Phase diagram and dynamics of the SU($\boldsymbol N$) symmetric Kondo lattice model

TL;DR

This study explores the phase diagram and dynamics of the SU(N) symmetric Kondo lattice model using quantum Monte Carlo simulations, revealing only two phases and confirming the large-N theory's validity for describing quantum critical heavy-fermion systems.

Contribution

It demonstrates that the SU(N) Kondo lattice model hosts only antiferromagnetic and Kondo-screened phases, confirming the large-N theory as a valid approximation and clarifying the evolution of physical properties across the transition.

Findings

Only two phases (AF and Kondo-screened) are present for all finite N.

The large-N theory accurately describes the phase diagram and quantum fluctuations.

The coherence temperature behavior changes abruptly at larger N.

Abstract

In heavy-fermion systems, the competition between the local Kondo physics and intersite magnetic fluctuations results in unconventional quantum critical phenomena which are frequently addressed within the Kondo lattice model (KLM). Here we study this interplay in the SU($N$) symmetric generalization of the two-dimensional half-filled KLM by quantum Monte Carlo simulations with $N$ up to 8. While the long-range antiferromagnetic (AF) order in SU($N$) quantum spin systems typically gives way to spin-singlet ground states with spontaneously broken lattice symmetry, we find that the SU($N$) KLM is unique in that for each finite $N$ its ground-state phase diagram hosts only two phases -- AF order and the Kondo-screened phase. The absence of any intermediate phase between the $N=2$ and large-$N$ cases establishes adiabatic correspondence between both limits and confirms that the large-$N$ theory is a correct saddle point of the KLM fermionic path integral and a good starting point to include quantum fluctuations. In addition, we determine the evolution of the single-particle gap, quasiparticle residue of the doped hole at momentum $(\pi,\pi)$, and spin gap across the magnetic order-disorder transition. Our results indicate that increasing $N$ modifies the behavior of the coherence temperature: while it evolves smoothly across the magnetic transition at $N=2$ it develops an abrupt jump -- of up to an order of magnitude -- at larger but finite $N$. We discuss the magnetic order-disorder transition from a quantum-field-theoretic perspective and comment on implications of our findings for the interpretation of experiments on quantum critical heavy-fermion compounds.