Related papers: Numerical simulation of non-abelian anyons
Spin models are the prime example of simplified manybody Hamiltonians used to model complex, real-world strongly correlated materials. However, despite their simplified character, their dynamics often cannot be simulated exactly on…
Anyonic chains provide lattice realizations of a rich set of quantum field theories in two space-time dimensions. The latter play a central role in the investigation of generalized symmetries, renormalization group flows and numerous exotic…
An anyon exclusion statistics, which generalizes the Bose-Einstein and Fermi-Dirac statistics of bosons and fermions, was proposed by Haldane[1]. The relevant past studies had considered only anyon systems without any physical boundary but…
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…
Realization of non-Abelian anyons in topological phases is a crucial step toward topological quantum computation. We propose a scheme to realize a non-Abelian quantum spin liquid (QSL) phase in a three-component Bose gas with contact…
There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. It has previously been shown that the Laughlin state can be…
A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…
Recent cold atom experiments have realized one-dimensional anyons and enabled the tuning of 1D~statistics between bosons and fermions. Here, we analyze the symmetries, integrability, and resulting degeneracies of the underlying…
We develop a density functional treatment of non-interacting abelian anyons, which is capable, in principle, of dealing with a system of a large number of anyons in an external potential. Comparison with exact results for few particles…
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum…
One-dimensional lattice model of SU(2)_{4} anyons containing a transition into the topological ordered phase state is considered. An effective low-energy Hamiltonian is found for half-integer and integer indices of the type of strongly…
Benchmarking numerical methods in quantum chemistry is one of the key opportunities that quantum simulators can offer. Here, we propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We…
Using the Anyon-Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose-Hubbard model using the…
A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results…
Two-dimensional many-body quantum systems can exhibit topological order and support collective excitations with anyonic statistics different from the usual fermionic or bosonic ones. With the emergence of these exotic point-like particles,…
Boundary conformal field theory is brought to bear on the study of topological insulating phases of non-abelian anyonic chains. These topologically non-trivial phases display protected anyonic end modes. We consider antiferromagnetically…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
We study the emergence of topological matter in two-dimensional systems of neutral Rydberg atoms in Ruby lattices. While Abelian anyons have been predicted in such systems, non-Abelian anyons, which would form a substrate for fault-tolerant…
We introduce a two-body quantum Hamiltonian model with spins-$\half$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non-perturbative effect.…
Anyons obeying fractional exchange statistics arise naturally in two dimensions: hard-core two-body constraints make the configuration space of particles not simply-connected. The braid group describes how topologically-inequivalent…