Related papers: Richardson-Gaudin States
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
We introduce the Rydberg Composite, a new class of Rydberg matter where a single Rydberg atom is interfaced with a dense environment of neutral ground state atoms. The properties of the Composite depend on both the Rydberg excitation, which…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper…
We calculate the ground state phase diagram of the homogeneous electron gas in two dimensions within the Hartree-Fock approximation. At high density, we find stable solutions, where the electronic charge and spin density form an…
This paper explores the use of low-dimensional parametric representations of neutron-star equations of state that include discontinuities caused by phase transitions. The accuracies of optimal piecewise-analytic and spectral representations…
The paper summarizes elements of theories and computational methods that we have constructed and applied over the years for the nonperturbative solution of many electron problems, in the absence or presence of strong external fields,…
In this paper we present a model for the electronic excited states of $\pi$ conjugated -acene molecules such as tetracene, pentacene, and hexacene. We use a simple Hubbard model with a limited basis to describe the low lying excitations…
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential…
We derive simplified Faddeev type equations for the three particle T-matrix which are valid in the Hubbard model where only electrons with opposite spins interact. Using the approximation of dynamical mean field theory these equations are…
Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and require solving the…
"Generalized Hydrodynamics" (GHD) stands for a model that describes one-dimensional \textit{integrable} systems in quantum physics, such as ultra-cold atoms or spin chains. Mathematically, GHD corresponds to nonlinear equations of kinetic…
The diagrammatic theory is proposed for the strongly correlated impurity Anderson model. The strongly correlated impurity electrons are hybridized with free conduction electrons. For this system the new diagrammatic approach is formulated.…
In a tight binding framework, we analyze the characteristics of electronic states in strongly disordered materials (hopping sites are placed randomly with no local order) with tunneling matrix elements decaying exponentially in the atomic…
Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n-1)-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure n-qudit states…
Motivated by recent proposals of correlation induced insensitivity of d-wave superconductors to impurities, we develop a simple pairing theory for these systems for up to a moderate strength of disorder. Our description implements the key…
A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on the interior edges of the finite element partition or/and on…
Minimum-uncertainty squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples…
Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description.…
We present the inner products of eigenstates in integrable Richardson-Gaudin models from two different perspectives and derive two classes of Gaudin-like determinant expressions for such inner products. The requirement that one of the…