# Physics of Arbitrary Doped Kondo Lattices: from a Commensurate Insulator to a Heavy Luttinger Liquid and a Protected Helical Metal

## TL;DR

This paper develops an analytical theory for one-dimensional Kondo lattices with high impurity density, revealing various electronic phases including insulators, metals, and a helical metal with potential for protected ballistic transport.

## Contribution

It provides the first comprehensive analytical framework for doped Kondo lattices at arbitrary doping, predicting multiple electronic phases based on impurity interactions.

## Key findings

- Identification of commensurate insulators at specific fillings
- Prediction of a helical metal phase with protected transport
- Agreement with previous numerical results

## Abstract

We study one-dimensional Kondo Lattices (KL) which consist of itinerant electrons interacting with Kondo impurities (KI) - localized quantum magnetic moments. We focus on KL with isotropic exchange interaction between electrons and KI and with a high KI density. The latter determines the principal r\'ole of the indirect interaction between KI for the low energy physics. Namely, the Kondo physics becomes suppressed and all properties are governed by spin ordering. We present a first-ever comprehensive analytical theory of such KL at an arbitrary doping and predict a variety of regimes with different electronic phases. They range from commensurate insulators (at filling factors 1/2, 1/4 and 3/4) to metals with strongly interacting conduction electrons (close to these three special cases) to an exotic phase of a helical metal. The helical metals can provide a unique platform for realization of an emergent protection of ballistic transport in quantum wires. We compare out theory with previously obtained numerical results and discuss possible experiments where the theory could be tested.