Partition functions and thermodynamic properties of paraboson and parafermion systems

显而易见的仲费米子

Parafermions in plain sight

研究具有离散能谱的势，发现理想玻色子与费米子配分函数在ξ=-1/m处的插值对应m个费米子占据单量子态的零温基态能量，其巨正则配分函数可源于仲统计。

Quantum criticality in many-body parafermion chains

We construct local generalizations of 3-state Potts models with exotic critical points. We analytically show that these are described by non-diagonal modular invariant partition functions of products of $Z_3$ parafermion or $u(1)_6$ conformal field theories (CFTs). These correspond either to non-trivial permutation invariants or block diagonal invariants, that one can understand in terms of anyon condensation. In terms of lattice parafermion operators, the constructed models correspond to parafermion chains with many-body terms. Our construction is based on how the partition function of a CFT …

Topological Defects on the Lattice: Dualities and Degeneracies

We construct topological defects in two-dimensional classical lattice models and quantum chains. The defects satisfy local commutation relations guaranteeing that the partition function is independent of their path. These relations and their solutions are extended to allow defect lines to fuse, branch and satisfy all the properties of a fusion category. We show how the two-dimensional classical lattice models and their topological defects are naturally described by boundary conditions of a Turaev-Viro-Barrett-Westbury partition function. These defects allow Kramers-Wannier duality to be genera…