相关论文: Geometric Defects in Quantum Hall States

The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in…

Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized,…

It has been shown that different Abelian and non-Abelian fraction quantum Hall states can be characterized by patterns of zeros described by sequences of integers {S_a}. In this paper, we will show how to use the data {S_a} to calculate…

We analyze the effect of exchanging quasiholes described by Gaffnian quantum Hall trial state wave functions. This exchange is carried out via adiabatic transport using the recently developed coherent state Ansatz. We argue that our Ansatz…

Motivated by the quasiparticle wavefunction in the composite fermion (CF) theory for fractional quantum Hall filling factor $\nu = 1/m$, I consider a suitable quasiparticle operator in differential form, as a modified form of Laughlin's…

Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic…

We study the generating functional, the adiabatic curvature and the adiabatic phase for the integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating functional we derive its asymptotic expansion for the large flux…

We present and analyze a protocol in which polaritons in a noncoplanar optical cavity form fractional quantum Hall states. We model the formation of these states and present techniques for subsequently creating anyons and measuring their…

Density oscillations in quantum fluids can reveal their fundamental characteristic features. In this work, we study the density oscillation of incompressible fractional quantum Hall (FQH) fluids created by flux insertion. For the model…

In the pattern-of-zeros approach to quantum Hall states, a set of data {n;m;S_a|a=1,...,n; n,m,S_a in N} (called the pattern of zeros) is introduced to characterize a quantum Hall wave function. In this paper we find sufficient conditions…

We propose a quasi-particle formulation of effective edge theories for the fractional quantum Hall effect. For the edge of a Laughlin state with filling fraction \nu=1/m, our fundamental quasi-particles are edge electrons of charge -e and…

Qubits in topological quantum computation are built from non-Abelian anyons. Adiabatic braiding of anyons is exploited as topologically protected logical gate operations. Thus, the adiabaticity upon which the notion of quantum statistics is…

While the values for the fractional charge and fractional statistics coincide for fractional Hall (FQH) states in the Laughlin sequence, they do not for more general FQH states, such as those in the Jain sequence. This mismatch leads to…

Defects between gapped boundaries provide a possible physical realization of projective non-abelian braid statistics. A notable example is the projective Majorana/parafermion braid statistics of boundary defects in fractional quantum…

The Laughlin state embodies a universal class of fractional quantum Hall effects arising in two-dimensional electron systems subjected to strong perpendicular magnetic fields. Conventionally described by a single-component wavefunction, the…

Materials hosting topologically protected non-Abelian zero modes offer the exciting possibility of storing and manipulating quantum information in a manner that is protected from decoherence at the hardware level. In this work, we study the…

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…

We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction…

The quantum Hall (QH) effect represents a unique playground where quantum coherence of electrons can be exploited for various applications, from metrology to quantum computation. In the fractional regime it also hosts anyons, emergent…

The quantum geometric tensor (QGT) characterizes the complete geometric properties of quantum states, with the symmetric part being the quantum metric, and the antisymmetric part being the Berry curvature. We propose a generic Hamiltonian…