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.

scholarly journals Andreev reflection of fractional quantum Hall quasiparticles

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M. Hashisaka ◽  
T. Jonckheere ◽  
T. Akiho ◽  
S. Sasaki ◽  
J. Rech ◽  
...  
Keyword(s):  
Andreev Reflection ◽  
Quantum Hall ◽  
Many Body ◽  
Fractional Quantum ◽  
Body Effect ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Body State ◽  
Topological Quantum ◽  
Integer Quantum

AbstractElectron correlation in a quantum many-body state appears as peculiar scattering behaviour at its boundary, symbolic of which is Andreev reflection at a metal-superconductor interface. Despite being fundamental in nature, dictated by the charge conservation law, however, the process has had no analogues outside the realm of superconductivity so far. Here, we report the observation of an Andreev-like process originating from a topological quantum many-body effect instead of superconductivity. A narrow junction between fractional and integer quantum Hall states shows a two-terminal conductance exceeding that of the constituent fractional state. This remarkable behaviour, while theoretically predicted more than two decades ago but not detected to date, can be interpreted as Andreev reflection of fractionally charged quasiparticles. The observed fractional quantum Hall Andreev reflection provides a fundamental picture that captures microscopic charge dynamics at the boundaries of topological quantum many-body states.

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 NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

scholarly journals Local incompressibility of fractional quantum Hall states at a filling factor of 3/2

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
L. V. Kulik ◽  
V. A. Kuznetsov ◽  
A. S. Zhuravlev ◽  
V. Umansky ◽  
I. V. Kukushkin
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Hall States
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