Universal low-temperature properties of quantum and classical ferromagnetic chains

We identify the critical theory controlling the universal, low temperature, macroscopic properties of both quantum and classical ferromagnetic chains. The theory is the quantum mechanics of a single rotor. The mapping leads to an efficient method for computing scaling functions to high accuracy.Comment: 4 pages, 2 tables and 3 Postscript figure

Coexistence of double alternating antiferromagnetic chains in (VO)_2P_2O_7 : NMR study

Nuclear magnetic resonance (NMR) of 31P and 51V nuclei has been measured in a spin-1/2 alternating-chain compound (VO)_2P_2O_7. By analyzing the temperature variation of the 31P NMR spectra, we have found that (VO)_2P_2O_7 has two independent spin components with different spin-gap energies. The spin gaps are determined from the temperature dependence of the shifts at 31P and 51V sites to be 35 K and 68 K, which are in excellent agreement with those observed in the recent inelastic neutron scattering experiments [A.W. Garrett et al., Phys. Rev. Lett. 79, 745 (1997)]. This suggests that (VO)_2P_2O_7 is composed of two magnetic subsystems showing distinct magnetic excitations, which are associated with the two crystallographically-inequivalent V chains running along the b axis. The difference of the spin-gap energies between the chains is attributed to the small differences in the V-V distances, which may result in the different exchange alternation in each magnetic chain. The exchange interactions in each alternating chain are estimated and are discussed based on the empirical relation between the exchange interaction and the interatomic distance.Comment: 10 pages, 11 embedded eps figures, REVTeX, Submitted to Phys. Rev.

A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU--GPU parallelism are discussed.Comment: Accepted for publication in BIT Numerical Mathematic

Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations

The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important model system for the high-$T_c$ superconductors based on cuprates. Using the technique of self-similar continuous unitary transformations we derive effective Hamiltonians for the charge motion in these ladders. The key advantage of this technique is that it provides effective models explicitly in the thermodynamic limit. A real space restriction of the generator of the transformation allows us to explore the experimentally relevant parameter space. From the effective Hamiltonians we calculate the dispersions for single holes. Further calculations will enable the calculation of the interaction of two holes so that a handle of Cooper pair formation is within reach.Comment: 16 pages, 26 figure

Competing orders in a magnetic field: spin and charge order in the cuprate superconductors

We describe two-dimensional quantum spin fluctuations in a superconducting Abrikosov flux lattice induced by a magnetic field applied to a doped Mott insulator. Complete numerical solutions of a self-consistent large N theory provide detailed information on the phase diagram and on the spatial structure of the dynamic spin spectrum. Our results apply to phases with and without long-range spin density wave order and to the magnetic quantum critical point separating these phases. We discuss the relationship of our results to a number of recent neutron scattering measurements on the cuprate superconductors in the presence of an applied field. We compute the pinning of static charge order by the vortex cores in the `spin gap' phase where the spin order remains dynamically fluctuating, and argue that these results apply to recent scanning tunnelling microscopy (STM) measurements. We show that with a single typical set of values for the coupling constants, our model describes the field dependence of the elastic neutron scattering intensities, the absence of satellite Bragg peaks associated with the vortex lattice in existing neutron scattering observations, and the spatial extent of charge order in STM observations. We mention implications of our theory for NMR experiments. We also present a theoretical discussion of more exotic states that can be built out of the spin and charge order parameters, including spin nematics and phases with `exciton fractionalization'.Comment: 36 pages, 33 figures; for a popular introduction, see http://onsager.physics.yale.edu/superflow.html; (v2) Added reference to new work of Chen and Ting; (v3) reorganized presentation for improved clarity, and added new appendix on microscopic origin; (v4) final published version with minor change

Screening of qubit from zero-temperature reservoir

We suggest an application of dynamical Zeno effect to isolate a qubit in the quantum memory unit against decoherence caused by coupling with the reservoir having zero temperature. The method is based on using an auxiliary casing system that mediate the qubit-reservoir interaction and is simultaneously frequently erased to ground state. This screening procedure can be implemented in the cavity QED experiments to store the atomic and photonic qubit states.Comment: 4 pages, 5 figure

Excitation spectrum of the S=1/2 quantum spin ladder with frustration: elementary quasiparticles and many-particle bound states

We study the excitation spectrum of the two-chain S=1/2 Heisenberg spin ladder with additional inter-chain second-neighbor frustrating interactions. The one and two-particle excitations are analyzed by using a mapping of the model onto a Bose gas of hard-core triplets. We find that low-lying singlet and triplet two-particle bound states are present and their binding energy increases with increasing frustration. In addition, many-particle bound states are found by a combination of variational and exact diagonalization techniques. We prove that the larger the number of bound quasiparticles the larger the binding energy. Thus the excitation spectrum has a complex structure and consists of elementary triplets and collective many-particle singlet and triplet excitations which generally mix with the elementary ones. The model exhibits a quantum phase transition from an antiferromagnetic ladder phase (small frustration) into Haldane phase (effectively ferromagnetic ladder for large frustration). We argue that near the transition point the spectrum in both triplet and singlet channels becomes gapless. The excitation wave function is dominated by large-size bound states which leads to the vanishing of the quasiparticle residue.Comment: RevTeX, 23 pages, 12 figure

Jordan-Wigner approach to dynamic correlations in spin-ladders

We present a method for studying the excitations of low-dimensional quantum spin systems based on the Jordan-Wigner transformation. Using an extended RPA-scheme we calculate the correlation function of neighboring spin flips which well approximates the optical conductivity of ${\rm Sr_2CuO_3}$. We extend this approach to the two-leg $S=1/2$--ladder by numbering the spin operators in a meander-like sequence. We obtain good agreement with the optical conductivity of the spin ladder compound (La,Ca)$_{14}$Cu$_{24}$O$_{41}$ for polarization along the rungs. For polarization along the legs higher order correlations are important to explain the weight of high-energy continuum excitations and we estimate the contribution of 4-- and 6--fermion processes.Comment: 15 pages, 16 figure

Effective Field Theory for Layered Quantum Antiferromagnets with Non-Magnetic Impurities

We propose an effective two-dimensional quantum non-linear sigma model combined with classical percolation theory to study the magnetic properties of site diluted layered quantum antiferromagnets like La$_{2}$Cu$_{1-x}$M$_x$O$_{4}$ (M$=$Zn, Mg). We calculate the staggered magnetization at zero temperature, $M_s(x)$, the magnetic correlation length, $\xi(x,T)$, the NMR relaxation rate, $1/T_1(x,T)$, and the N\'eel temperature, $T_N(x)$, in the renormalized classical regime. Due to quantum fluctuations we find a quantum critical point (QCP) at $x_c \approx 0.305$ at lower doping than the two-dimensional percolation threshold $x_p \approx 0.41$. We compare our results with the available experimental data.Comment: Final version accepted for publication as a Rapid Communication on Physical Review B. A new discussion on the effect of disorder in layered quantum antiferromagnets is include

Non-Fermi liquid regime of a doped Mott insulator

We study the doping of a Mott insulator in the presence of quenched frustrating disorder in the magnetic exchange. A low doping regime $\delta<J/t$ is found, in which the quasiparticle coherent scale is low : $\epsilon_F^* = J (\delta/\delta^*)^2$ with $\delta^*=J/t$ (the ratio of typical exchange to hopping). In the ``quantum critical regime'' $\epsilon_F^*<T<J$, several physical quantities display Marginal Fermi Liquid behaviour : NMR relaxation time $1/T_1\sim const.$, resistivity $\rho_{dc}(T) \propto T$, optical lifetime \tau_{opt}^{-1}\propto \omega/\ln(\omega/\epstar) and response functions obey $\omega/T$ scaling, e.g. $J\sum_q \chi''(q,\omega) \propto \tanh (\omega/2T)$. In contrast, single-electron properties display stronger deviations from Fermi liquid theory in this regime with a $\sqrt{\omega}$ dependence of the inverse single-particle lifetime and a $1/\sqrt{\omega}$ decay of the photoemission intensity. On the basis of this model and of various experimental evidence, it is argued that the proximity of a quantum critical point separating a glassy Mott-Anderson insulator from a metallic ground-state is an important ingredient in the physics of the normal state of cuprate superconductors (particularly the Zn-doped materials). In this picture the corresponding quantum critical regime is a ``slushy'' state of spins and holes with slow spin and charge dynamics responsible for the anomalous properties of the normal state.Comment: 40 pages, RevTeX, including 13 figures in EPS. v2 : minor changes, some references adde