A Generalization of the Goldberg-Sachs Theorem and its Consequences

The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds endowed with torsion-free connection compatible with the metric, the treatment includes all signatures as well as complex manifolds. It is shown that when the Weyl tensor is algebraically special severe geometric restrictions are imposed. In particular it is demonstrated that the simple self-dual eigenbivectors of the Weyl tensor generate integrable isotropic planes. Another result obtained here is that if the self-dual part of the Weyl tensor vanishes in a Ricci-flat manifold of (2,2) signature the manifold must be Calabi-Yau or symplectic and admits a solution for the source-free Einstein-Maxwell equations.Comment: 14 pages. This version matches the published on

Algebraic Approach to Interacting Quantum Systems

We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different (spin-particle-gauge) {\it languages} by means of exact mappings (isomorphisms) that we name {\it dictionaries} and prove a fundamental theorem establishing when two arbitrary languages can be connected. These mappings serve to unravel symmetries which are hidden in one representation but become manifest in another. In addition, we establish a formal link between seemingly unrelated physical phenomena by changing the language of our model description. This link leads to the idea of {\it universality} or equivalence. Moreover, we introduce the novel concept of {\it emergent symmetry} as another symmetry guiding principle. By introducing the notion of {\it hierarchical languages}, we determine the quantum phase diagram of lattice models (previously unsolved) and unveil hidden order parameters to explore new states of matter. Hierarchical languages also constitute an essential tool to provide a unified description of phases which compete and coexist. Overall, our framework provides a simple and systematic methodology to predict and discover new kinds of orders. Another aspect exploited by the present formalism is the relation between condensed matter and lattice gauge theories through quantum link models. We conclude discussing applications of these dictionaries to the area of quantum information and computation with emphasis in building new models of computation and quantum programming languages.Comment: 44 pages, 14 psfigures. Advances in Physics 53, 1 (2004

Tunable Emergent Heterostructures in a Prototypical Correlated Metal

At the interface between two distinct materials desirable properties, such as superconductivity, can be greatly enhanced, or entirely new functionalities may emerge. Similar to in artificially engineered heterostructures, clean functional interfaces alternatively exist in electronically textured bulk materials. Electronic textures emerge spontaneously due to competing atomic-scale interactions, the control of which, would enable a top-down approach for designing tunable intrinsic heterostructures. This is particularly attractive for correlated electron materials, where spontaneous heterostructures strongly affect the interplay between charge and spin degrees of freedom. Here we report high-resolution neutron spectroscopy on the prototypical strongly-correlated metal CeRhIn5, revealing competition between magnetic frustration and easy-axis anisotropy -- a well-established mechanism for generating spontaneous superstructures. Because the observed easy-axis anisotropy is field-induced and anomalously large, it can be controlled efficiently with small magnetic fields. The resulting field-controlled magnetic superstructure is closely tied to the formation of superconducting and electronic nematic textures in CeRhIn5, suggesting that in-situ tunable heterostructures can be realized in correlated electron materials

What is ‘anti’ about anti-reaches? Reference frames selectively affect reaction times and endpoint variability

Reach movement planning involves the representation of spatial target information in different reference frames. Neurons at parietal and premotor stages of the cortical sensorimotor system represent target information in eye- or hand-centered reference frames, respectively. How the different neuronal representations affect behavioral parameters of motor planning and control, i.e. which stage of neural representation is relevant for which aspect of behavior, is not obvious from the physiology. Here, we test with a behavioral experiment if different kinematic movement parameters are affected to a different degree by either an eye- or hand-reference frame. We used a generalized anti-reach task to test the influence of stimulus-response compatibility (SRC) in eye- and hand-reference frames on reach reaction times, movement times, and endpoint variability. While in a standard anti-reach task, the SRC is identical in the eye- and hand-reference frames, we could separate SRC for the two reference frames. We found that reaction times were influenced by the SRC in eye- and hand-reference frame. In contrast, movement times were only influenced by the SRC in hand-reference frame, and endpoint variability was only influenced by the SRC in eye-reference frame. Since movement time and endpoint variability are the result of planning and control processes, while reaction times are consequences of only the planning process, we suggest that SRC effects on reaction times are highly suited to investigate reference frames of movement planning, and that eye- and hand-reference frames have distinct effects on different phases of motor action and different kinematic movement parameters