Related papers: Loop Braiding Statistics and Interacting Fermionic…
The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels.…
Discrete finite-group global symmetries may suffer from nonperturbative 't-Hooft anomalies. Such global anomalies can be canceled by anomalous symmetry-preserving topological quantum field theories (TQFTs), which contain no local point…
The complex energy bands of non-Hermitian systems braid in momentum space even in one dimension. Here, we reveal that the non-Hermitian braiding underlies the Hermitian topological physics with chiral symmetry under a general framework that…
The anomalous surface states of symmetry protected topological (SPT) phases are usually thought to be only possible in conjunction with the higher dimensional topological bulk. However, it has recently been realized that a class of…
It has been argued that fluctuations of fermion parity are harmful for the demonstration of non-Abelian anyonic statistics. Here, we demonstrate a striking exception in which such fluctuations are actively used. We present a theory of…
Three-dimensional topological insulators can be described by an effective field theory involving two `hydrodynamic' Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes…
The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically…
We introduce and develop a theory of fusion and statistical processes of gapped excitations in Abelian fracton phases. The key idea is to incorporate lattice translation symmetry via its action on superselection sectors, which results in a…
We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+1) quantum electrodynamics of an Abelian $U(1)$ gauge field coupled to a symmetry-protected topological matter sector, by…
We study symmetries and defects of a wide class of two dimensional Abelian topological phases characterized by Lie algebras. We formulate the symmetry group of all Abelian topological field theories. The symmetries relabel quasiparticles…
The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions. As opposed to…
The inclusion of fermionic loops contribution in Numerical Stochastic Perturbation Theory (NSPT) has a nice feature: it does not cost so much (provided only that an FFT can be implemented in a fairly efficient way). Focusing on Lattice…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
Condensed matter physics of gauge theories coupled to fermions can exhibit a rich phase structure, but are nevertheless very difficult to study in Monte Carlo simulations when they are afflicted by a sign problem. As an alternate approach,…
The fermionic minimal models are a recently-introduced family of two-dimensional spin conformal field theories. We determine all of their conformal boundary states and potentially anomalous $\mathbb{Z}_2$ global symmetries. The latter task…
Continuous quantum phase transitions that are beyond the conventional paradigm of fluctuations of a symmetry breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the…
Gapless topological phases of matter may host emergent quasiparticle excitations which have no analog in quantum field theory. This is the case of so called triple point fermions (TPF), quasiparticle excitations protected by crystal…
Quantum anomalies, breakdown of classical symmetries by quantum effects, provide a sharp definition of symmetry protected topological phases. In particular, they can diagnose interaction effects on the non-interacting classification of…
The fermionic Hubbard model (FHM)[1], despite its simple form, captures essential features of strongly correlated electron physics. Ultracold fermions in optical lattices[2, 3] provide a clean and well-controlled platform for simulating…
Symmetry-protected topological superconductors (TSCs) can host multiple Majorana zero modes (MZMs) at their edges or vortex cores, while whether the Majorana braiding in such systems is non-Abelian in general remains an open question. Here…