The S=1/2S=1/2 Kagome Heisenberg Antiferromagnet Revisited

We examine the perennial quantum spin-liquid candidate $S=1/2$ Heisenberg antiferromagnet on the kagome lattice. Our study is based on achieving Lanczos diagonalization of the Hamiltonian on a $48$ site cluster in sectors with dimensions as a large as $5 \times 10^{11}$. The results reveal novel intricate structures in the low-lying energy spectrum. These structures by no means unambiguously support an emerging consensus of a $\mathbb{Z}_2$ spin liquid ground state, but instead appear compatible with several scenarios, including four-fold topological degeneracy, inversion symmetry breaking and a combination thereof. We discuss finite-size effects, such as the apparent absence of ETH, and note that while considerably reduced, some are still present for the largest cluster. Finally, we observe that an XXZ model in the Ising limit reproduces remarkably well the most striking features of finite-size spectra.Comment: 8 pages, 5 figure

Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results

We present a comprehensive list of ground state energies and spin gaps of finite kagome clusters with up to 42 spins obtained using large-scale exact diagonalization techniques. This represents the current limit of this exact approach. For a fixed number of spins N we study several cluster shapes under periodic boundary conditions in both directions resulting in a toroidal geometry. The clusters are characterized by their side length and diagonal as well as the shortest "Manhattan" diameter of the torii. A finite-size scaling analysis of the ground state energy as well as the spin gap is then performed in terms of the shortest toroidal diameter as well as the shortest "Manhattan" diameter. The structure of the spin-spin correlations further supports the importance of short loops wrapping around the torii.Comment: 4 pages, 4 figures, added one referenc

GRBs from unstable Poynting dominated outflows

Poynting flux driven outflows from magnetized rotators are a plausible explanation for gamma-ray burst engines. We suggest a new possibility for how such outflows might transfer energy into radiating particles. We argue that the Poynting flux drives non-linearly unstable large amplitude electromagnetic waves (LAEMW) which ``break'' at radii $r_t \sim 10^{14}$ cm where the MHD approximation becomes inapplicable. In the ``foaming'' (relativisticly reconnecting) regions formed during the wave breaks the random electric fields stochastically accelerate particles to ultrarelativistic energies which then radiate in turbulent electromagnetic fields. The typical energy of the emitted photons is a fraction of the fundamental Compton energy $\epsilon \sim f \hbar c/r_e$ with $f \sim 10^{-3}$ plus additional boosting due to the bulk motion of the medium. The emission properties are similar to synchrotron radiation, with a typical cooling time $\sim 10^{-4}$ sec. During the wave break, the plasma is also bulk accelerated in the outward radial direction and at larger radii can produce afterglows due to the interactions with external medium. The near equipartition fields required by afterglow models maybe due to magnetic field regeneration in the outflowing plasma (similarly to the field generation by LAEMW of laser-plasma interactions) and mixing with the upstream plasma.Comment: 15 pages, 1 figur

Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field

We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J_1-J_2 chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states towards spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional $S=1/2$ quantum magnets in a magnetic field.Comment: 4+ pages, 4 figure

The vanishing ideal of a finite set of points with multiplicity structures

Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.Comment: 12 pages,12 figures,ASCM 201

Formation and Primary Heating of The Solar Corona - Theory and Simulation

An integrated Magneto-Fluid model, that accords full treatment to the Velocity fields associated with the directed plasma motion, is developed to investigate the dynamics of coronal structures. It is suggested that the interaction of the fluid and the magnetic aspects of plasma may be a crucial element in creating so much diversity in the solar atmosphere. It is shown that the structures which comprise the solar corona can be created by particle (plasma) flows observed near the Sun's surface - the primary heating of these structures is caused by the viscous dissipation of the flow kinetic energy.Comment: 46 pages including 7 pages of figures, Submitted to Phys.Plasma

A New View on Worst-Case to Average-Case Reductions for NP Problems

We study the result by Bogdanov and Trevisan (FOCS, 2003), who show that under reasonable assumptions, there is no non-adaptive worst-case to average-case reduction that bases the average-case hardness of an NP-problem on the worst-case complexity of an NP-complete problem. We replace the hiding and the heavy samples protocol in [BT03] by employing the histogram verification protocol of Haitner, Mahmoody and Xiao (CCC, 2010), which proves to be very useful in this context. Once the histogram is verified, our hiding protocol is directly public-coin, whereas the intuition behind the original protocol inherently relies on private coins

NMR relaxation rate in the field-induced octupolar liquid phase of spin-1/2 J1-J2 frustrated chains

In the spin-1/2 frustrated chain with nearest-neighbor ferromagnetic exchange J1 and next-nearest-neighbor antiferromagnetic exchange J2 under magnetic field, magnetic multipolar-liquid (quadrupolar, octupolar, and hexadecapolar) phases are widely expanded from the saturation down to a low-field regime. Recently, we have clarified characteristic temperature and field dependence of the NMR relaxation rate 1/T_1 in the quadrupolar phase. In this paper, we examine those of 1/T_1 in the octupolar phase combining field theoretical method with numerical data. The relevance of the results to quasi one-dimensional J1-J2 magnets such as PbCuSO4(OH)2, Rb2Cu2Mo3O12 and Li2ZrCuO4 is shortly discussed.Comment: 6 pages (1 column), 3 figure

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction