Related papers: A $\mathbb{Z}_{2}$-Topological Index for Quasi-Fre…

Using results on topological band theory of phases of matter and discrete symmetries, we study topological properties of band structure of physical systems involving spin $\frac{1}{2}$ and $\frac{3}{2}$ fermions. We apply this approach to…

In this letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting non-local zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the…

We prove that the split property is a stable feature for spin chain states which are related by composition with *-automorphisms generated by power-law decaying interactions. We apply this to the theory of the $\mathbb{Z}_2$-index for…

The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts…

We explore an exact duality in $(2+1)$d between the fermionization of a bosonic theory with a $\mathbb{Z}_2$ subsystem symmetry and a fermionic theory with a $\mathbb{Z}_2$ subsystem fermion parity symmetry. A typical example is the duality…

We study the topology of the regular loci of two complexified Hamiltonian integrable systems using the Zariski-van Kampen method. In particular, we show that the fundamental group of the regular locus for the complexified planar Kepler…

We provide a general formula for the partition function of three-dimensional $\mathcal{N}=2$ gauge theories placed on $S^2 \times S^1$ with a topological twist along $S^2$, which can be interpreted as an index for chiral states of the…

Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological…

We investigate the properties of Lindblad equations on $d$-dimensional lattices supporting a unique steady-state configuration. We consider the case of a time evolution weakly symmetric under the action of a finite group $G$, which is also…

We develop a common semantic framework for the interpretation both of $\mathbf{IPC}$, the intuitionistic propositional calculus, and of logics weaker than $\mathbf{IPC}$ (substructural and subintuitionistic logics). This is done by proving…

We present a theoretical study of two spinless fermion wires coupled to a three dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block…

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…

In this paper we study a $2+1$ dimensional system in which fermions are coupled to the self-dual topological vortex in $U(1) \times U(1)$ Chern-Simons theory, where both $U(1)$ gauge symmetries are spontaneously broken. We consider two…

Framed combinatorial topology is a recent approach to tame geometry which expresses higher-dimensional stratified spaces via tractable combinatorial data. The resulting theory of spaces is well-behaved and computable. In this paper we…

Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological…

We develop an exact map of all states and operators from 2D lattices of spins-$1/2$ into lattices of fermions and bosons with mutual semionic statistical interaction that goes beyond previous dualities of $\mathbb{Z}_2$ lattice gauge…

Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three…

We construct a supersymmetric model based on $T'\otimes Z_3\otimes Z_9$ flavor symmetry. At the leading order, the charged lepton mass matrix is not diagonal, $T'$ is broken completely, and the hierarchy in the charged lepton masses is…

We develop a comprehensive theory of reflectionless canonical systems with an arbitrary Dirichlet-regular Widom spectrum with the Direct Cauchy Theorem property. This generalizes, to an infinite gap setting, the constructions of finite gap…

In this paper, we construct an exactly solvable lattice Hamiltonian model to investigate the properties of a composite system consisting of multiple topological orders separated by gapped domain walls. There are interdomain elementary…