The Fractional Quantum Hall Effect In Composite Fermion Systems

Jacak, Lucjan; Sitko, Piotr; Wieczorek, Konrad; Wójs, Arkadiusz

doi:10.1093/acprof:oso/9780198528708.003.0007

Cited by 6 publications

(8 citation statements)

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“…Since the famous work of Laughlin [123], there has been enormous progress in our understanding of the fractional quantum Hall effect (FQHE) [124]. Nevertheless, many challenges remain open: direct observation of the anyonic character of excitations, observation of other kinds of strongly correlated states, etc.…”

Section: Cold Atoms and The Challenges Of Condensed Matter Physicsmentioning

confidence: 99%

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

Lewenstein

Sanpera

Ahufinger

et al. 2007

Advances in Physics

2,072

2,345

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We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

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Section: Cold Atoms and The Challenges Of Condensed Matter Physicsmentioning

confidence: 99%

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

Lewenstein

Sanpera

Ahufinger

et al. 2007

Advances in Physics

2,072

2,345

View full text Add to dashboard Cite

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“…Classes of topologically non-equivalent closed loops in the configuration space of the system of N identical particles build up the π 1 homotopy group, called in this case the braid group (full and pure for indistinguishable and distinguishable particles, respectively) [18][19][20][21].…”

Section: Statistics and Braid Groupsmentioning

confidence: 99%

“…For the permutation group S N , being the full braid group for R n , n 3, there exist only two 1DURs: σ i → e iπ or σ i → e i0 (σ i is the interchange of the i th and (i + 1)th particles), corresponding to fermions and bosons, respectively. For R 2 the braid group is substantially richer than S N and has an infinite number of 1DURs [19,21,22], defined for the group generators as:…”

Section: Statistics and Braid Groupsmentioning

confidence: 99%

Cyclotron braid group structure for composite fermions

Jacak¹,

Jóźwiak²,

Jacak³

et al. 2010

J. Phys.: Condens. Matter

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Although they describe properties of 2D Hall systems in the fractional quantum regime well, composite fermions suffer from the unexplained character of the localized magnetic field flux-tubes attached to each particle in order to reproduce the Laughlin correlations via Aharonov-Bohm phase shifts. The identification of the cyclotron trajectories of 2D charged particles as accessible classical trajectories within the braid group approach at the magnetic field presence, allows, however, for the avoidance of the construction with fluxes. We introduce cyclotron braid subgroups for charged 2D systems at the fractional Landau-level filling associated in a more natural way with composite fermions without invoking field flux-tubes. The Aharonov-Bohm phase shifts caused by fluxes are replaced with the phase gain due to multi-loop cyclotron trajectories unavoidably occurring at the fractional filling of 1/p (p is an odd integer). Another approach to composite particles, using so-called vortices, is also discussed from the point of view of the cyclotron braid group description (for both odd and even p integers).

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“…Too-short cyclotron trajectories at strong magnetic fields. -One-dimensional unitary representations (1DURs) of the full braid group [9,[13][14][15] (π 1 homotopy group of undistinguishable N -particle configuration space [13]), define weights for the path integral (a) E-mail: ljacak@pwr.wroc.pl summation over trajectories [8,9]. If the trajectories fall into separated homotopy classes that are distinguished by non-equivalent closed loops attached to an open trajectory λ a,b (linking points a and b in the configuration space), then an additional unitary factor (the weight of the particular trajectory class) should be included [8,9] in the path integral: I a→b = l∈π1 e iα l dλ l e iS[λ l(a,b) ] , where π 1 stands for the full braid group.…”

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confidence: 99%