Topological entropy of realistic quantum Hall wave functions

Friedman, Barry; Levine, Gregory

doi:10.1103/physrevb.78.035320

Cited by 19 publications

(31 citation statements)

References 29 publications

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“…Possible further information of CFT can be encoded in a multi-interval entanglement entropy. [6][7][8] As another example, the existence of topological order in gapped systems can be detected by measuring a constant contribution to the entanglement entropy 9,10 ͑with recent applications to fractional quantum Hall states 11,12 and Z 2 spin liquids [13][14][15][16][17] ͒.…”

Section: Introductionmentioning

confidence: 99%

Shannon and entanglement entropies of one- and two-dimensional critical wave functions

et al. 2009

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International audienceWe study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant S_0. In c=1 critical systems (Tomonaga-Luttinger liquids), we find that S_0 is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, S_0 is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a c=1/2 critical point

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Section: Introductionmentioning

confidence: 99%

Shannon and entanglement entropies of one- and two-dimensional critical wave functions

et al. 2009

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“…We note that recently, entanglement entropy in the SLL including finite thickness effects has been investi- gated 83,84 . However, the previous study did calculations using the torus geometry, in contrast to our spherical geometry, and attempted to isolate and calculate the socalled topological term of the entanglement entropy.…”

Section: A Entanglement Entropymentioning

confidence: 96%

Entanglement measures for quasi-two-dimensional fractional quantum Hall states

2011

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We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy and the entanglement spectrum as a function of the finite layer thickness d of the quasi-two-dimensional system for a number of filling fractions ν in the lowest and the second Landau levels: ν = 1/3, 7/3, 1/2, and 5/2. We observe that the entanglement measures are dependent on which Landau level the electrons fractionally occupy, and find that filling fractions 1/3 and 7/3, which are considered to be Laughlin states, weaken with d in the lowest Landau level (ν=1/3) and strengthen with d in the second Landau level (ν=7/3). For the enigmatic even-denominator ν = 5/2 state, we find that entanglement in the ground state is consistent with that of the non-Abelian Moore-Read Pfaffian state at an optimal thickness d. We also find that the single-layer ν = 1/2 system is not a fractional quantum Hall state consistent with the experimental observation. In general, our theoretical findings based on entanglement considerations are completely consistent with the results based on wavefunction overlap calculations.

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“…One can approach the limit of very large system sizes through clusters of any fixed aspect ratio and since we are concerned with quantum liquid states, aspect ratio one has been chosen. This numerical approach has previously been used to study the entanglement entropy without a disorder potential 5,7 . The random potential 10 U(r) is taken to be delta correlated i.e.…”

Section: Weak Disordermentioning

confidence: 99%

“…A natural interpretation of these graphs is a quantum phase transition from the Moore-Read state for disorder strength U R ≈ 0.04. Previous numerical studies5,14,27 indicate that the ground state for pure Coulomb potential (no disorder) is topologically equivalent to the Moore-Read state. We therefore suggest that the sharp drop off infigure 8aand particularly 8b as contrasted to the smoother curves in 7a and 7b is a transition due to the destruction of the Moore-Read state by disorder.…”

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confidence: 93%

Entanglement entropy of random fractional quantum Hall systems

2011

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The entanglement entropy of the ν = 1/3 and ν = 5/2 quantum Hall states in the presence of short range random disorder has been calculated by direct diagonalization. A microscopic model of electron-electron interaction is used, spin polarized electrons are confined to a single Landau level and interact with long range Coulomb interaction. For very weak disorder, the values of the topological entanglement entropy are roughly consistent with expected theoretical results. By considering a broader range of disorder strengths, the entanglement entropy was studied in an effort to detect quantum phase transitions. In particular, there is a signature of a transition as a function of the disorder strength for the ν = 5/2 state. Prospects for using the density matrix renormalization group to compute the entanglement entropy for larger system sizes are discussed.

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Topological entropy of realistic quantum Hall wave functions

Cited by 19 publications

References 29 publications

Shannon and entanglement entropies of one- and two-dimensional critical wave functions

Shannon and entanglement entropies of one- and two-dimensional critical wave functions

Entanglement measures for quasi-two-dimensional fractional quantum Hall states

Entanglement entropy of random fractional quantum Hall systems

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