Algorithmic differentiation and the calculation of forces by quantum Monte Carlo

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future.Comment: 32 pages, 4 figure, to appear in The Journal of Chemical Physic

Ising transition in the two-dimensional quantum J1−J2J_1-J_2 Heisenberg model

We study the thermodynamics of the spin-$S$ two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor couplings in its collinear phase ($J_2/J_1>0.5$), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio $J_2/J_1$ is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin- and temperature-dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li$_2$VOSiO$_4$ and related compounds.Comment: 4 page, 4 figure

Using compound earcons to represent hierarchies

Previous research on non-speech audio messages called <i>earcons</i> showed that they could provide powerful navigation cues in menu hierarchies. This work used <i>hierarchical</i> earcons. In this paper we suggest <i>compound</i> earcons provide a more flexible method for presenting this information. A set of sounds was created to represent the numbers 0-4 and dot. Sounds could then be created for any node in a hierarchy by concatenating these simple sounds. A hierarchy of four levels and 27 nodes was constructed. An experiment was conducted in which participants had to identify their location in the hierarchy by listening to an earcon. Results showed that participants could identify their location with over 97% accuracy, significantly better than with hierarchical earcons. Participants were also able to recognise previously unheard earcons with over 97% accuracy. These results showed that compound earcons are an effective way of representing hierarchies in sound

Effect of local charge fluctuations on spin physics in the Neel state of La2_2CuO4_4

We explore the effect of local charge fluctuations on the spin response of a Mott insulator by deriving an effective spin model, and studying it using Schwinger boson mean field theory. Applying this to La$_2$CuO$_4$, we show that an accurate fit to the magnon dispersion relation, measured by Coldea {\em et al.} [Phys. Rev. Lett. {\bf 86}, 5377 (2001)] is obtained with Hubbard model parameters $U \approx 2.34 eV$, and $t \approx 360 meV$. These parameters lead to estimates of the staggered magnetization ($m_s \approx 0.25$), spin wave velocity ($c\approx 800 meV$-\AA), and spin stiffness ($\rho_s \approx 24 meV$). In particular the staggered moment as well as the effective local moment are renormalized to smaller values compared to the Heisenberg model due to local charge fluctuations in the Hubbard model. The dynamical structure factor shows considerable weight in the continuum along the zone boundary as well as secondary peaks that may be observed in high resolution neutron scattering experiments.Comment: Manuscript considerably revised following referee comments. Also added a brief discussion of sum rules. 8 pages, 6 eps figure

Spin-lattice coupling in frustrated antiferromagnets

We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks the inversion symmetry and gives rise to a chiral pyrochlore lattice, in which frustrated bonds form helices with a definite handedness. The chirality is transferred to the spin system through spin-orbit coupling, resulting in a long-period spiral state, as observed in spinel CdCr2O4. We discuss explicit models of spin-lattice coupling using local phonon modes, and their applications in other frustrated magnets.Comment: 23 pages, 6 figures. Lecture notes for Trieste Summer School, August 2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mil

Thermodynamics of the quantum easy-plane antiferromagnet on the triangular lattice

The classical XXZ triangular-lattice antiferromagnet (TAF) shows both an Ising and a BKT transition, related to the chirality and the in-plane spin components, respectively. In this paper the quantum effects on the thermodynamic quantities are evaluated by means of the pure-quantum self-consistent harmonic approximation (PQSCHA), that allows one to deal with any spin value through classical MC simulations. We report the internal energy, the specific heat, and the in-plane correlation length of the quantum XX0 TAF, for S=1/2, 1, 5/2. The quantum transition temperatures turn out to be smaller the smaller the spin, and agree with the few available theoretical and numerical estimates.Comment: 4 pages,3 postscript figure

Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), we study a frustrated $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice. The classical $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice has N\'eel order for $J_2 J_1/6$, it exhibits a one-parameter family of degenerate incommensurate spin spiral ground states where the spiral wave vector can point in any direction. Spin wave fluctuations at leading order lift this accidental degeneracy in favor of specific wave vectors, leading to spiral order by disorder. For spin $S=1/2$, quantum fluctuations are, however, likely to be strong enough to melt the spiral order parameter over a wide range of $J_2/J_1$. Over a part of this range, we argue that the resulting state is a valence bond solid (VBS) with staggered dimer order - this VBS is a nematic which breaks lattice rotational symmetry. Our arguments are supported by comparing the spin wave energy with the energy of the dimer solid obtained using a bond operator formalism. Turning to the effect of thermal fluctuations on the spiral ordered state, any nonzero temperature destroys the magnetic order, but the discrete rotational symmetry of the lattice remains broken resulting in a thermal analogue of the nematic VBS. We present arguments, supported by classical Monte Carlo simulations, that this nematic transforms into the high temperature symmetric paramagnet via a thermal phase transition which is in the universality class of the classical 3-state Potts (clock) model in 2D. We discuss the possible relevance of our results for honeycomb magnets, such as Bi$_3$M$_4$O$_{12}$(NO$_3$) (with M=Mn,V,Cr), and bilayer triangular lattice magnets.Comment: Slightly revise

Inhomogeneity Induces Resonance Coherence Peaks in Superconducting BSCCO

In this paper we analyze, using scanning tunneling spectroscopy, the density of electronic states in nearly optimally doped BSCCO in zero field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a 2 xi_0 * 2 xi_0 patch with an enhanced or supressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.Comment: 4 pages, 3 figure

Dirac method and symplectic submanifolds in the cotangent bundle of a factorizable Lie group

In this work we study some symplectic submanifolds in the cotangent bundle of a factorizable Lie group defined by second class constraints. By applying the Dirac method, we study many issues of these spaces as fundamental Dirac brackets, symmetries, and collective dynamics. This last item allows to study integrability as inherited from a system on the whole cotangent bundle, leading in a natural way to the AKS theory for integrable systems

Comparing Fixed-amount and Progressive-amount DRO Schedules for Tic Suppression in Youth with Chronic Tic Disorders

Chronic tic disorders (CTDs) involve motor and/or vocal tics that often cause substantial distress and impairment. Differential reinforcement of other behavior (DRO) schedules of reinforcement produce robust, but incomplete, reductions in tic frequency in youth with CTDs; however, a more robust reduction may be needed to affect durable clinical change. Standard, fixed‐amount DRO schedules have not commonly yielded such reductions, so we evaluated a novel, progressive‐amount DRO schedule, based on its ability to facilitate sustained abstinence from functionally similar behaviors. Five youth with CTDs were exposed to periods of baseline, fixed‐amount DRO (DRO‐F), and progressive‐amount DRO (DRO‐P). Both DRO schedules produced decreases in tic rate and increases in intertic interval duration, but no systematic differences were seen between the two schedules on any dimension of tic occurrence. The DRO‐F schedule was generally preferred to the DRO‐P schedule. Possible procedural improvements and other future directions are discussed