Effective Hamiltonian with holomorphic variables

TL;DR

This paper reformulates the pure-quantum self-consistent harmonic approximation using holomorphic variables, enabling direct analysis of Hamiltonians expressed with bosonic creation and annihilation operators.

Contribution

It introduces a holomorphic variable approach to PQSCHA, broadening its applicability to general bosonic Hamiltonians.

Findings

Allows direct treatment of bosonic Hamiltonians

Provides a new holomorphic path integral formulation

Enhances the analytical tools for quantum systems

Abstract

The pure-quantum self-consistent harmonic approximation (PQSCHA) permits to study a quantum system by means of an effective classical Hamiltonian. In this work the PQSCHA is reformulated in terms of the holomorphic variables connected to a set of bosonic operators. The holomorphic formulation, based on the olomorphic path integral for the Weyl symbol of the density matrix, makes it possible to directly approach general Hamiltonians given in terms of bosonic creation and annihilation operators.