Related papers: A Unified Graph-Theoretic Framework for Free-Fermi…
The incompatibility of measurements is the key feature of quantum theory that distinguishes it from the classical description of nature. Here, we consider groups of d-outcome quantum observables with prime d represented by non-Hermitian…
The stability of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group framework. A brief introduction to $\phi^4$ theory in four dimensions and the path integral formulation for fermions is given.…
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 complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the…
We study the dissipative dynamics of a class of interacting ``gamma-matrix'' spin models coupled to a Markovian environment. For spins on an arbitrary graph, we construct a Lindbladian that maps to a non-Hermitian model of free Majorana…
Free fermions on Hamming graphs $H(d,q)$ are considered and the entanglement entropy for two types of subsystems is computed. For subsets of vertices that form Hamming subgraphs, an analytical expression is obtained. For subsets…
We study the entanglement Hamiltonian for the ground state of one-dimensional free fermions in the presence of an inhomogeneous chemical potential. In particular, we consider a lattice with a linear, as well as a continuum system with a…
Recent case-by-case studies revealed that the dispersion of low energy excitations in gapless frustration-free Hamiltonians is often quadratic or softer. In this work, we argue that this is actually a general property of such systems. By…
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 with the hidden fermions. This way we can exactly solve the…
The report discusses the slave-fermion representations of the t-J model and describes another representation, in which fermions and bosons are completely commuting and in which the properties of fermions are directly related to the…
We study a generic one-dimensonal quantum model of two flavors (pseudospins) chiral complex fermions by exact diagonalization, which can have local interflavor interaction and superconducting pairings (with all irrelevant terms ignored).…
A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…
We present an infinite sequence of finite graphs with trivial automorphism group and non-trivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are…
Free fermions on Johnson graphs $J(n,k)$ are considered and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an analytical expression is provided by the decomposition in…
We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a…
We present a new technique for efficiently simulating (in polynomial time) a class of one-dimensional (1D) dissipative spin chains that, when mapped to fermions, have quadratic Hamiltonians, with the only nonlinearity coming from…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
We develop a new formulation of the functional renormalization group (RG) for interacting fermions. Our approach unifies the purely fermionic formulation based on the Grassmannian functional integral, which has been used in recent years by…
The formation of coplanar spin spirals is a common motif in the magnetic ordering of many frustrated magnets. For classical antiferromagnets, geometric frustration can lead to a massively degenerate ground state manifold of spirals whose…
Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement…