Related papers: Non-hermitian bosonization
This is an expanded version of a lecture given at the {\it Workshop on Theoretical Methods for Strongly Correlated Fermions}, held at the {\it Centre de Recherches Math\'ematiques}, in Montr\'eal, from May 26 to May 30, 1999. After general…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
Bosonization is one of the most significant frameworks to analyze fermionic systems. In this work, we propose a new bosonization of Dirac fermion coupled with $U(1)$ background gauge field consistent with gauge invariance, global chiral…
We recently derived the Hamiltonian of fermionic composites by an exact procedure of bosonization. In the present paper expand this Hamiltonian in the inverse of the number of fermionic states in the composite wave function and give the…
We develop a bosonization formalism that captures non-perturbatively the interaction effects on the $\mathbf{Q}=0$ continuum of excitations of nodal fermions above one dimension. Our approach is a natural extension of the classic…
Superbosonization formula aims at rigorously calculating fermionic integrals via employing supersymmetry. We derive such a supermatrix representation of superfield integrals and specify integration contours for the supermatrices. The…
We demonstrate that Hermitian, nonlocal parametric pairing processes can induce non-Hermitian topology and skin modes, offering a simple alternative to complex bath engineering. Our model, stabilized by local dissipation and operating in…
We discuss various bosonization schemes from a path integral perspective. Our analysis shows that the existence of different bosonization schemes, such as abelian bosonization of non-abelian models and non-abelian bosonization of fermions…
We analyze the universality of the bosonization rules in non-relativistic fermionic systems in $(2+1)d$. We show that, in the case of linear fermionic dispersion relations, a general fermionic theory can be mapped into a gauge theory in…
We bosonise the complex-boson realisations of the $W_\infty$ and $W_{1+\infty}$ algebras. We obtain nonlinear realisations of $W_\infty$ and $W_{1+\infty}$ in terms of a pair of fermions and a real scalar. By further bosonising the…
We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…
(Revised, with postscript figures appended, corrections and added comments.) We develop and describe new approaches to the problem of interacting Fermions in spatial dimensions greater than one. These approaches are based on generalizations…
Bosonization of degenerate fermions yields insight both into Landau Fermi liquids, and into non-Fermi liquids. We begin our review with a pedagogical introduction to bosonization, emphasizing its applicability in spatial dimensions greater…
We formulate a complete path integral bosonization procedure for any fermionic theory in two dimensions. The method works equally well for massive and massless fermions, and is a generalization of an approach suggested earlier by Andrianov.…
In this chapter we present the sums of Hermitian squares approach to noncommutative polynomial optimization problems. This is an extension of the sums of squares approach for polynomial optimization arising from real algebraic geometry. We…
We review a recently proposed approach to the problem of alternating signs for fermionic many body Monte Carlo simulations in finite temperature simulations. We derive an estimate for fermion wandering lengths and introduce the notion of…
We show that a dynamical supersymmetry can appear in a purely fermionic system. This ``supersymmetry without bosons" is constructed by application of a recently introduced boson-fermion Dyson mapping from a fermion space to a space…
General results on the structure of the bosonization of fermionic systems in $(2+1)$d are obtained. In particular, the universal character of the bosonized topological current is established and applied to generic fermionic current…
It is well known that bosons and fermions exhibit opposite behaviors when experiencing interference, in the sense that bosons have a tendency to bunch whereas fermions have a tendency to antibunch. Recently, this complementarity was…
Boson Sampling is a task that is conjectured to be computationally hard for a classical computer, but which can be efficiently solved by linear-optical interferometers with Fock state inputs. Significant advances have been reported in the…