastrophe in the continuum limit via bosonization. The interacting many-fermion problem in the continuum limit is solved exactly using simple momentum conservation arguments.

Fabrizio G. Oliviero, Weslei Bernardino Fontana, Rodrigo G. Pereira

We use junctions of critical spin-1 chains as the basic elements to construct a honeycomb network that harbors a gapless chiral spin liquid phase. The low-energy modes are described by spin-1 Majorana fermions that form a two-dimensional Fermi surface when the interactions at the junctions are tuned to the vicinity of chiral fixed points with staggered chirality. We discuss the physical properties and the stability of this chiral spin liquid phase against perturbations from the point of view of the effective field theory for the network. We find clear connections with the excitation spectrum obtained in parton constructions on the kagome lattice.

Jan Smit A