Related papers: Edge $\mathbb{Z}_3$ parafermions in fermionic latt…
Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which…
Anyons are particles obeying statistics of neither bosons nor fermions. Non-Abelian anyons, whose exchanges are described by a non-Abelian group acting on a set of wave functions, are attracting a great attention because of possible…
Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and…
We study the bulk-boundary correspondences for zigzag ribbons (ZRs) of massless Dirac fermion in two-dimensional $\alpha$-${T}_3$ lattice. By tuning the hopping parameter $\alpha\in[0,1]$, the $\alpha$-${T}_3$ lattice interpolates between…
We develop an approach to describe antiferromagnetic magnons on a bipartite lattice supporting the N\'{e}el state using fractionalized degrees of freedom typically inherent to quantum spin liquids. In particular we consider a long-range…
Nontrivial topology in physical systems is the driving force behind many phenomena. Notably, phases of matter must be classified in part by their topological properties. Phases with topological order (TO), such as the fractional quantum…
Topological excitations in many-body systems are one of the paradigmatic cornerstones of modern condensed matter physics. In particular, parafermions are elusive fractional excitations potentially emerging in fractional quantum…
Compact quantum electrodynamics (CQED$_3$) with Dirac fermionic matter provides an adequate framework for elucidating the universal low-energy physics of a wide variety of (2+1)D strongly correlated systems. Fractionalized states of matter…
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a…
The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact…
We compute the spectra of anyon quasiparticles in all three super-selection sectors of the Kitaev model (i.e., visons, fermions and bosons), perturbed by a Zeeman field away from its exactly solvable limit, to gain insights on the…
We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from…
We introduce and describe in second quantization a family of particle species with \(p=2,3,\dots\) exclusion and \(\theta=2\pi/p\) exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally…
Recent work shows that a quantum spin liquid can arise in realistic fermionic models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg honeycomb model, considering couplings J1, J2, and J3 up to third nearest neighbors. We…
We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can…
A great part of the mathematical foundations of topological quantum computation is given by the theory of modular categories which provides a description of the topological phases of matter such as anyon systems. In the near future the…
One-dimensional topological phases can host localized zero-energy modes that enable high-fidelity storage and manipulation of quantum information. Majorana fermion chains support a classic example of such a phase, having zero modes that…
Green parafermions, originally introduced by Green and extended by Greenberg and Messiah through trilinear and relative trilinear commutation relations beyond Bose-Fermi statistics, are generally regarded as mathematical curiosities without…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…