The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional extensions forbid the existence of a unique, symmetric, and gapped ground state at fractional fillings in quantum many-body systems with a conserved particle number (or spin angular momentum) and the conventional translation symmetry of Euclidean lattices. In this work, we propose a generalization of the LSM theorem to quantum many-body systems on hyperbolic lattices, i.e., regular tessellations of two-dimensional negatively curved space. By leveraging concepts from hyperbolic band theory in a many-body setting, we adapt Oshikawa's flux-threading argument to periodic hyperbolic lattices with a non-Euclidean (Fuchsian) translation symmetry and compute a lower-bound to the ground-state degeneracy as a function of filling and lattice geometry. We explore the consequences of LSM constraints for gapped phases of hyperbolic quantum matter and suggest frustrated spin models on hyperbolic analogs of the square and triangular lattices as promising platforms for realizing symmetric spin liquids in hyperbolic space.The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional extensions forbid the existence of a unique, symmetric, and gapped ground state at fractional fillings in quantum many-body systems with a conserved particle number (or spin angular momentum) and the conventional translation symmetry of Euclidean lattices. In this work, we propose a generalization of the LSM theorem to quantum many-body systems on hyperbolic lattices, i.e., regular tessellations of two-dimensional negatively curved space. By leveraging concepts from hyperbolic band theory in a many-body setting, we adapt Oshikawa's flux-threading argument to periodic hyperbolic lattices with a non-Euclidean (Fuchsian) translation symmetry and compute a lower-bound to the ground-state degeneracy as a function of filling and lattice geometry. We explore the consequences of LSM constraints for gapped phases of hyperbolic quantum matter and suggest frustrated spin models on hyperbolic analogs of the square and triangular lattices as promising platforms for realizing symmetric spin liquids in hyperbolic space.

cond-mat.str-elCross-listedarXiv:2605.15974Physical review. B./Physical review. BMay 18, 20260 citations

Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU( N ) Kondo lattice model

P. Lecheminant, Keisuke Totsuka

The nature of the insulating phases of the $\mathrm{SU}(N$ )-generalization of the one-dimensional Kondo lattice model is investigated by means of nonperturbative approaches. By extending the Lieb-Schultz-Mattis (LSM) argument to multicomponent fermion systems with translation and global $\mathrm{SU}(N$ ) symmetries, we derive two indices which depend on the filling and the `` $\mathrm{SU}(N$ )-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 $\mathrm{SU}(N$ ), a featureless Kondo insulator is possible only at filling $f=1\ensuremath{-}1/N$. 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 $\mathrm{SU}(N$ ) Kondo-Heisenberg model]. A conjectured global phase diagram of the $\mathrm{SU}(N$ ) Kondo lattice model as a function of the filling and the Kondo coupling is then obtained by a combination of different analytical approaches.The nature of the insulating phases of the $\mathrm{SU}(N$)-generalization of the one-dimensional Kondo lattice model is investigated by means of nonperturbative approaches. By extending the Lieb-Schultz-Mattis (LSM) argument to multicomponent fermion systems with translation and global $\mathrm{SU}(N$) symmetries, we derive two indices which depend on the filling and the ``$\mathrm{SU}(N$)-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 $\mathrm{SU}(N$), a featureless Kondo insulator is possible only at filling $f=1\ensuremath{-}1/N$. 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 $\mathrm{SU}(N$) Kondo-Heisenberg model]. A conjectured global phase diagram of the $\mathrm{SU}(N$) Kondo lattice model as a function of the filling and the Kondo coupling is then obtained by a combination of different analytical approaches.

arXiv:2404.11030Physical review. B./Physical review. BAug 5, 20243 citations

QUANTUM ANTIFERROMAGNETS IN TWO DIMENSIONS

Subir Sachdev A

Feb 1, 19956 citations

The nature of the insulating phases of the

\mathrm{SU}(N

)-generalization of the one-dimensional Kondo lattice model is investigated by means of nonperturbative approaches. By extending the Lieb-Schultz-Mattis (LSM) argument to multicomponent fermion systems with translation and global

\mathrm{SU}(N

) symmetries, we derive two indices which depend on the filling and the ``

\mathrm{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

\mathrm{SU}(N

), a featureless Kondo insulator is possible only at filling $f=1\ensuremath{-}1/N$. 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

\mathrm{SU}(N

) Kondo-Heisenberg model]. A conjectured global phase diagram of the

\mathrm{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.