Variational approach to the Caldeira-Leggett model

TL;DR

This paper investigates the phase transitions of a quantum particle in a one-dimensional box coupled to an Ohmic environment using a variational approach, revealing temperature-dependent coherence changes and finite-size effects.

Contribution

It introduces a variational method to analyze the Caldeira-Leggett model in a tight-binding chain, highlighting phase transitions and finite-size effects.

Findings

Zero-temperature phase transition to localized phase for even chain lengths

Finite-temperature transition from coherent to incoherent regimes

Comparison with numerical techniques confirms the variational results

Abstract

We apply the displaced-oscillator variational ansatz to the Caldeira-Leggett model for a quantum particle in a one-dimensional box described by a tight-binding chain. We focus on the case of an Ohmic environment and study the phase diagram for different chain lengths. At zero temperature there is a phase transition to a localized phase when the number of sites is even. At finite temperature, a transition from a coherent to an incoherent regime is predicted for all the chain lengths considered. Finally, the results are compared to those obtained with numerical techniques.