Related papers: Fusion Surface Models: 2+1d Lattice Models from Fu…

We construct supersymmetric composite models of quarks and leptons from type IIA T^6/(Z_2 x Z_2) orientifolds with intersecting D6-branes. In case of T^6 = T^2 x T^2 x T^2 with no tilted T^2, a composite model of the supersymmetric SU(5)…

In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…

The study of gapless phases with categorical (or so-called non-invertible) symmetries is a formidable task, in particular in higher than two space-time dimensions. In this paper we build on previous works arXiv:2408.05266 and…

In recent work, we developed a method to construct invertible and non-invertible symmetries of finite-group gauge theories as topological domain walls on the lattice. In the present work, we consider abelian and non-abelian finite-group…

Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between…

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the…

We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently…

The description of a system of vortices in terms of dual fields provides a window to new phases of the system. It was found recently that dualizing a 3+1-d boson-fermion system leads to a system of fermions and vortices interacting via a…

We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes…

We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the "tensor symmetry". We consider a general form of lattice Hamiltonians which allow a certain level of…

Patterned two-dimensional (2D) magnetic nanostructures constitute geometry-engineered spin systems in which exchange, anisotropy, dipolar coupling, and finite-size effects operate on comparable energy scales. Spatial modulation of…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…

Certain patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. An important…

I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a…

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…

We show that anyon chains, after stabilizing with infinite-dimensional ancilla spaces, factorize locally as tensor products of infinite-dimensional Hilbert spaces. This implies that any unitary fusion category can be realized as symmetries…

We provide a general prescription for gauging finite non-invertible symmetries in 1+1d lattice Hamiltonian systems. Our primary example is the Rep(D$_8$) fusion category generated by the Kennedy-Tasaki transformation, which is the simplest…

Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates…

We design a (2+1))-dimensional [(2+1)D] quantum spin model in which spin-1/2 ladders are coupled through antiferromagnetic Ising interactions. The model hosts a quantum phase transition in the (2+1)D $Z_2$ universality class from the…