Related papers: Generating function for Hermitian and non-Hermitia…

We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin integrals. The…

Non-Hermitian (NH) lattice Hamiltonians display a unique kind of energy gap and extreme sensitivity to boundary conditions. Due to the NH skin effect, the separation between edge and bulk states is blurred and the (conventional)…

Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the…

A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and…

The Hermitian matrix model with general linear symmetry is argued to decouple into a finite unitary matrix model that contains metastable multidimensional lattice configurations and a fermion determinant. The simplest metastable state is a…

Topological edge states in gaps of non-Hermitian systems are robust due to topological protection. Using the non-Hermitian Floquet Su-Schrieffer-Heeger model, we show that this robustness can break down: edge states may be suppressed by…

We examine the notion and properties of the non-Hermitian effective Hamiltonian of an unstable system using as an example potential resonance scattering with a fixed angular momentum. We present a consistent self-adjoint formulation of the…

We first construct a dynamical systems model which in its steady-state serves as an analytic continuation of the completed Riemann zeta function over the entire critical strip. The resulting mathematical construct involves a linear…

We apply the recently introduced method of hermitization to study in the large $N$ limit non-hermitean random matrices that are drawn from a large class of circularly symmetric non-Gaussian probability distributions, thus extending the…

Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk…

We construct an exactly solvable $\mathscr{PT}-$symmetric non-Hermitian model where a spin$-\frac{1}{2}$ isotropic quantum Heisenberg spin chain is coupled to two spin$-\frac{1}{2}$ Kondo impurities at its boundaries with coupling strengths…

We define discrete generating series for arbitrary functions \( f \colon \mathbb{Z}^n \rightarrow \mathbb{C} \) and derive functional relations that these series satisfy. For linear difference equations with constant coefficients, we…

Starting with a quantum particle on a closed manifold without boundary, we consider the process of generating boundaries by modding out by a group action with fixed points, and we study the emergent quantum dynamics on the quotient…

A single quantum emitter coupled to a structured non-Hermitian environment shows anomalous bound states and real-time dynamics without Hermitian counterparts, as shown in [Gong et al., Phys. Rev. Lett. 129, 223601 (2022)]. In this work, we…

Let $G$ be a split real connected Lie group with finite center. In the first part of the paper we define and study formal elementary spherical functions. They are formal power series analogues of elementary spherical functions on $G$ in…

Using the Cornwall-Jackiw-Tomboulis effective action $\Gamma(S)$ for composite operators ($S$ is the full fermion propagator), the phase structure of the massless (2 + 1)-dimensional Thirring model with four-component spinors is…

We investigate the generating functions of multi-colored discrete disks with non-homogenous boundary conditions in the context of the Hermitian multi-matrix model where the matrices are coupled in an open chain. We show that the study of…

Excited bound states are often understood within scattering based theories as resulting from the collision of a particle on a target via a short-range potential. We show that the resulting formalism is non-Hermitian and describe the Hilbert…

Critical edge states appear at the bulk gap closing points of topological transitions. Their emergence signify the existence of topologically nontrivial critical points, whose descriptions fall outside the scope of gapped topological…

The non-Hermitian skin effect is an intriguing physical phenomenon, in which all eigen-modes of a non-Hermitian lattice become localized at boundary regions. While such an exotic behavior has been demonstrated in various physical platforms,…