Bose condensation is central to our understanding of quantum phases of matter. Here, we
review Bose condensation in topologically ordered phases (also called topological …

We study effectively one-dimensional systems that emerge at the edge of a two-dimensional
topologically ordered state, or at the boundary between two topologically ordered states. We …

We reformulate the topological symmetry-breaking scheme for phase transitions in systems
with anyons in a graphical manner. A set of quantities called vertex lifiting coefficients …

Boson condensation in topological quantum field theories (TQFT) has been previously
investigated through the formalism of Frobenius algebras and the use of vertex lifting …

We provide a framework for understanding the gapless Kitaev spin liquid (KSL) in the
language of the tensor network (TN). Without introducing a Majorana fermion, most of the …

We study the condensation of Abelian bosons in string-net models by constructing a family
of Hamiltonians that can be tuned through any such transition. We show that these …

We show that all so (N) 1 universality class quantum criticalities emerge when one-
dimensional generalized cluster models are perturbed with Ising or Zeeman terms. Each …

We introduce a family of SO (n)-symmetric spin chains which generalize the transverse-field
Ising chain for n= 1. These spin chains are defined with gamma matrices and can be exactly …

Thermal quantum critical systems, with partition functions expressed as conformal tensor
networks, are revealed to exhibit universal entropy corrections on nonorientable manifolds …

An infinite number of spin chains are solved and it is derived that the ground-state phase
transitions belong to the universality classes with central charge c= m/2, where m is an …