# Ghost-spin chains, entanglement and $bc$-ghost CFTs

## TL;DR

This paper investigates one-dimensional ghost-spin chains with various interactions, establishing their connection to $bc$-ghost conformal field theories in the continuum limit through analytical and transformation techniques.

## Contribution

It introduces new models of ghost-spin chains with different Hamiltonians and demonstrates their continuum limit corresponds to $bc$-ghost CFTs, expanding understanding of ghost-spin systems.

## Key findings

- Finite ghost-spin chains with Ising interactions clarified entanglement properties.
- Infinite ghost-spin chains with hopping interactions linked to $bc$-ghost CFTs.
- Fermionic variables via Jordan-Wigner transformation established for continuum limit analysis.

## Abstract

We study 1-dimensional chains of ghost-spins with nearest neighbour interactions amongst them, developing further the study of ghost-spins in previous work, defined as 2-state spin variables with indefinite norm. First we study finite ghost-spin chains with Ising-like nearest neighbour interactions: this helps organize and clarify the study of entanglement earlier and we develop this further. Then we study a family of infinite ghost-spin chains with a different Hamiltonian containing nearest neighbour hopping-type interactions. By defining fermionic ghost-spin variables through a Jordan-Wigner transformation, we argue that these ghost-spin chains lead in the continuum limit to the $bc$-ghost CFTs.