# Exactly Solvable Kondo Lattice Model in Anisotropic Limit

## TL;DR

This paper introduces an exactly solvable Kondo lattice model that captures magnetic and electronic phases, including antiferromagnetic insulators and metallic states, with potential relevance to heavy fermion and hidden order materials.

## Contribution

The model is exactly solvable without fine-tuning, describing itinerant electrons coupled to localized moments via longitudinal exchange, valid for arbitrary lattice geometry and filling.

## Key findings

- Ground state is a Néel antiferromagnetic insulator at half-filling.
- Finite temperature phases include a Mott insulator and a correlated metal.
- Transition to antiferromagnetic insulator is a continuous 2D Ising transition.

## Abstract

In this paper we introduce an exactly solvable Kondo lattice model without any fine-tuning local gauge symmetry. This model describes itinerant electrons interplaying with a localized magnetic moment via only longitudinal Kondo exchange. Its solvability results from conservation of the localized moment at each site, and is valid for arbitrary lattice geometry and electron filling. A case study on square lattice shows that the ground state is a N\'{e}el antiferromagnetic insulator at half-filling. At finite temperature, paramagnetic phases including a Mott insulator and correlated metal are found. The former is a melting antiferromagnetic insulator with a strong short-range magnetic fluctuation, while the latter corresponds to a Fermi liquid-like metal. Monte Carlo simulation and theoretical analysis demonstrate that the transition from paramagnetic phases into the antiferromagnetic insulator is a continuous $2D$ Ising transition. Away from half-filling, patterns of spin stripes (inhomogeneous magnetic order) at weak coupling, and phase separation at strong coupling are predicted. With established Ising antiferromagnetism and spin stripe orders, our model may be relevant to a heavy fermion compound CeCo(In$_{1-x}$Hg$_{x}$)$_{5}$ and novel quantum liquid-crystal order in a hidden order compound URu$_{2}$Si$_{2}$.