Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Order One and Two

Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lame polynomials of order one and two. Some of the models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model, (iii) coupled saturated discrete nonlinear Schrodinger equation, (iv) coupled phi4 model, and (v) coupled phi6 model. Furthermore, we show that most of these coupled models in fact also possess an even broader class of exact solutions.Comment: 31 pages, to appear in Pramana (Journal of Physics) 201

Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Arbitrary Order

Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lam\'e polynomials of arbitrary order. The models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model, (iii) coupled $\phi^4$ model, and (iv) coupled $\phi^6$ model. In all these cases we show that the coefficients of the Lam\'e polynomials are such that the Lam\'e polynomials can be reexpressed in terms of Chebyshev polynomials of the relevant Jacobi elliptic function

Experimental signatures of emergent quantum electrodynamics in Pr2_2Hf2_2O7_7

In a quantum spin liquid, the magnetic moments of the constituent electron spins evade classical long-range order to form an exotic state that is quantum entangled and coherent over macroscopic length scales [1-2]. Such phases offer promising perspectives for device applications in quantum information technologies, and their study can reveal fundamentally novel physics in quantum matter. Quantum spin ice is an appealing proposal of one such state, in which the fundamental ground state properties and excitations are described by an emergent U(1) lattice gauge theory [3-7]. This quantum-coherent regime has quasiparticles that are predicted to behave like magnetic and electric monopoles, along with a gauge boson playing the role of an artificial photon. However, this emergent lattice quantum electrodynamics has proved elusive in experiments. Here we report neutron scattering measurements of the rare-earth pyrochlore magnet Pr$_2$Hf$_2$O$_7$ that provide evidence for a quantum spin ice ground state. We find a quasi-elastic structure factor with pinch points - a signature of a classical spin ice - that are partially suppressed, as expected in the quantum-coherent regime of the lattice field theory at finite temperature. Our result allows an estimate for the speed of light associated with magnetic photon excitations. We also reveal a continuum of inelastic spin excitations, which resemble predictions for the fractionalized, topological excitations of a quantum spin ice. Taken together, these two signatures suggest that the low-energy physics of Pr$_2$Hf$_2$O$_7$ can be described by emergent quantum electrodynamics. If confirmed, the observation of a quantum spin ice ground state would constitute a concrete example of a three-dimensional quantum spin liquid - a topical state of matter which has so far mostly been explored in lower dimensionalities.Comment: 15 pages, 3 figure

Magnetic order, magnetic correlations, and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7

Er2Ti2O7 is believed to be a realization of an XY antiferromagnet on a frustrated lattice of corner-sharing regular tetrahedra. It is presented as an example of the order-by-disorder mechanism in which fluctuations lift the degeneracy of the ground state, leading to an ordered state. Here we report detailed measurements of the low-temperature magnetic properties of Er2Ti2O7, which displays a second-order phase transition at TN≃1.2 K with coexisting short- and long-range orders. Magnetic susceptibility studies show that there is no spin-glass-like irreversible effect. Heat capacity measurements reveal that the paramagnetic critical exponent is typical of a 3-dimensional XY magnet while the low-temperature specific heat sets an upper limit on the possible spin-gap value and provides an estimate for the spin-wave velocity. Muon spin relaxation measurements show the presence of spin dynamics in the nanosecond time scale down to 21 mK. This time range is intermediate between the shorter time characterizing the spin dynamics in Tb2Sn2O7, which also displays long- and short-range magnetic order, and the time scale typical of conventional magnets. Hence the ground state is characterized by exotic spin dynamics. We determine the parameters of a symmetry-dictated Hamiltonian restricted to the spins in a tetrahedron, by fitting the paramagnetic diffuse neutron scattering intensity for two reciprocal lattice planes. These data are recorded in a temperature region where the assumption that the correlations are limited to nearest neighbors is fair