Uploaded January 2024 | Updated September 2026, 2 weeks ago
Speaker: David Berenstein (University of California, Santa Barbara)
Abstract: I will discuss a novel construction of field theories based on the idea that one has only a half boson degree of freedom per lattice site. Basically, instead of having a pair of canonical conjugate commuting variables at each site, one has only one degree of freedom and the non-trivial commutators arise from connections to the nearest neighbors. The construction is very similar to staggered fermions and naturally produces gapless systems with interesting topological properties. When considering gauging discrete translations on the phase space in one dimensional examples, one gets interesting critical spin chains, examples of which include the critical Ising model in a transverse magnetic field and the 3-state Potts model at criticality. I will explain how these staggered boson variables are very natural for describing non-invertible symmetries.
Speaker: David Berenstein (University of California, Santa Barbara)
Abstract: I will discuss a novel construction of field theories based on the idea that one has only a half boson degree of freedom per lattice site. Basically, instead of having a pair of canonical conjugate commuting variables at each site, one has only one degree of freedom and the non-trivial commutators arise from connections to the nearest neighbors. The construction is very similar to staggered fermions and naturally produces gapless systems with interesting topological properties. When considering gauging discrete translations on the phase space in one dimensional examples, one gets interesting critical spin chains, examples of which include the critical Ising model in a transverse magnetic field and the 3-state Potts model at criticality. I will explain how these staggered boson variables are very natural for describing non-invertible symmetries.
