Aharonov-Bohm and Statistical Phases in the Fractional Quantum Hall Effect

1991 ◽  
Vol 05 (10) ◽  
pp. 1731-1738
Author(s):  
W. P. Su
Keyword(s):  
Ground State ◽  
State Energy ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Path Integral Formulation ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Phase Cancellation ◽  
Quantum Hall States ◽  
Aharonov Bohm

The ν=1/q quantum Hall states are characterized by a perfect cancellation of the magnetic (Aharonov-Bohm) and the Fermi statistical phases. The lowering of the ground state energy due to this phase cancellation is illustrated by using a partial analogy with the Helium II problem and via a path integral formulation. For general filling fractions ν=p/q, a cluster of p electrons is considered instead of a single electron. There is again a perfect cancellation of the effective Aharonov-Bohm phase and the statistical phase of the clusters provided that q is odd.

scholarly journals STATISTICS TRANSMUTATIONS IN TWO-DIMENSIONAL SYSTEMS AND THE FRACTIONAL QUANTUM HALL EFFECT

1994 ◽  
Vol 08 (06) ◽  
pp. 375-380 ◽  
Author(s):  
PIOTR SITKO
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
State Energy ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Two Dimensional ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Hartree Fock

Statistics transmutations to superfermions in fractional quantum Hall effect systems are considered in the Hartree-Fock approximation and in the RPA. The Hartree-Fock ground state energy shows that the transmutations are not energetically preferable. Within the RPA it is found that the system exhibits a fractional quantum Hall effect.

scholarly journals A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Ajit Coimbatore Balram
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Topological Structure ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=2+3/8, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.

scholarly journals Non-Hermitian fractional quantum Hall states

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tsuneya Yoshida ◽  
Koji Kudo ◽  
Yasuhiro Hatsugai
Keyword(s):  
Ground State ◽  
Cold Atoms ◽  
Quantum Hall ◽  
Quantum Zeno Effect ◽  
Many Body ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Zeno Effect ◽  
Quantum Hall States ◽  
The Many

AbstractWe demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing Ctot = 1. The robust topological degeneracy against non-Hermiticity arises from the manybody translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.

A Microscopic Hierarchy Theory of the Fractional Quantum Hall Effect

1997 ◽  
Vol 11 (06) ◽  
pp. 707-728 ◽  
Author(s):  
Jian Yang ◽  
Wu-Pei Su
Keyword(s):  
Quantum Hall Effect ◽  
Ground State ◽  
Collective Excitation ◽  
Quantum Hall ◽  
Electron System ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Hierarchy Theory ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

In this paper we present a microscopic hierarchy theory of the fractional quantum Hall effect. The wave functions of the ground state and the collective excitation states are obtained in terms of the electron coordinates. Working in the subspace spanned by the quasiparticles of the 1/m L Laughlin ground state, with m L an odd integer, it is shown that there exists a simple mapping between electron states in the quasiparticle subspace and states of an auxiliary boson system which is defined such that the number of the bosons is the same as that of the quasiparticles and the total magnetic flux quanta seen by the bosons equals the number of electrons. For the auxiliary boson system, one can write down the Laughlin state as well as the density wave states, analogous to the electron system at filling factor 1/m L . By mapping these states onto the quasiparticle subspace of the electrons, we find that the resulting wave functions provide a quite good description for the ground state and the collective excitations respectively of the original electron system at filling factor ν=1/(m L (± 1/2p)) with p a positive integer. This construction of the ground state and the collective excitation states can be repeated for higher filling factors. The theory presented in this paper can be viewed as a microscopic realization of Haldane's original hierarchy picture.

Sign in / Sign up

Export Citation Format

Share Document