Fermionic minimal models

TL;DR

The work proves the existence of fermionic minimal CFTs for all unitary minimal models with central charge $c=1-rac{6}{m(m+1)}$ ($m\ge3$), extending known fermionic cases. It achieves this by applying a fermionization procedure that couples a bosonic minimal model with a non-anomalous $\mathbb{Z}_2$ symmetry to a Kitaev chain, yielding explicit lattice Majorana-chain realizations and a detailed operator content in the fermionic theories. The authors provide a continuum analysis and a spin-chain construction, showing that the fermionic sectors include half-integer spins in $V$, with $U$ and $T$ patterns distinguishing $m$ even/odd cases, and they connect the chiral algebras to SUSY and $W$-type generators depending on $m$. A concrete Potts-based embedding illustrates the construction on a lattice, and numerical checks at the $m=5$ point ($c=4/5$) corroborate the predicted CFT features, linking 1+1d CFT classification to explicit microscopic models.

Abstract

We show that there is a fermionic minimal model, i.e. a 1+1d conformal field theory which contains operators of half-integral spins in its spectrum, for each $c=1-6/m(m+1)$, $m\ge 3$. This generalizes the Majorana fermion for $c=1/2$, $m=3$ and the smallest $\mathcal{N}{=}1$ supersymmetric minimal model for $c=7/10$, $m=4$. We provide explicit Hamiltonians on Majorana chains realizing these fermionic minimal models.

Figures (1)

• Figure 1: The entanglement entropy of the converted 3-state Potts model at $J=f=1$, $U=10^4$, on a chain of $N=100$ pairs of spin $1/2$ sites. The dots show the numerically computed values; the curved line is the theoretical prediction.