Related papers: Numerical simulation of non-abelian anyons
A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into…
Topological quantum computers provide a fault-tolerant method for performing quantum computation. Topological quantum computers manipulate topological defects with exotic exchange statistics called anyons. The simplest anyon model for…
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest…
The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an…
Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting…
We introduce a family of quantum spin Hamiltonians on $\mathbb{Z}^2$ that can be regarded as perturbations of Kitaev's abelian quantum double models that preserve the gauge and duality symmetries of these models. We analyze in detail the…
The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or…
Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing…
The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both $SU(2)$ spin and $SU(N_f)$ orbital degrees of freedom to the thermodynamic properties…
For over twenty years, ultra-cold atomic systems have formed an almost perfect arena for simulating different quantum many-body phenomena and exposing their non-obvious and very often counterintuitive features. Thanks to extremely precise…
Far-from-equilibrium dynamics of SU(2) gauge theory with Wilson fermions is studied in 1+1 space-time dimensions using a real-time lattice approach. Lattice improved Hamiltonians are shown to be very efficient in simulating Schwinger pair…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
We propose a scheme to demonstrate fractional statistics of anyons in an exactly solvable lattice model proposed by Kitaev that involves four-body interactions. The required many-body ground state, as well as the anyon excitations and their…
We study the limit of large onsite repulsion of the one-dimensional Bose-Hubbard model at low densities, and derive a strong-coupling effective Hamiltonian. By taking the lattice parameter to zero, the Hamiltonian becomes a continuum model…
Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle…
Compact scalar field theories on lattices are capable of describing a large class of many-body systems, such as interacting bosons, superconducting circuit networks, spin systems and more. We show that a generic quantum geometric many-body…
Bloch oscillations are exotic phenomena describing the periodic motion of a wave packet subjected to the external force in a lattice, where the system possessing single- or multipleparticles could exhibit distinct oscillation behaviors. In…
We show that anyonic statistics fundamentally reshapes non-Hermitian many-body physics by intrinsically breaking pseudo-Hermiticity, leading to a unique real-complex spectral transition with characteristically dense states in Im$E$. This…
In this set of lectures, we will start with a brief pedagogical introduction to abelian anyons and their properties. This will essentially cover the background material with an introduction to basic concepts in anyon physics, fractional…
In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system-environment…