Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems

In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite size. This exploration is done mainly in one and two spatial dimensions (1d and 2d). We describe a number of numerical algorithms based on corner matri- ces and tensors to approximate different ground state properties of these systems. The proposed methods make also use of matrix product operators and projected entangled pair operators, and naturally preserve spatial symmetries of the system such as translation invariance. In order to assess the validity of our algorithms, we provide preliminary benchmarking calculations for the spin-1/2 quantum Ising model in a transverse field in both 1d and 2d. Our methods are a plausible alternative to other well-established tensor network approaches such as iDMRG and iTEBD in 1d, and iPEPS and TERG in 2d. The computational complexity of the proposed algorithms is also considered and, in 2d, important differences are found depending on the chosen simulation scheme. We also discuss further possibilities, such as 3d quantum lattice systems, periodic boundary conditions, and real time evolution. This discussion leads us to reinterpret the standard iTEBD and iPEPS algorithms in terms of corner transfer matrices and corner tensors. Our paper also offers a perspective on many properties of the corner transfer matrix and its higher-dimensional generalizations in the light of novel tensor network methods.Comment: 25 pages, 32 figures, 2 tables. Revised version. Technical details on some of the algorithms have been moved to appendices. To appear in PR

Actitudes hacia la ciencia a lo largo de BUP y COU : un estudio longitudinal

We have performed a longitudinal study among BUP and COU students, from fourteen to eighteen years old, and their attitudes to Science. This attitude becomes neither linear nor more negative through successive years. On the contrary, we have observed a «saw tooth» profile

Actitudes hacia la ciencia y asignaturas pendientes : dos factores que afectan al rendimiento en ciencias

This paper analyses the influence of the attitude towarda Science with which some students attain secondary education (BUP) and the role of outstanding subjecrs in their school record

Actitudes hacia la ciencia en estudiantes universitarios de ciencias

We have performed a longitudinal study among university students, from eighteen to twenty-three years old, and their attitudes toward Science. This attitude does not become neither linear nor more negative through successive years. In contrast, we have observed a «saw tooth~pr ofile, which is clearer when the number of courses analysed increases and the sex variable is taken into account. In general, the maximums of one sex are coincidental with the minimums of the other

La medida de las actitudes usando las técnicas de Likert y de diferencial semántico

We have established a comparison between two popular methods to assess the attitude toward experimental sciences: The summated rating method, generally known as the Likert scale; and the semantic differential method. This study is carried out with university students of chemistry and high school students, finding that both attitude measuring techniques are equally suitable in our educative system. Moreover, the sex variable is not significant

Registro de la deformación a escala microestructural en el cabalgamiento de Gavarnie (Zona Axial Pirenaica)

El cabalgamiento de Gavarnie presenta una zona de falla de unos 30m de espesor desarrollada en ampelitas y carbonatos silúricos, con registro de deformación dúctil (milonitas) en zonas próximas al plano de cabalgamiento principal y un aumento progresivo de la deformación frágil hacia zonas externas en la zona de falla. El análisis de láminas delgadas, bajo microscopio de luz reflejada y transmitida, revela el control y distribución de la deformación por la calcita y los filosilicatos s.l., desarrollando respectivamente foliaciones miloníticas y estructuras semi-dúctiles S-C-C’. Procesos de recristalización dinámica, disolución-precipitación y deformación intracristalina conllevan la generación de orientaciones preferentes de forma en los granos minerales de calcita. Los principales indicadores cinemáticos (S-CC’, fracturas frágiles de Riedel, foliaciones oblícuas, sombras de presión en piritas...) son compatibles con la vergencia Sur del Cabalgamiento de Gavarnie, sin observarse componentes oblicuas relevantes en el desplazamiento. The Gavarnie Thrust shows a 30m thick fault zone developed in the ampelitic and calcareous Silurian rocks, with a record of ductile deformation (mylonites) close to the main thrust plane and a progressive increase of the brittle deformation towards the marginal areas of the fault zone. The analysis of thin-sections under reflected and transmitted light with optical microscope reveals that calcite and phyllosilicates control the strain distribution in the fault rocks, leading to generation of mylonitic foliations and ductile-brittle S-C-C’ structures, respectively. Dinamic recrystallization, solution-precipitation and intracrystalline deformation generate shape preferred orientation in calcite grains. The main shear indicators (S-C-C’, brittle Riedel fractures, oblique foliations, pressure-shadows on pyrites…) are compatible with the South vergence of the Gavarnie Thrust, and no relevant oblique component of displacement has been observed

College Dreams à la Mexicana . . . Agency and Strategy among American-Mexican Transnational Students

Drawing from in-depth interviews with university-level transnational students in Mexico, we highlight these students’ resistance and agency in the face of US legal and educational policies that have marginalized them and other undocumented students. We also illustrate pitfalls and possibilities that students encounter in a Mexican system that has not anticipated their presence. The interviewed students viewed return migration for higher education in Mexico as a strategy that could allow them to access/develop their imagined identities as college-educated professionals and one day, legalized citizens of the United States. At the time they made their decisions, before Deferred Action for Childhood Arrivals, two students saw returning to Mexico as their best option for eventually becoming college-educated, US citizens and two others were trying to build their lives as global citizens. We conclude with a consideration of the implications of the existence of students like this for higher education and social policy in both Mexico and the United States

Brane world corrections to scalar vacuum force in RSII-p

Vacuum force is an interesting low energy test for brane worlds due to its dependence on field's modes and its role in submillimeter gravity experiments. In this work we generalize a previous model example: the scalar field vacuum force between two parallel plates lying in the brane of a Randall-Sundrum scenario extended by $p$ compact dimensions (RSII-$p$). Upon use of Green's function technique, for the massless scalar field, the 4D force is obtained from a zero mode while corrections turn out attractive and depend on the separation between plates as $l^{-(6+p)}$. For the massive scalar field a quasilocalized mode yields the 4D force with attractive corrections behaving like $l^{-(10+p)}$. Corrections are negligible w.r.t. 4D force for $AdS_{(5+p)}$ radius less than $\sim 10^{-6}$m. Although the $p=0$ case is not physically viable due to the different behavior in regard to localization for the massless scalar and electromagnetic fields it yields an useful comparison between the dimensional regularization and Green's function techniques as we describe in the discussion.Comment: 14 pages, v2: discussion clarified, reference adde