Related papers: Topological Quantum Liquids with Long-Range Coupli…
Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective…
In this project, we study the properties of a non-trivial topological system which exhibits localized edge states. In our study, we adress the Kitaev chain, a one-dimensional chain of atoms deposited on top of a p-wave superconductor that…
Bulk-boundary correspondence is a concept for topological insulators and superconductors that determines the existence of topological boundary states within the tenfold classification table. Contrary to this belief, we demonstrate that…
Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this…
We propose a minimalist architecture for achieving various crystalline-symmetry-protected Majorana modes in an array of coupled quantum dots. Our framework is motivated by the recent experimental demonstrations of two-site and three-site…
Identifying and characterizing quantum phases of matter in the presence of long range correlations and/or spatial disorder is, generally, a challenging and relevant task. Here, we study a generalization of the Kiteav chain with…
Majorana bound states, with their non-Abelian properties, are candidates for the realization of fault-tolerant quantum computation. Here we study the influence of long-range many-body interactions on Majorana zero modes present in Kitaev…
Topological order in strongly correlated systems, including quantum spin liquids, quantum Hall states in lattices and topological superconductivity is treated. Various metallic non-Fermi-liquid states are discussed, including fractionalized…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections…
We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence…
The Kitaev chain model with a spatially modulated phase in the superconducting order parameter exhibits two types of topological transitions, namely a band topology transition between trivial and topological gapped phases, and a Fermi…
One-dimensional spinless Fermi gas with attractive dipole-dipole interaction is investigated. Results obtained show when the interaction is weak, the excitation spectrum is linear and the superconducting correlation function decays as power…
What distinguishes trivial from topological superluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting…
Imaginary-time evolution by a local Hamiltonian cannot induce a phase transition in one dimension, but longer-range interactions may subvert such constraints. Starting from the ground state of the Kitaev Majorana chain, we modify the wave…
Highly entangled excitations such as Majorana fermions of Kitaev quantum spin liquids have been proposed to be utilized for future quantum science and technology, and a deeper understanding of such excitations has been strongly desired.…
From our general index theorem that characterises faithfully the boundary-bulk correspondence of topological superconductors and insulators, we reveal rigorously that four topologically distinct types of Majorana zero-modes can emerge at…
We construct a global Lindblad master equation for a Kitaev quantum wire of finite length, weakly coupled to an arbitrary number of thermal baths, within the Born-Markov and secular approximations. We find that the coupling of an external…
Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous…
We provide a comprehensive microscopic understanding of the nucleation of topological quantum liquids, a general mechanism where interactions between non-Abelian anyons cause a transition to another topological phase, which we study in the…