Related papers: A Brief History of Free Parafermions
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 simple generalisation of this idea to $Z(N)$-symmetric clock…
The spectrum of the quantum Ising chain can be found by expressing the spins in terms of free fermions. An analogous transformation exists for clock chains with $Z_n$ symmetry, but is of less use because the resulting parafermionic…
We consider the calculation of ground-state expectation values for the non-Hermitian Z(N) spin chain described by free parafermions. For N=2 the model reduces to the quantum Ising chain in a transverse field with open boundary conditions.…
I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local…
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 models are described in terms of free-fermionic…
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 free fermions emerge as a result of a rather intricate…
The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows…
We introduce a new a family of $Z(N)$ multispins quantum chains with a free-fermionic ($N=2$) or free-parafermionic ($N>2$) eigenspectrum. The models have $(p+1)$ interacting spins ($p=1,2,\dots$), being Hermitian in the $Z(2)$ (Ising) case…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
A large family of multispin interacting one-dimensional quantum spin models with $Z(N)$ symmetry and a free-particle eigenspectra are known in the literature. They are free-fermionic ($N=2$) and free-parafermionic ($N\geq 2$) quantum…
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 frustration graph $G$ of a Hamiltonian $H$, i.e., the network of…
We calculated the spectral properties of two related families of non-Hermitian free-particle quantum chains with $N$-multispin interactions ($N=2,3,\ldots$). The first family have a $Z(N)$ symmetry and are described by free parafermions.…
Results are given for the ground state energy and excitation spectrum of a simple $N$-state $Z_N$ spin chain described by free parafermions. The model is non-Hermitian for $N \ge 3$ with a real ground state energy and a complex excitation…
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 with inhomogeneous couplings -- which have the same…
We consider the general $\mathbb{Z}_2$-symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and $\mathbb{Z}_n$-symmetric BBS $\tau^{(2)}$-model…
Extensive numerical analysis of the eigenspectra of the $SU_q(N)$ invariant Perk-Schultz Hamiltonian shows some simple regularities for a significant part of the eigenspectrum. Inspired by those results we have found two set of solutions of…
We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in \cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density…
Many years ago Baxter introduced an inhomogeneous two-dimensional classical spin model, now called the $\tau_2(t)$ model with free boundary conditions, and he specialized the resulting quantum spin-chain Hamiltonian in a special limit to a…
Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…
Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech.,…