Related papers: Gell-Mann and Low formula for degenerate unperturb…
The non-Hermiticity of the system gives rise to a distinct knot topology in the complex eigenvalue spectrum, which has no counterpart in Hermitian systems. In contrast, the singular values of a non-Hermitian (NH) Hamiltonian are always real…
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator…
Motivated by recent neutron and x-ray observations in V$_2$O$_3$, we derive the effective Hamiltonian in the strong coupling limit of an Hubbard model with three degenerate t_{2g} states containing two electrons coupled to spin S = 1, and…
We clarify the notion of Wilsonian renormalization group (RG) invariance in supersymmetric gauge theories, which states that the low-energy physics can be kept fixed when one changes the ultraviolet cutoff, provided appropriate changes are…
We study the tangential interpolation problem for a passive transfer function in standard state-space form. We derive new interpolation conditions based on the computation of a deflating subspace associated with a selection of spectral…
The conventional toy-model constructions of phase diagrams often use various versions of the standard Hermitian Bose-Hubbard Hamiltonians $H$. These studies were recently extended to cover several non-Hermitian PT-symmetric versions of the…
In this paper we continue our analysis on deformed canonical commutation relations and on their related pseudo-bosons and bi-coherent states. In particular, we show how to extend the original approach outside the Hilbert space…
Given a graph $\Gamma = (V, E)$ on $n$ vertices and $m$ edges, we define the Erd\H{o}s-R\'{e}nyi graph process with host $\Gamma$ as follows. A permutation $e_1,\dots,e_m$ of $E$ is chosen uniformly at random, and for $t\leq m$ we let…
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by showing that approximate symmetry operators---unitary operators whose commutators with the Hamiltonian…
Considering a "random walk in a random environment" in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization"…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
Non-Hermitian systems exhibiting topological properties are attracting growing interest. In this work, we propose an algorithm for solving the ground state of a non-Hermitian system in the matrix product state (MPS) formalism based on a…
We consider a charged particle, spin 1/2, with relativistic kinetic energy and minimally coupled to the quantized Maxwell field. Since the total momentum is conserved, the Hamiltonian admits a fiber decomposition as $H(P)$, $P\in \BbbR^3$.…
A one-parameter generalized Wigner-Heisenberg algebra( WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule $[\hat{x}, \hat{p}_{\lambda}] = i(1 + 2\lambda \hat{R})$ and also highlights the dynamical…
For a general self-adjoint Hamiltonian operator $H_0$ on the Hilbert space $L^2(\RE^d)$, we determine the set of all self-adjoint Hamiltonians $H$ on $L^2(\RE^d)$ that dynamically confine the system to an open set $\Omega \subset \RE^d$…
The t-J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields…
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
We consider perturbed discrete tight-binding models in $\ell^2(\mathbb{Z_h},\mathcal{G})$ describing union of quantum particles with localized interactions, where $\mathbb{Z_h}$ is the 1D lattice $h\mathbb{Z_h}$, $h > 0$, and $\mathcal G$…
The dynamics of open quantum systems is determined by avoided and true crossings of eigenvalue trajectories of a non-Hermitian Hamiltonian. The phases of the eigenfunctions are not rigid so that environmentally induced spectroscopic…