# Quantum fluctuations beyond the Gutzwiller approximation

## TL;DR

This paper introduces a straightforward scheme to incorporate quantum fluctuation corrections into the Gutzwiller approximation for lattice Hamiltonians, improving the accuracy of response function calculations.

## Contribution

The method is applicable to generic multi-band models without assumptions on the dynamics of variational parameters, extending the Gutzwiller approximation's capabilities.

## Key findings

- Quantum fluctuations reproduce the magnetic susceptibility behavior seen in dynamical mean field theory.
- The method accurately captures the smooth behavior of susceptibility across the Mott transition.
- It recovers known results and provides new insights into quantum fluctuation effects.

## Abstract

We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multi-band lattice Hamiltonian without any assumption about the dynamics of the variational correlation parameters that define the Gutzwiller wavefunction, and which thus behave as genuine dynamical degrees of freedom that add on those of the variational uncorrelated Slater determinant. We apply the method to the standard half-filled single-band Hubbard model. We are able to recover known results, but, as by-product, we also obtain few novel ones. In particular, we show that quantum fluctuations can reproduce almost quantitatively the behaviour of the uniform magnetic susceptibility uncovered by dynamical mean field theory, which, though enhanced by correlations, is found to be smooth across the paramagnetic Mott transition. By contrast, the simple Gutzwiller approximation predicts that susceptibility to diverge at the transition.