Related papers: Disentangling modular Walker-Wang models via fermi…
This paper continues with Part I. We define the module for a $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra that is twisted by an involution and show that the axioms are sufficient to guarantee the convergence of…
Despite great successes in the study of gapped phases, a comprehensive understanding of the gapless phases and their transitions is still under developments. In this paper, we study a general phenomenon in the space of (1+1)$d$ critical…
We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the…
Magnetic domain walls (DWs) are topological defects that exhibit robust low-energy modes that can be harnessed for classical and neuromorphic computing. However, the quantum nature of these modes has been elusive thus far. Using the…
Topological insulators, in contrast to ordinary semiconductors, accompany protected metallic surfaces described by Dirac-type fermions. Here, we theoretically show another emergent two-dimensional metal embedded in the bulk insulator is…
In this paper we give a general family of conformal invariants associated to bordered Riemann surfaces endowed with boundary parametrizations, or equivalently compact surfaces endowed with conformal maps. Each invariant is specified by a…
In this letter we demonstrate that the fermionic zero modes on a superconducting domain wall can be associated to an one dimensional $N=6$ supersymmetry that contains non-trivial topological charges. In addition, the system also possesses…
We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the…
Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the…
We extend work by Callan and Harvey and show how the phase of the chiral fermion determinant in four dimensions is reproduced by zeromodes bound to a domain wall in five dimensions. The analysis could shed light on the applicability of…
In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In…
We propose an exactly solvable lattice Hamiltonian model of topological phases in $3+1$ dimensions, based on a generic finite group $G$ and a $4$-cocycle $\omega$ over $G$. We show that our model has topologically protected degenerate…
Fermionic model of Superconformal field theory with boundary is considered. There were written the ''boundary'' Ward Identity for this theory and also constructed boundary states for fermionic and spin models. For this model were derived…
I review the Thirring model in 2+1$d$ dimensions, focussing in particular on possible strongly-interacting UV-stable fixed points of the renormalisation group, corresponding to a continuous phase transition where a U($2N$) global symmetry…
The defining feature of topological insulators is that their valence states are not continuously deformable to a suitably defined atomic limit without breaking the symmetry or closing the energy gap. When the atomic limit is given by…
Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models…
A hallmark of certain topology, including the Chern number, is the obstruction to constructing exponentially localized Wannier functions in the bulk bands. Conversely, other types of topology do not necessarily impose Wannier obstructions.…
We define an index for invertible phases of two-dimensional fermionic and bosonic quantum spin systems without any additional symmetry. Conjecturally, it provides a microscopic definition of an invariant related to the chiral central charge…
We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The…