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We analytically calculate gaps for the 1/3, 2/5, and 3/7 polarized and partially polarized Fractional Quantum Hall states based on the Hamiltonian Chern-Simons theory we have developed. For a class of potentials that are soft at high…
The nanofabrication technology has taught us that an $m$-dimensional confining potential imposed upon an $n$-dimensional electron gas paves the way to a quasi-($n-m$)-dimensional electron gas, with $m \le n$ and $1\le n, m \le 3$. This is…
Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in…
We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling $1/m$. We introduce a variant of the Laughlin wavefunction for electrons…
Laughlin quasiparticles are the elementary excitations of a highly-correlated fractional quantum Hall electron fluid. They have fractional charge and obey fractional statistics. The quasiparticles can propagate quantum-coherently in chiral…
Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It…
Development of quantum architectures during the last decade has inspired hybrid classical-quantum algorithms in physics and quantum chemistry that promise simulations of fermionic systems beyond the capability of modern classical computers,…
We argue that the success of DFT can be understood in terms of a semiclassical expansion around a very specific limit. This limit was identified long ago by Lieb and Simon for the total electronic energy of a system. This is a universal…
Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of…
Quasiparticle interference imaging (QPI) provides a route to characterize electronic structure from real space images acquired using scanning tunneling microscopy. It emerges due to scattering of electrons at defects in the material. The…
We develop a theory for the pseudorelativistic fractional quantum Hall effect in graphene, which is based on a multicomponent abelian Chern-Simons theory in the fermionic functional integral approach. Calculations are performed in the…
While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual…
We derive a path-integral Schwinger-Keldysh approach for quantum spin systems. This is achieved by means of a semionic representation of spins as fermions with imaginary chemical potential. The major simplifying feature in comparison with…
We develop a quasiclassical method based on the path integral formalism, to study the influence of disorder on magnetooscillations of the density of states and conductivity. The treatment is appropriate for electron systems in the presence…
Understanding the quantum dynamics of spin defects and their coherence properties requires accurate modeling of spin-spin interaction in solids and molecules, for example by using spin Hamiltonians with parameters obtained from…
Electrokinetic transport phenomena can strongly influence the behaviour of macromolecules and colloidal particles in solution, with applications in, e.g., DNA translocation through nanopores, electro-osmotic flow in nanocapillaries, and…
Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on…
We present a 48-element programmable phase plate for coherent electron waves produced by a combination of photolithography and focused ion beam. This brings the highly successful concept of wavefront shaping from light optics into the realm…
We discuss the rich vibrational dynamics of nanometer-scale semiconducting and insulating crystals as probed by localized electronic impurity states, with an emphasis on nanoparticles that are only weakly coupled to their environment. Two…
The universal functional of Hohenberg-Kohn is given as a coupling-constant integral over the density as a functional of the potential. Conditions are derived under which potential-functional approximations are variational. Construction via…