scholarly journals TOPOLOGICAL ENTANGLEMENT ENTROPY IN THE SECOND LANDAU LEVEL

2010 ◽  
Vol 24 (24) ◽  
pp. 4707-4715 ◽  
Author(s):  
B. A. FRIEDMAN ◽  
G. C. LEVINE
Keyword(s):  
Landau Level ◽  
Coulomb Potential ◽  
Ground State ◽  
Entanglement Entropy ◽  
Finite Thickness ◽  
Quantum Hall ◽  
Topological Order ◽  
Quantum Hall System ◽  
Topological Entanglement Entropy ◽  
Area Law

The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level is studied by direct diagonalization. The subdominant term of the area law, the topological entanglement entropy, which is believed to carry information about topological order in the ground state, was extracted for filling factors ν = 12/5 and ν = 7/3. While it is difficult to make strong conclusions about ν = 12/5, the ν = 7/3 state appears to be very consistent with the topological entanglement entropy for the k = 4 Read–Rezayi state. The effect of finite thickness corrections to the Coulomb potential used in the direct diagonalization is also systematically studied.

scholarly journals Edge States and Entanglement Entropy

1997 ◽  
Vol 12 (03) ◽  
pp. 625-641 ◽  
Author(s):  
A. P. Balachandran ◽  
Arshad Momen ◽  
L. Chandar
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Coarse Graining ◽  
Gauge Fields ◽  
Edge States ◽  
Area Law

It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular, we show that the entanglement entropy of the ground state for the quantum Hall effect on a disk exhibits an approximate "area" law.

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

scholarly journals THE HYDRODYNAMICAL LIMIT OF QUANTUM HALL SYSTEM

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2771-2781 ◽  
Author(s):  
D. SREEDHAR BABU ◽  
R. SHANKAR ◽  
M. SIVAKUMAR
Keyword(s):  
Landau Level ◽  
Small Amplitude ◽  
Quantum Hall ◽  
Collective Excitations ◽  
Current Form ◽  
Long Wavelength ◽  
Lowest Landau Level ◽  
Hydrodynamical Limit ◽  
Quantum Hall System ◽  
A Current

We study the current algebra of FQHE systems in the hydrodynamical limit of small amplitude, long-wavelength fluctuations. We show that the algebra simplifies considerably in this limit. The Hamiltonian is expressed in a current–current form and the operators creating inter-Landau level and lowest Landau level collective excitations are identified.

scholarly journals Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons

2017 ◽  
Vol 29 (06) ◽  
pp. 1750018 ◽  
Author(s):  
Sven Bachmann
Keyword(s):  
Ground State ◽  
Entanglement Entropy ◽  
Orientable Surface ◽  
Cell Complex ◽  
Local Order ◽  
Topological Order ◽  
Cohomology Groups ◽  
Closed Orientable Surface ◽  
Ground State Degeneracy ◽  
Comprehensive Study

In this comprehensive study of Kitaev’s abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterize the elementary anyonic excitations. The homology and cohomology groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterizations of topological order.

Dynamics of the inter-Landau-level magnetoplasmon coherence in a quantum Hall system

2005 ◽  
Author(s):  
K.M. Dani ◽  
J. Tignon ◽  
M. Breit ◽  
D.S. Chemla ◽  
E.G. Kavousanaki ◽  
...  
Keyword(s):  
Landau Level ◽  
Quantum Hall ◽  
Quantum Hall System

scholarly journals Power law corrections to BTZ black hole entropy

2014 ◽  
Vol 24 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Dharm Veer Singh
Keyword(s):  
Black Hole ◽  
Excited State ◽  
Power Law ◽  
Ground State ◽  
Entanglement Entropy ◽  
Black Hole Entropy ◽  
Mixed States ◽  
Btz Black Hole ◽  
First Excited State ◽  
Area Law

We study the quantum scalar field in the background of BTZ black hole and evaluate the entanglement entropy of the nonvacuum states. The entropy is proportional to the area of event horizon for the ground state, but the area law is violated in the case of nonvacuum states (first excited state and mixed states) and the corrections scale as power law.

scholarly journals Topological Entanglement Entropy of Black Hole Interiors

2020 ◽  
pp. 1940001
Author(s):  
Eric Howard
Keyword(s):  
Black Hole ◽  
Long Range ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Black Hole Entropy ◽  
Topological Quantum ◽  
Boundary Correspondence ◽  
Entropy Of Black Hole ◽  
Topological Entanglement Entropy ◽  
Chern Simons

Recent theoretical progress shows that ([Formula: see text]) black hole solution manifests long-range topological quantum entanglement similar to exotic non-Abelian excitations with fractional quantum statistics. In topologically ordered systems, there is a deep connection between physics of the bulk and that at the boundaries. Boundary terms play an important role in explaining the black hole entropy in general. We find several common properties between BTZ black holes and the Quantum Hall effect in ([Formula: see text])-dimensional bulk/boundary theories. We calculate the topological entanglement entropy of a ([Formula: see text]) black hole and recover the Bekenstein–Hawking entropy, showing that black hole entropy and topological entanglement entropy are related. Using Chern–Simons and Liouville theories, we find that long-range entanglement describes the interior geometry of a black hole and identify it with the boundary entropy as the bond required by the connectivity of spacetime, gluing the short-range entanglement described by the area law. The IR bulk–UV boundary correspondence can be realized as a UV low-excitation theory on the bulk matching the IR long-range excitations on the boundary theory. Several aspects of the current findings are discussed.

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