Related papers: 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…
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 generalization of free fermions, which have long…
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 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…
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…
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…
We study the entanglement Hamiltonian for fermionic hopping models on rings and open chains and determine single-particle spectra, eigenfunctions and the form in real space. For the chain, we find a commuting operator as for the ring and…
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…
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 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…
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…
Using a parent Hermitian tight-binding model on a bipartite lattice with chiral symmetry, we theoretically generate non-Hermitian models for free fermions with $p$ orbitals per unit cell satisfying a complex generalization of chiral…
We study the entanglement Hamiltonian for finite intervals in infinite quantum chains for two different free-particle systems: coupled harmonic oscillators and fermionic hopping models with dimerization. Working in the ground state, the…
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…
The spectrum of the non-hermitian asymmetric XXZ-chain with additional non-diagonal boundary terms is studied. The lowest lying eigenvalues are determined numerically. For the ferromagnetic and completely asymmetric chain that corresponds…
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…
We study the entanglement Hamiltonian for free-fermion chains with a particular form of inhomogeneity. The hopping amplitudes and chemical potentials are chosen such that the single-particle eigenstates are related to discrete orthogonal…
A family of $\mathbb Z_n$-symmetric non-Hermitian models of Baxter was shown by Fendley to be exactly solvable via a parafermionic generalization of the Clifford algebra. We study these models with spatially random couplings, and obtain…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…