Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

Abstract

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, ${\alpha }_n(N)$ and ${\beta }_n(N)$, asymptotic forms $\alpha (z)$ and $\beta (z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\mathcal{E}}_0=\inf \left[\alpha (z)-2\beta (z)\right]$.

10 pages REVTex3.0, 3 PS figures

Cited by in corpus (17)

• Two-Body Random Ensembles: From Nuclear Spectra to Random Polynomials
• Quantum computed moments correction to variational estimates
• 2D XXZ Model ground state Properties using an analytic Lanczos Expansion
• On the finite size behavior of quantum collective spin systems
• The Lanczos Algorithm for extensive Many-Body Systems in the Thermodynamic Limit
• Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method
• Noise-robust ground state energy estimates from deep quantum circuits
• Precision ground-state energy calculation for the water molecule on a superconducting quantum processor
• Reaching the continuum limit in lattice gauge theory - without a computer
• Long Range Interactions in Quantum Many Body Problem in One-Dimension:Ground State
• Eigenvalue distributions from a star product approach
• Arbitrary Ground State Observables from Quantum Computed Moments
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Analytic calculation of the mass gap in U(1)_{2+1} lattice gauge theory
• Moments-based quantum computation of the electric dipole moment of molecular systems
• Chemistry beyond the Hartree-Fock limit via quantum computed moments
• Quantum solver for single-impurity Anderson models with particle-hole symmetry