相关论文: Geometric Defects in Quantum Hall States

We study the recently observed graphene fractional quantum Hall state at a filling factor $\nu_G=1/3$ using a four-component trial wave function and exact diagonalization calculations. Although it is adiabatically connected to a 1/3…

The fractional quantum Hall (FQH) states are exotic quantum many-body phases whose elementary charged excitations are neither bosons nor fermions but anyons, obeying fractional braiding statistics. While most FQH states are believed to have…

We show the low-lying excitations at filling factor $\nu=n+1/3$ with realistic interactions are contained completely within the well-defined Hilbert space of "Gaffnian quasiholes". Each Laughlin quasihole can thus be understood as a bound…

A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…

We develop a general framework to (numerically) study adiabatic braiding of quasiholes in fractional quantum Hall systems. Specifically, we investigate the Moore-Read (MR) state at $\nu=1/2$ filling factor, a known candidate for non-Abelian…

We investigate the way that the degenerate manifold of midgap edge states in quasicircular graphene quantum dots with zig-zag boundaries supports, under free-magnetic-field conditions, strongly correlated many-body behavior analogous to the…

It was recently discovered that fractional quantum Hall (FQH) states can be classified by the way ground state wave functions go to zero when electrons are brought close together. Quasiparticles in the FQH states can be classified in a…

Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction ($\hat{V}^\text{Pf}_3$) between electrons…

The idea that quantum gravity effects might leak outside the horizon of a black hole has recently been intensively considered. In this study, we calculate the quasinormal modes as a function of the location and amplitude of a generic metric…

We present here a complete microscopic theory of a family of neutral excitations in the fractional quantum Hall fluids, related to the geometric fluctuations of the quantum Hall ground states. Many of the physical properties of such…

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two- component FQH systems at total filling fraction $\nu = n+ 2/3$, for integer $n$. Some of…

Classical constraints on the reduced density matrix of quantum fluids in a single Landau level, termed as local exclusion conditions (LECs) [B. Yang, arXiv:1901.00047], have recently been shown to characterize the ground state of many FQH…

We consider the fractional quantum Hall effect (FQHE) at the filling factor $8/17$, where signatures of incompressibility have been observed in the zeroth Landau level of bilayer graphene. We propose an Abelian state described by the…

We study the surface defect in $\mathcal{N}=2^*$ $U(N)$ gauge theory in four dimensions and its relation to quantum Hall states in two dimensions. We first prove that the defect partition function becomes the Jack polynomial of the…

We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to…

The structure of extrinsic defects in topologically ordered states of matter is host to a rich set of universal physics. Extrinsic defects in 2+1 dimensional topological states include line-like defects, such as boundaries between…

We consider localized qubits evolving around a black hole following a quantum adiabatic dynamics. We develop a geometric structure (based on fibre bundles) permitting to describe the quantum states of a qubit and the spacetime geometry in a…

Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of…

A key property of topologically ordered systems, such as Quantum Hall states, is the existence of excitations obeying fractional quantum statistics - anyons. We develop a theory for multicomponent counterflow states where an ordinary…

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving…