Related papers: Parafermionic phases with symmetry-breaking and to…
We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin--Kadanoff transformation the parafermion chain is…
We show that Majorana fermions (MFs) exist in two- and three-dimensional (2D,3D) fermionic optical lattices with strictly 1D spin-orbit coupling (SOC) which has already been realized in ex- periments. For a quasi-1D topological BCS…
We investigate the realization of a topological superconductor in a generic bucked honeycomb system equipped with four types of mass-generating terms, where the superconductor gap is introduced by attaching the honeycomb system to an…
We introduce a parafermionic version of the Jaynes Cummings Hamiltonian, by coupling $k$ Fock parafermions (nilpotent of order $F$) to a 1D harmonic oscillator, representing the interaction with a single mode of the electromagnetic field.…
We investigate the robustness of Majorana edge modes under disorder and interactions. We exploit a recently found mapping of the interacting Kitaev chain in the symmetric region ($\mu = 0$, $t = \Delta$) to free fermions. Extending the…
Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes. Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a…
We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal…
In this chapter we review recent experimental and theoretical work on various novel superfluid phases in fermion systems, that result from pairing fermions of different species with unequal densities. After briefly reviewing existing…
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases - namely topological phases. These phases occur when the extended objects, called ``string-nets'', become highly fluctuating and…
We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize…
The review is aimed at highlighting the aspects of topological superconductivity in the absence of spin-orbit interaction in two-dimensional systems with long-range non-collinear spin ordering or magnetic skyrmions. Another purpose is to…
The possibility of realizing non-Abelian excitations (non-Abelions) in two-dimensional (2D) Abelian states of matter has generated a lot of interest recently. A well-known example of such non-Abelions are parafermion zeros modes (PFZMs)…
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
Topological phases exhibit unconventional order that cannot be detected by any local order parameter. In the framework of Projected Entangled Pair States(PEPS), topological order is characterized by an entanglement symmetry of the local…
Non-Abelian anyons--particles whose exchange noncommutatively transforms a system's quantum state--are widely sought for the exotic fundamental physics they harbor as well as for quantum computing applications. There now exist numerous…
Semiconductor-superconductor hybrid systems are promising candidates for the realization Majorana fermions and topological order, i.e. topologically protected degeneracies, in solid state devices. We show that the topological order is…
We analyze the ground state of a strongly interacting fermion chain with a supersymmetry. We conjecture a number of exact results, such as a hidden duality between weak and strong couplings. By exploiting a scale free property of the…
We show that a one dimensional ultra-cold Fermi gas with Rashba-like spin orbit coupling, a Zeeman field and intrinsic attractive interactions exhibits a novel topological superfluid state, which forms in spite of total number conservation…
Majorana Fermions, strange particles that are their own antiparticles, were predicted in 1937 and have been sought after ever since. In condensed matter they are predicted to exist as vortex core or edge excitations in certain exotic…
There is presently a tremendous activity around the field of topological superconductivity and Majorana fermions. Among the many questions raised, it has become increasingly important to establish the topological or non-topological origin…