Frustration-free Hamiltonians, such as the AKLT model and the Kitaev toric code, have helped us understand non-trivial topological phases of matters. In recent years, studies on gapless frustration-free Hamiltonians revealed that their finite-size gaps and low-energy excitations tend to behave differently from conventional systems. As a consequence, spontaneous breaking of continuous symmetries may occur even in one dimension, contrary to the Hohenberg-Mermin-Wagner theorem. In this talk, we will review recent theoretical advances in understanding on the general properties of gapless frustration-free systems.

References

HW, H. Katsura, J.-Y. Lee, arXiv:2310.16881
R. Masaoka, T. Soejima, HW, arXiv:2406.06414
R. Masaoka, T. Soejima, HW, arXiv:2406.06415
 

Please contact phweb@ust.hk should you have questions about the talk.