Conformal invariance of chiral edge theories

Read, N.

doi:10.1103/physrevb.79.245304

Cited by 175 publications

(369 citation statements)

References 38 publications

(103 reference statements)

Supporting

Mentioning

356

Contrasting

Order By: Relevance

“…Furthermore, we have created an integer quantum Hall system in curved space, a longstanding challenge in condensed matter physics. We can extend our tests of the Wen-Zee theory by measuring fractional state number excess in higher Landau levels and examining the connection between the mean orbital spin and the Hall viscosity [30] (see Supplementary Information). Our approach clears a path to the photonic fractional quantum Hall regime, as it is compatible with Rydberg-mediated strong photon-photon interactions [16], and does not require the low particle densities (and thus weakened interactions) necessary to map Laughlin physics onto a lattice.…”

Section: Figmentioning

confidence: 99%

See 1 more Smart Citation

Synthetic Landau levels for photons

Schine

Ryou

Gromov

et al. 2016

Nature

211

243

View full text Add to dashboard Cite

Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties [1][2][3][4][5]. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science [6][7][8]. Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip [9]. This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock-Darwin Hamiltonian for photons in a magnetic field and harmonic trap [10]. Using spatialand energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit [10,11], we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen-Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space [12][13][14][15]. This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids [16,17] and direct detection of anyons [18,19].The Lorentz force on a charged particle moving in a magnetic field leads to the unique topological features of quantum Hall systems, including precisely quantized Hall conductance, topologically protected edge transport, and, in the presence of interactions, the predicted anyonic and non-abelian braiding statistics that form the basis of topological quantum computing [20]. To controllably explore the emergence of these phenomena, efforts have recently focused on realizing synthetic materials in artificial magnetic fields, and in particular, upon implementations for cold atoms and photons. Successful photonic implementations have employed lattices with engineered tunneling [6,[21][22][23][24]. However, it is desirable to realize artificial magnetic fields in the simpler case of a continuum (lattice-free) material [7,25,26], where strong interactions are more easily accessible and the theory maps more directly to fractional quantum Hall systems. In this work, we develop a new approach and demonstrate the first continuum synthetic magnetic field for light.To achieve photonic Landau levels we harness the powerful analogy between photons in a near-degenerate multimode cavity and massive, trapped 2d particles [27,28]. Owing to mirror curvature, the transverse dynamics of a running wave resonator are equivalent to those of a 2D quantum h...

show abstract

Section: Figmentioning

confidence: 99%

“…The latter allows us to calculate the value of a dissipationless, quantized transport coefficient known as the Hall viscosity, η H , which we now describe 30 . Similarly to how the Chern-Simons term encoded Hall conductivity, σ H , the Wen-Zee term encodes the Hall viscosity.…”

Section: Measurable Quantities Of Quantum Hall Systems: Topological Smentioning

confidence: 99%

Synthetic Landau levels for photons

Schine

Ryou

Gromov

et al. 2016

Nature

211

243

View full text Add to dashboard Cite

show abstract

“…We note that 5) such that ∂F/∂F = 0, ∂F /∂F = 1; the first condition is equivalent to the Beltrami equation. If we change from our coordinates z,z to another set ζ,ζ (which are functions of z,z), but leave the almostcomplex structure unchanged, then dF is unchanged, but µ is replaced by µ ζ ζ , with…”

Section: Differential-geometric Preliminariesmentioning

confidence: 99%

“…The archetypal example of this is the quantized Hall conductivity in the integer and fractional quantum Hall effects, which can be expressed as a Berry curvature via the Kubo formula 1,2 . Additionally, the Hall viscosity-an analogous non-dissipative contribution to the viscosity tensor of a fluid-can be expressed as a Berry curvature associated with adiabatic changes of the aspect ratio or metric tensor of a system on a torus [3][4][5] , and is related 5,6 to the so-called shift in the number of flux in the ground state on a sphere 7 . Moreover, these properties are related to Chern-Simons terms in the effective (induced) action of the system (the first Wen-Zee term 7 in the case of Hall viscosity).…”

Section: Introductionmentioning

confidence: 99%

Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

Bradlyn

Read

2015

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

We show that the topological central charge of a topological phase can be directly accessed from the ground-state wavefunctions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to addition of another topological invariant that arises in some cases. For trial wavefunctions that are given by conformal blocks (chiral correlation functions) in a conformal field theory (CFT), we carry out this calculation analytically, using the hypothesis of generalized screening. The topological central charge is found to be that of the underlying CFT used in the construction, as expected. The calculation makes use of the gravitational anomaly in the chiral CFT. It is also shown that the Hall conductivity can be obtained in an analogous way from the U(1) gauge anomaly.

show abstract

“…However, there are solid arguments [15,16] that the wavefunctions constructed using non-unitary CFT cannot describe topological gapped quantum phases. In this respect, a recent work [17] has proposed that unitary Abelian theories may be built from non-unitary ones.…”

Section: Introductionmentioning

confidence: 99%

Clustering properties, Jack polynomials and unitary conformal field theories

Estienne¹,

Regnault²,

Santachiara³

2010

Nuclear Physics B

View full text Add to dashboard Cite

Recently, Jack polynomials have been proposed as natural generalizations of Z k Read-Rezayi states describing non-Abelian fractional quantum Hall systems. These polynomials are conjectured to be related to correlation functions of a class of W-conformal field theories based on the Lie algebra A k−1 . These theories can be considered as non-unitary solutions of a more general series of CFTs with Z k symmetry, the parafermionic theories. Starting from the observation that some parafermionic theories admit unitary solutions as well, we show, by computing the corresponding correlation functions, that these theories provide trial wavefunctions which satisfy the same clustering properties as the non-unitary ones. We show explicitly that, although the wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack polynomial, they still show a fine structure where the mathematical properties of the Jack polynomials play a major role.

show abstract

Conformal invariance of chiral edge theories

Cited by 175 publications

References 38 publications

Synthetic Landau levels for photons

Synthetic Landau levels for photons

Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

Clustering properties, Jack polynomials and unitary conformal field theories

Contact Info

Product

Resources

About