Calculating the Luttinger liquid parameter for an interacting Kitaev chain quantum simulator

TL;DR

This paper proposes a solid-state quantum simulator platform based on spin centers to emulate an interacting Kitaev chain, revealing complex quantum phases and introducing efficient methods to calculate the Luttinger liquid parameter.

Contribution

It introduces a tunable solid-state platform for simulating the interacting Kitaev chain and develops novel methods for calculating the Luttinger liquid parameter with reduced computational effort.

Findings

Identification of floating, Z2 symmetry-breaking, and BKT transitions.

Development of methods to calculate the Luttinger liquid parameter efficiently.

Demonstration of rich quantum behavior in the proposed simulator.

Abstract

In this work, we introduce a solid-state platform for building quantum simulators using implanted spin centers in solid-state materials. We build upon the proposal for an $S=1$ chain of spin centers coupled through the magnetic dipole-dipole interaction and subjected to an external magnetic field as a quantum simulator for critical floating phases. We introduce another magnetic field and map the system to the interacting Kitaev chain. This setup, tunable through the applied fields and the orientation of the spin centers within the crystal, exhibits a variety of rich quantum behavior which notably includes floating phases, a $Z_2$ symmetry-breaking phase, and lines of both Berezinskii-Kosterlitz-Thouless (BKT) and Pokrovsky-Talapov transitions. Furthermore, we employ several novel methods to calculate the Luttinger liquid parameter in our model with incommensurate correlations. We find that these methods provide a route to identify BKT transitions with less computational resources than utilizing entanglement entropy and central charge.