Related papers: Interaction driven quantum phase transition in fra…
The energy levels and optical transitions of tetrahedral core/shell InP/ZnSe quantum dots (QDs) are investigated by means of multi-band k$\cdot$p theory. Despite the $\overline{T}_d$ symmetry relaxing spherical selection rules, the…
The interplay between interactions and topology in quantum materials is of extensive current interest. Strong correlations are known to be important for insulating topological states, as exemplified by the fractional quantum Hall effect.…
We study the fractional quantum Hall effect at filling fractions 7/3 and 5/2 in the presence of the spin-orbit interaction, using the exact diagonalization method and the density matrix renormalization group (DMRG) method in a spherical…
Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling…
The quantum phase diagram of the Hubbard chain with correlated hopping is accurately determined through jumps in $\pi$ in the charge and spin Berry phases. The nature of each thermodynamic phase, and the existence of charge and spin gaps,…
We propose an experimentally-feasible system based on spin transitions in the fractional quantum Hall effect regime where parafermions, high-order non-abelian excitations, can be potentially realized. We provide a proof-of-concept…
We study the fractional quantum Hall phases of a pseudospin-1/2 Bose gas in an artificial gauge field. In addition to an external magnetic field, the gauge field also mimics an intrinsic spin-orbit coupling of the Rashba type. While the…
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study…
The interplay between topology and strong interactions gives rise to a variety of exotic quantum phases, including fractional quantum Hall (FQH) states and their lattice analogs - fractional Chern insulators (FCIs). Such topologically…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in interacting chaotic few- and many-body systems,…
Quantum geometric electronic responses are often viewed through a non-interacting lens: independent quasiparticles accumulate Berry phases as they move through a static crystal and background potential. Here we argue that the combined…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides…
We investigate integer and fractional quantum Hall states in quantum point contacts (QPCs) of different geometries, defined in AlGaAs/GaAs heterostructures employing different doping and screening techniques. We find that, even in the…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
We present minimal toy models for topological skyrmion phases of matter, which generically realize type-II topological phase transitions in effectively non-interacting systems, those which occur without closing of the minimum direct bulk…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
Non-interacting topological states of matter can be realized in band insulators with intrinsic spin-orbital couplings as a result of the nontrivial band topology. In recent years, the possibility of realizing novel interaction-driven…
In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on…
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics…