Related papers: Duality and topology
A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We…
We initiate the study of the effects of strongly-coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time reversal…
We establish that the recently discovered fermionic T-duality can be viewed as a canonical transformation in phase space. This requires a careful treatment of constrained Hamiltonian systems. Additionally, we show how the canonical…
The Jordan-Schwinger map is widely employed to switch between bosonic or fermionic mode operators and spin observables, with numerous applications ranging from quantum field theories of magnetism and ultracold quantum gases to quantum…
We generalize our previous lattice construction of the abelian bosonization duality in $2+1$ dimensions to the entire web of dualities as well as the $N_f=2$ self-duality, via the lattice implementation of a set of modular transformations…
A large family of diffusive models of transport that has been considered in the past years admits a transformation into the same model in contact with an equilibrium bath. This mapping holds at the full dynamical level, and is independent…
This work develops a duality theory for partially observed linear Gaussian models in discrete time. The state process evolves according to a causal but non-Markovian (or higher-order Gauss-Markov) structure, captured by a lower-triangular…
The external controllability of topological superconductors and Majorana fermions would be important both for fundamental and practical interests. Here we predict the electric-field control of Majorana fermions in two-dimensional…
We demonstrate that level crossings at the Fermi energy serve as robust indicators for higher-order topology in two-dimensional superconductors of symmetry class D. These crossings occur when the boundary condition in one direction is…
There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of…
Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through non-Hermitian Hamiltonians appear in the…
We study formation and evolution of solitons within a model with two real scalar fields with the potential having a saddle point. The set of these configurations can be split into disjoint equivalence classes. We give a simple expression…
We establish the consistency of duality transformations for generic systems of $N=2$ vector supermultiplets in the presence of a chiral background field. This is relevant, for instance, when dealing with spurion fields or when considering…
The fermion doubling theorem plays a pivotal role in Hermitian topological materials. It states, for example, that Weyl points must come in pairs in three-dimensional semimetals. Here, we present an extension of the doubling theorem to…
We study integrals over Hermitian supermatrices of arbitrary size $p+q$, that are parametrized by an external field $X$ and a source $Y$, of respective size $m+n$ and $p+q$. We show that these integrals exhibit a simple topological…
The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial / topological argument. These functions are then extended into a larger family of…
It is known that a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry can be fermionized. Recent work shows that if the bosonic theory also has non-anomalous time-reversal symmetry, fermionization extends to…
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…
I derive a dual description of lattice fermions, specifically focusing on the t-J and Hubbard models, that allow diagrammatic techniques to be employed efficiently in the strongly correlated regime, as well as for systems with a restricted…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…