Related papers: Entanglement in Fermionic Chains and Bispectrality
We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fr\"ohlich, Su-Schrieffer-Heeger, and Heisenberg models with quantum phonons,…
We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically…
Fermionic artificial matter realized with cold atoms grants access to an unprecedented degree of control on sophisticated many-body effects with an enhanced flexibility of the operating conditions. We consider three-component fermions with…
We derive the relativistic energy spectrum for the modified Dirac equation by adding a harmonic oscillator potential where the coordinates and momenta are assumed to obey the commutation relation…
We discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and…
Theory of quantum electrodynamics in three spatial-time dimension is applied to the two-dimensional $S=1/2$ quantum Heisenberg antiferromagnet in order to investigate a doped hole in high-temperature superconductors. Strong coupling…
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82,…
We present an extensive search for a general class of flipped $SU(5)$ models built within the free fermionic formulation of the heterotic string. We describe a set of algorithms which constitute the basis for a computer program capable of…
We present a detailed study of the fidelity, the entanglement entropy, and the entanglement spectrum, for a dimerized chain of spinless fermions---a simplified Su-Schrieffer-Heeger (SSH) model---with open boundary conditions which is a…
Electronic transmission in bent quantum wires modeled by the tight binding Hamiltonian, and clamped between ideal, semi-infinite leads is studied. The effect of `bending' the chain is simulated by introducing a non-zero hopping between the…
We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that…
We consider the symmetry resolved R\'enyi entropies in the one dimensional tight binding model, equivalent to the spin-1/2 XX chain in a magnetic field. We exploit the generalised Fisher-Hartwig conjecture to obtain the asymptotic behaviour…
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential…
We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and…
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. These Hamiltonians, say $K_{1}$ and $K_{2}$, result to be…
The dualities that map hard-to-solve, interacting theories to free, non-interacting ones often trigger a deeper understanding of the systems to which they apply. However, simplifying assumptions such as Lorentz invariance, low…
We investigate the dynamics of Entanglement Hamiltonians (EHs) in dissipative free-fermionic systems using a recent operator-based formulation of the quasiparticle picture. Focusing on gain and loss dissipation, we study the post-quench…
A new one-dimensional fermion model depending on two independent interaction parameters is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian of the model contains the Hubbard interaction and correlated hopping as…
In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between…
We calculate the entanglement entropy of a non-contiguous subsystem of a chain of free fermions. The starting point is a formula suggested by Jin and Korepin, \texttt{arXiv:1104.1004}, for the reduced density of states of two disjoint…