Single crystal neutron diffraction, inelastic neutron scattering and electron spin resonance experiments are used to study the magnetic structure and spin waves in Pb2VO(PO4)2, a prototypical layered S = 1/2 ferromagnet with frustrating next nearest neighbor antiferromagnetic interactions. The observed excitation spectrum is found to be inconsistent with a simple square lattice model previously proposed for this material. At least four distinct exchange coupling constants are required to reproduce the measured spin wave dispersion. The degree of magnetic frustration is correspondingly revised and found to be substantially smaller than in all previous estimates.arXiv :1902.11172v2 [cond-mat.str-el]

We prove two Lieb-Schultz-Mattis type theorems that apply to any translationally invariant and local fermionic d-dimensional lattice Hamiltonians for which fermion-number conservation is broken down to the conservation of fermion parity. We show that when the internal symmetry group Gf is realized locally (in a repeat unit cell of the lattice) by a nontrivial projective representation, then the ground state cannot be simultaneously nondegenerate, symmetric (with respect to lattice translations and Gf), and gapped. We also show that when the repeat unit cell hosts an odd number of Majorana degrees of freedom and the cardinality of the lattice is even, then the ground state cannot be simultaneously nondegenerate, gapped, and translation symmetric.

Invertible fermionic topological (IFT) phases are gapped phases of matter with nondegenerate ground states on any closed spatial manifold. When open boundary conditions are imposed, nontrivial IFT phases support gapless boundary degrees of freedom. Distinct IFT phases in one-dimensional space with an internal symmetry group G f have been characterized by a triplet of indices ([(ν, ρ)], [μ]). Our main result is an elementary derivation of the fermionic stacking rules of one-dimensional IFT phases for any given internal symmetry group G f from the perspective of the boundary, i.e., we give an explicit operational definition for the boundary representation ([(ν ∧ , ρ ∧ )], [μ ∧ ]) obtained from stacking two IFT phases characterized by the triplets of boundary indices ([(ν 1 , ρ 1 )], [μ 1 ]) and ([(ν 2 , ρ 2 )], [μ 2 ]), respectively.

We study the stability of topological crystalline superconductors in the symmetry class DIIIR and in twodimensional space when perturbed by quartic contact interactions. It is known that no less than eight copies of helical pairs of Majorana edge modes can be gapped out by an appropriate interaction without spontaneously breaking any one of the protecting symmetries. Hence, the noninteracting classification Z reduces to Z 8 when these interactions are present. It is also known that the stability when there are less than eight modes can be understood in terms of the presence of topological obstructions in the low-energy bosonic effective theories, which prevent opening of a gap. Here, we investigate the stability of the edge theories with four, two, and one edge modes, respectively. We give an analytical derivation of the topological term for the first case, because of which the edge theory remains gapless. For two edge modes, we employ bosonization methods to derive an effective bosonic action. When gapped, this bosonic theory is necessarily associated to the spontaneous symmetry breaking of either one of time-reversal or reflection symmetry whenever translation symmetry remains on the boundary. For one edge mode, stability is explicitly established in the Majorana representation of the edge theory.

Fermi surfaces can undergo sharp transitions under smooth changes of parameters. Such transitions can have a topological character, as is the case when a higher-order singularity, one that requires cubic or higher-order terms to describe the electronic dispersion near the singularity, develops at the transition. When time-reversal and inversion symmetries are present, odd singularities can only appear in pairs within the Brillouin zone. In this case, the combination of the enhanced density of states that accompanies these singularities and the nesting between the pairs of singularities leads to interaction-driven instabilities. We present examples of single n = 3 (monkeysaddle) singularities when time-reversal and inversion symmetries are broken. We then turn to the question of what instabilities are possible when the singularities are isolated. For spinful electrons, we find that the inclusion of repulsive interactions destroys any isolated monkey-saddle singularity present in the noninteracting spectrum by developing Stoner or Lifshitz instabilities. In contrast, for spinless electrons and at the mean-field level, we show that an isolated monkey-saddle singularity can be stabilized in the presence of short-range repulsive interactions.