Holographic Symmetries and Generalized Order Parameters for Topological Matter

We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in disparate systems including non-Landau systems with topological order. A key notion that we advance is that of {\em holographic symmetry}. It reflects situations wherein global symmetries become, under a duality mapping, symmetries that act solely on the system's boundary. Holographic symmetries are naturally related to edge modes and localization. The utility of our approach is illustrated by systematically deriving generalized order parameters for pure and matter-coupled Abelian gauge theories, and for some models of topological matter.Comment: v2, 10 pages, 3 figures. Accepted for publication in Physical Review B Rapid Communication

Unified approach to Quantum and Classical Dualities

We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are characterized as unitary mappings implementing such morphisms, whose even powers become symmetries of the quantum problem. Dual variables -which were guessed in the past- can be derived in our formalism. We obtain new self-dualities for four-dimensional Abelian gauge field theories.Comment: 4+3 pages, 3 figure

Symmetry and Topological Order

We prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local gauge symmetries) and their associated defects, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges), discuss associated braiding, and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on certain suggested quantum computing schemes and lead to "thermal fragility". Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.Comment: 10 pages, 2 figures. Minimal changes relative to published version- most notably the above shortened title (which was too late to change upon request in the galley proofs). An elaborate description of all of the results in this article appeared in subsequent works, principally in arXiv:cond-mat/0702377 which was published in the Annals of Physics 324, 977- 1057 (2009

Can past gamma-ray bursts explain both INTEGRAL and ATIC/PAMELA/Fermi anomalies simultaneously?

Gamma-ray bursts (GRBs) have been invoked to explain both the 511 keV emission from the galactic bulge and the high-energy positron excess inferred from the ATIC, PAMELA, and Fermi data. While independent explanations can be responsible for these phenomena, we explore the possibility of their common GRB-related origin by modeling the GRB distribution and estimating the rates. For an expected Milky Way long GRB rate, neither of the two signals is generic; the local excess requires a 2% coincidence, while the signal from the galactic center requires a 20% coincidence with respect to the timing of the latest GRB. The simultaneous explanation requires a 0.4% coincidence. Considering the large number of statistical "trials" created by multiple searches for new physics, the coincidences of a few per cent cannot be dismissed as unlikely. Alternatively, both phenomena can be explained by GRBs if the galactic rate is higher than expected. We also show that a similar result is difficult to obtain assuming a simplified short GRB distribution.Comment: 4 pages; version accepted for publicatio

Algebraic symmetries of generic (m+1)(m+1) dimensional periodic Costas arrays

In this work we present two generators for the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\mathbb{Z}_p)^m$ groups: one that is defined by multiplication on $m$ dimensions and the other by shear (addition) on $m$ dimensions. Through exhaustive search we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\mathbb{Z}_p)^m$ groups

Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations

In this work, we illustrate how a Jordan-Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan-Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves, and (v) express the anyonic character of the excitations in this system and the local symmetries that it harbors in terms of fermions.Comment: 14 pages, 7 figure

Repulsive interactions in quantum Hall systems as a pairing problem

23 págs.; 4 figs.; 5 tabs. ; PACS number(s): 73.43.Cd, 02.30.Ik, 74.20.RpA subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in (px+ipy) superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting (px+ip y)-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a >squeezing principle> that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) >incompressible filling factors> for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the quantum Hall systems precise. © 2013 American Physical Society.This work has been partially supported by the National Science Foundation under NSF Grants No. DMR-1206781 (A.S.) and No. DMR-1106293 (Z.N.), and by the Spanish MICINN Grant No. FIS2012-34479. G.O. would like to thank the Max-Planck-Institute in GarchingPeer Reviewe

Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure

Imprints of clustering in multiplicity fluctuations

In this paper, we investigate the multiplicity fluctuations of charged particles observed in high-energy nuclear collisions and relate them to the size of hadronizing systems which happen during such processes. We use the average multiplicities $\langle N\rangle$ and variances $Var\left(N\right)$ of multiplicity distributions of charged particles produced in centrality selected collisions of relativistic heavy-ion nuclei to evaluate the dynamic variable $\Omega$ and study its dependence on the size of colliding nuclei. We connect the observed system-size dependence of multiplicity fluctuations with the clustering phenomena and the finiteness of the hadronizing sources and the thermal bath