Driving a first order quantum phase transition by coupling a quantum dot to a 1D charge density wave

TL;DR

This paper investigates how coupling a quantum dot to a 1D charge density wave can induce a first order quantum phase transition, revealing distinct thermodynamic behaviors compared to the Luttinger liquid phase.

Contribution

It demonstrates that in the charge density wave phase, the system exhibits a first order quantum phase transition driven by gate voltage tuning, contrasting with previous Luttinger liquid results.

Findings

Electron number remains constant in the charge density wave phase.

Total energy becomes linear with gate voltage.

Gate tuning can invert site populations, inducing a phase transition.

Abstract

The ground state properties of a one-dimensional system with particle-hole symmetry, consisting of a gate controlled dot coupled to an interacting reservoir, are explored using the numerical DMRG method. It was previously shown that the system's thermodynamic properties as a function of the gate voltage in the Luttinger liquid phase are qualitatively similar to the behavior of a non-interacting wire with an effective (renormalized) dot-lead coupling. Here we examine the thermodynamic properties of the wire in the charge density wave phase, and show that these properties behave quite differently. The number of electrons in the system remains constant as a function of the gate voltage, while the total energy becomes linear. Moreover, by tuning the gate voltage on the dot in the charge density wave phase it is possible to drive the wire through a first order quantum phase transition in which the population of each site in the wire is inverted.