We study integrable spin chains and quantum and classical cellular automata with
interaction range ℓ≥ 3. This is a family of integrable models for which there was no general …

We study the effects of quenched disorder in a class of quantum chains with (p+ 1)-multispin
interactions exhibiting a free fermionic spectrum, paying special attention to the case p= 2 …

A new family of free fermionic quantum spin chains with multispin interactions was recently
introduced. Here we show that it is possible to build standard quantum Ising chains—but …

We show that a quantum spin system has an exact description by non-interacting fermions if
its frustration graph is claw-free and contains a simplicial clique. The frustration graph of a …

Recently multiple families of spin chain models were found, which have a free fermionic
spectrum, even though they are not solvable by a Jordan-Wigner transformation. Instead, the …

Certain spin chains, such as the quantum Ising chain, have free fermion spectra which can
be expressed as the sum of decoupled two-level fermionic systems. Free parafermions are a …

We show that a quantum spin system has an exact free-parafermion solution if its frustration
graph is an oriented indifference graph. Further, we show that if the frustration graph of a …

In this article we outline the historical development and key results obtained to date for free
parafermionic spin chains. The concept of free parafermions provides a natural N-state …

We calculate the spectral properties of two related families of non-Hermitian free-particle
quantum chains with N-multispin interactions (N= 2, 3,...). The first family have a Z (N) …

We consider quantum spin chains with a hidden free fermionic structure, distinct from the
Jordan-Wigner transformation and its generalizations. We express selected local operators …