The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335

Crystalline Confinement

We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators. While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact. An efficient cluster algorithm is used to study these exotic phases. The $(2+1)$-d system is confining at zero temperature with a spontaneously broken translation symmetry. A crystalline phase exhibits confinement via multi-stranded strings between charge-anti-charge pairs. A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate $SO(2)$ global symmetry. The low-energy physics is described by a $(2+1)$-d $\mathbb{R}P(1)$ effective field theory, perturbed by a dangerously irrelevant $SO(2)$ breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.Comment: Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 201

An observable for vacancy characterization and diffusion in crystals

To locate the position and characterize the dynamics of a vacancy in a crystal, we propose to represent it by the ground state density of a quantum probe quasi-particle for the Hamiltonian associated to the potential energy field generated by the atoms in the sample. In this description, the h^2/2mu coefficient of the kinetic energy term is a tunable parameter controlling the density localization in the regions of relevant minima of the potential energy field. Based on this description, we derive a set of collective variables that we use in rare event simulations to identify some of the vacancy diffusion paths in a 2D crystal. Our simulations reveal, in addition to the simple and expected nearest neighbor hopping path, a collective migration mechanism of the vacancy. This mechanism involves several lattice sites and produces a long range migration of the vacancy. Finally, we also observed a vacancy induced crystal reorientation process

Critical dynamics of a spin-5/2 2D isotropic antiferromagnet

We report a neutron scattering study of the dynamic spin correlations in Rb$_2$MnF$_4$, a two-dimensional spin-5/2 antiferromagnet. By tuning an external magnetic field to the value for the spin-flop line, we reduce the effective spin anisotropy to essentially zero, thereby obtaining a nearly ideal two-dimensional isotropic antiferromagnet. From the shape of the quasielastic peak as a function of temperature, we demonstrate dynamic scaling for this system and find a value for the dynamical exponent $z$. We compare these results to theoretical predictions for the dynamic behavior of the two-dimensional Heisenberg model, in which deviations from $z=1$ provide a measure of the corrections to scaling.Comment: 5 pages, 4 figures. Submitted to Physical Review B, Rapid Communication

Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques

We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fluctuations can be important, and at finite temperature where thermal fluctuations dominate. The numerical techniques necessary for implementing the formalism are discussed in detail, together with methods for extracting observables of interest. Numerous applications to a wide range of phenomena are presented.Comment: 110 pages, 32 figures. Updated to address referee comments. To appear in Advances in Physic