Related papers: Analytic Solution for the Ground State Energy of t…
We consider a Bose gas in spatial dimension $n>3$ with a repulsive, radially symmetric two-body potential $V$. In the limit of low density $\rho$, the ground state energy per particle in the thermodynamic limit is shown to be $(n-2)|\mathbb…
Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between…
We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit $\rho\to 0$, the ground state energy density satisfies $$e_0(\rho) =…
Knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. For the complete family of parent Hamiltonians with a ground state…
The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the Density Functional Theory, are reformulated in terms of a particular many-body density, which is translational invariant and therefore is relevant for…
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
We develop a general framework to calculate the many-body density of states (DOS) of isolated and interacting quantum systems. Based on the generalized coherent state formalism and the Simon-Lieb bounds for a quantum partition function, our…
A new method for computing the density of states in nuclei making use of an extrapolated form of the tri-diagonal matrix obtained from the Lanczos method is presented. It will be shown that the global, average properties of the entire…
We examine the ground state and excitations of the one dimensional extended Hubbard model with long range interaction. The ground state wavefunctions and low lying excitations are given explicitly in the form of a Jastrow product of two…
The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A…
For a general quantum many-body system, we show that its ground-state entanglement imposes a fundamental constraint on the low-energy excitations. For two-dimensional systems, our result implies that any system that supports anyons must…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…
We prove the following formula for the ground state energy density of a dilute Bose gas with density $\rho$ in $2$ dimensions in the thermodynamic limit \begin{align*} e^{\rm{2D}}(\rho) = 4\pi \rho^2 Y\left(1 - Y \vert \log Y \vert + \left(…
In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the…
We use a combinatorial approach to obtain exact expressions for the many-body density of states of fermionic and bosonic gases with equally spaced single-particle spectra. We identify a mapping that reveals a remarkable property, namely,…
In this study, we explore the precise physical quantities in the thermodynamic limit of the one-dimensional Hubbard model with nonparallel boundary magnetic fields based on the off-diagonal Bethe ansatz solution. A particular emphasis is…
A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-Andr\'e/Harper single-particle models under open boundary conditions is presented here, both…
We obtain the exact ground state for the Calogero-Sutherland problem in arbitrary dimensions. In the special case of two dimensions, we show that the problem is connected to the random matrix problem for complex matrices, provided the…
The quantum $N$-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form $[\hat x,\hat p]=i(1+\beta \hat p^2)$, leading to the existence of a minimal…