Effective Hamiltonian with holomorphic variables

TL;DR

This paper develops a holomorphic variable-based formulation of the PQSCHA, enabling effective classical Hamiltonians for quantum systems described by bosonic operators, facilitating analysis of complex quantum models.

Contribution

It introduces a holomorphic variables approach to PQSCHA, allowing direct treatment of Hamiltonians with bosonic creation and annihilation operators.

Findings

Derivation of PQSCHA in holomorphic variables

Application to general bosonic Hamiltonians

Facilitates classical-like analysis of quantum systems

Abstract

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