Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU(N) Kondo lattice model
arxiv(2024)
摘要
The nature of the insulating phases of the SU(N)-generalization of the
one-dimensional Kondo lattice model is investigated by means of
non-perturbative approaches. By extending the Lieb-Schultz-Mattis (LSM)
argument to multi-component fermion systems with translation and global SU(N)
symmetries, we derive two indices which depend on the filling and the
“SU(N)-spin” (representation) of the local moments. These indices strongly
constrain possible insulating phases; for instance, when the local moments
transform in the N-dimensional (defining) representation of SU(N), a
featureless Kondo insulator is possible only at filling f= 1-1/N. To obtain
further insight into the insulating phases suggested by the LSM argument, we
derive low-energy effective theories by adding an antiferromagnetic Heisenberg
exchange interaction among the local moments [the SU(N) Kondo-Heisenberg
model]. A conjectured global phase diagram of the SU(N) Kondo lattice model
as a function of the filling and the Kondo coupling is then obtained by a
combination of different analytical approaches.
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