Groundstatable fermionic wavefunctions and their associated many-body Hamiltonians

TL;DR

This paper investigates the conditions under which certain fermionic wavefunctions with specific correlations can be realized as ground states of many-body Hamiltonians, focusing on the concept of groundstatability and its relation to the sign problem.

Contribution

It introduces the concept of groundstatability for fermionic wavefunctions with fixed kinetic energy and explores its implications for constructing corresponding Hamiltonians, including the effects of Jastrow factors.

Findings

Identifies criteria for groundstatability of fermionic wavefunctions.

Demonstrates how to construct Hamiltonians for groundstatable states.

Analyzes the impact of correlations and Jastrow factors on groundstate realizability.

Abstract

In the vast majority of many-body problems, it is the kinetic energy part of the Hamiltonian that is best known microscopically, and it is the detailed form of the interactions between the particles, the potential energy term, that is harder to determine from first principles. An example is the case of high temperature superconductors: while a tight-binding model captures the kinetic term, it is not clear that there is superconductivity with only an onsite repulsion and, thus, that the problem is accurately described by the Hubbard model alone. Here we pose the question of whether, once the kinetic energy is fixed, a candidate ground state is {\it groundstatable or not}. The easiness to answer this question is strongly related to the presence or the absence of a sign problem in the system. When groundstatability is satisfied, it is simple to obtain the potential energy that will lead to such a ground state. As a concrete case study, we apply these ideas to different fermionic wavefunctions with superconductive or spin-density wave correlations and we also study the influence of Jastrow factors. The kinetic energy considered is a simple next nearest neighbor hopping term.