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

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 usingthe numerical DMRG method. It has previously been shown that the system’sthermodynamic properties as a function of the gate voltage in the Luttinger liquid phaseare qualitatively similar to the behaviour of a non-interacting wire with an effective(renormalized) dot–lead coupling. Here we examine the thermodynamic properties of thewire in the charge density wave phase, and show that these properties behave quitedifferently. The number of electrons in the system remains constant as a function of thegate voltage, while the total energy becomes linear. Moreover, by tuning the gate voltageon the dot in the charge density wave phase it is possible to drive the wire through a firstorder quantum phase transition in which the population of each site in the wire is inverted.