# Construction of Many-Body Eigenstates with Displacement Transformations

## TL;DR

This paper introduces a practical method using displacement transformations to compute local integrals of motion, enabling accurate construction of many-body eigenstates beyond Gaussian approximations, including excited states.

## Contribution

The authors develop a systematic approach combining energy minimization and exact diagonalization to efficiently compute many-body eigenstates and local integrals of motion.

## Key findings

- High-precision ground state calculations for large systems
- Efficient construction of multiple excited states
- Extension of Hartree-Fock and configuration interaction theories

## Abstract

Many-body eigenstates beyond the gaussian approximation can be constructed in terms of local integrals of motion (IOM), although their actual computation has been until now a daunting task. We present a new practical computation of IOMS based on displacement transformations. It represents a general and systematic way to extend Hartree-Fock and configuration interaction theories to higher order. Our method combines minimization of energy and energy variance of a reference state with exact diagonalization. We show that our implementation is able to perform ground state calculations with high precision for relatively large systems. Since it keeps track of the IMO's forming a reference state, our method is particularly efficient dealing with excited states, both in accuracy and the number of different states that can be constructed.