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 …

In these lecture notes we aim for a pedagogical introduction to both classical and quantum
integrability. Starting from Liouville integrability and passing through Lax pair and r-matrix …

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 …

An invaluable method for probing the physics of a quantum many-body spin system is a
mapping to noninteracting effective fermions. We find such mappings using only the …

A bstract In this paper we first demonstrate explicitly that the new models of integrable
nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 [36] satisfy …

We present a general study of a large family of exactly integrable quantum chains with
multispin interactions. The exact integrability follows from the algebraic properties of the …

We present a numerical method for the evaluation of the mass gap and the low-lying energy
gaps of a large family of free-fermionic and free-parafermionic quantum chains. The method …

The relationship between the eigenspectrum of Ising and XY quantum chains is well known.
Although the Ising model has a Z (2) symmetry and the XY model a U (1) symmetry, both …

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 …