Related papers: A $\mathbb{Z}_{2}$-Topological Index for Quasi-Fre…
We investigate topological charge and the index theorem on finite lattices numerically. Using mean field improved gauge field configurations we calculate the topological charge Q using the gluon field definition with ${\cal…
We classify superfusion categories describing two-dimensional fermionic systems equipped with the universal fermion-parity symmetry, implemented by a topological defect line (TDL) $Z$, and an additional $\mathbb{Z}_2$ flavor symmetry…
The Fu-Kane-Mele $\mathbb{Z}_2$ index characterizes two-dimensional time-reversal symmetric topological phases of matter. We shed some light on some features of this index by investigating projection-valued maps endowed with a fermionic…
We construct a Landau-Ginzburg model with the same data and symmetries as a $Z_2\times Z_2$ orbifold that corresponds to a class of realistic free-fermion models. Within the class of interest, we show that this orbifolding connects between…
We study homeomorphisms of a Cantor set with $k$ ($k < +\infty$) minimal invariant closed (but not open) subsets; we also study crossed product C*-algebras associated to these Cantor systems and their certain orbit-cut sub-C*-algebras. In…
We report two theoretical discoveries for $\mathbb{Z}_2$-topological metals and semimetals. It is shown first that any dimensional $\mathbb{Z}_2$ Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go…
One of the most challenging problems in correlated topological systems is a realization of the reduction of topological classification, but very few experimental platforms have been proposed so far. We here demonstrate that ultracold…
We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…
The conditions for both the stability and the breakdown of the topological classification of gapped ground states of noninteracting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions are given for any…
We show how the index of the fermion operator from the Euclidean action can be used to uncover the existence of gapless modes living on defects (such as edges and vortices) in topological insulators and superconductors. The 1-loop Feynman…
Let $\Gamma$ be a torsion free cocompact lattice in $\aut(\cl T_1)\times\aut(\cl T_2)$, where $\cl T_1$, $\cl T_2$ are trees whose vertices all have degree at least three. The group $H_2(\Gamma, \bb Z)$ is determined explicitly in terms of…
Guided by the many-particle quantum theory of interacting systems, we develop a uniform classification scheme for topological phases of disordered gapped free fermions, encompassing all symmetry classes of the Tenfold Way. We apply this…
We discuss non-geometric supersymmetric heterotic string models in D=4, in the framework of the free fermionic construction. We perform a systematic scan of models with four a priori left-right asymmetric Z_2 projections and shifts. We…
We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model…
The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used…
We consider a system of weakly interacting spinful lattice fermions coupled to a dynamical $\mathbb{Z}_2$ gauge field. Using reflection positivity, we prove that the ground state lies in the sector of a uniform $\pi$-flux per plaquette and…
We present the theory and experimental demonstration of a topological classification of finite tight binding Hamiltonians with chiral symmetry. Using the graph-theoretic notion of complete matchings, we show that many chiral tight binding…
At small lattice spacing QCD simulations are expected to become stuck in a single topological sector. Observables evaluated in a fixed topological sector differ from their counterparts in full QCD, i.e. at unfixed topology, by volume…
We study the topological B-model on a deformed $\Z_2$ orbifolded conifold by investigating variation of complex structures via quantum Kodaira-Spencer theories. The fermionic/brane formulation together with systematic utilization of…
The topological structure of the QCD vacuum can be probed by monitoring the spatial localization of the low-lying Dirac eigenmodes. This approach can be pursued on the lattice, and unlike the traditional one requires no smoothing of the…