A quantum information approach to statistical mechanics

We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all classical spin models (including models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proofs of these two results are based on a mapping from partition functions to quantum states and to quantum circuits, respectively. Finally, we show how classical spin models can be used to describe certain fluctuating lattices appearing in models of discrete quantum gravity.Comment: 9 pages, 9 figure

Simple universal models capture all classical spin physics

Spin models are used in many studies of complex systems---be it condensed matter physics, neural networks, or economics---as they exhibit rich macroscopic behaviour despite their microscopic simplicity. Here we prove that all the physics of every classical spin model is reproduced in the low-energy sector of certain `universal models'. This means that (i) the low energy spectrum of the universal model reproduces the entire spectrum of the original model to any desired precision, (ii) the corresponding spin configurations of the original model are also reproduced in the universal model, (iii) the partition function is approximated to any desired precision, and (iv) the overhead in terms of number of spins and interactions is at most polynomial. This holds for classical models with discrete or continuous degrees of freedom. We prove necessary and sufficient conditions for a spin model to be universal, and show that one of the simplest and most widely studied spin models, the 2D Ising model with fields, is universal.Comment: v1: 4 pages with 2 figures (main text) + 4 pages with 3 figures (supplementary info). v2: 12 pages with 3 figures (main text) + 35 pages with 6 figures (supplementary info) (all single column). v2 contains new results and major revisions (results for spin models with continuous degrees of freedom, explicit constructions, examples...). Close to published version. v3: minor typo correcte

Predictive validity of the Sidorkiewicz instrument in Spanish: Assessing individual drug adherence in psychiatric patients

Background/Objective: Concomitant prescription of two or more psychiatric med-ications has become the rule and patients could adhere differently to their variousdrugs prescribed. Sidorkiewicz et al. published a questionnaire for assessing adherenceto each specific drug. Method: This study explored the predictive validity of the Span-ish version of the Sidorkiewicz questionnaire in a sample of 470 consecutive psychiatricoutpatients using 897 psychiatric drugs. Results: The questionnaire showed adequate pre-dictive validity in both univariate and multivariate analyses (logistic regression and CHAIDsegmentation) since they demonstrated a significant association with the 10-item DrugAttitude Inventory and with the Necessity and Concern Scales of the Beliefs aboutMedications Questionnaire. Some demographic and clinical variables were significant inthe univariate analyses but lost significance in the multivariate analyses. Conclusions:The adherence of the psychiatric patient to his/her prescribed treatment may not besignificantly influenced by socio-demographic or clinical characteristics, but rather by atti-tudes toward medication, perceptions of personal necessity for medication, and concerns∗Antecedentes/Objetivo: La prescripción concomitante más de un psicofármaco enun mismo paciente se ha convertido en la regla de la práctica clínica psiquiátrica actual,pudiendo adherirse los pacientes de manera diferente a sus diversos fármacos prescritos.Sidorkiewicz y colaboradores publicaron un cuestionario para evaluar la adherencia a cadafármaco tomado por el paciente. Método: Este estudio valora la validez predictiva de la ver-sión espa˜nola del cuestionario de Sidorkiewicz en una muestra de 470 pacientes ambulatoriospsiquiátricos consecutivos que usaban 897 fármacos psiquiátricos. Resultados: El cuestionariomostró una adecuada validez predictiva, tanto en análisis univariados como multivariados(regresión logística y CHAID), registrándose asociaciones significativas con el DAI-10 y con lasescalas de Necesidad y Preocupación del BMQ. Algunas variables sociodemográficas y clínicasfueron significativas en el análisis univariado perdiendo su significación en el multivariado.Conclusiones: La adherencia del paciente psiquiátrico al tratamiento no está condicionada porcaracterísticas sociodemográficas o clínicas, sino por actitudes hacia la medicación y por laspercepciones de necesidad personal de la medicación y preocupaciones sobre sus posibles efec-tos adversos. La versión espa˜nola del cuestionario de Sidorkiewicz es un instrumento válidopara evaluar la adherencia a cada fármaco tomado por pacientes psiquiátricos ambulatoriospolimedicados

Maíz: Alimento fundamental en las tradiciones y costumbres mexicanas

El siguiente trabajo busca recalcar la importancia del maíz para el pueblo mexicano, que con el paso de los años ha logrado mantener su identidad no en vano por la fuerza y majestuosidad de sus tradiciones y costumbres. Es cierto que hoy en día es la base de la alimentación de muchas familias a lo largo del territorio de México, en cada hogar a la hora del almuerzo, la comida e incluso la merienda, el maíz está presente en una gran variedad de formas, texturas y colores. Esto nos hace pensar ¿Qué sería de las fiestas en México sin la presencia del maíz, que año con año se llevan a cabo por todo el territorio

Irreducible forms of Matrix Product States: Theory and Applications

The canonical form of Matrix Product States (MPS) and the associated fundamental theorem, which relates different MPS representations of a state, are the theoretical framework underlying many of the analytical results derived through MPS, such as the classification of symmetry-protected phases in one dimension. Yet, the canonical form is only defined for MPS without non-trivial periods, and thus cannot fully capture paradigmatic states such as the antiferromagnet. Here, we introduce a new standard form for MPS, the irreducible form, which is defined for arbitrary MPS, including periodic states, and show that any tensor can be transformed into a tensor in irreducible form describing the same MPS. We then prove a fundamental theorem for MPS in irreducible form: If two tensors in irreducible form give rise to the same MPS, then they must be related by a similarity transform, together with a matrix of phases. We provide two applications of this result: an equivalence between the refinement properties of a state and the divisibility properties of its transfer matrix, and a more general characterisation of tensors that give rise to matrix product states with symmetries.Comment: 12 page

Continuum limits of Matrix Product States

We determine which translationally invariant matrix product states have a continuum limit, that is, which can be considered as discretized versions of states defined in the continuum. To do this, we analyse a fine-graining renormalization procedure in real space, characterise the set of limiting states of its flow, and find that it strictly contains the set of continuous matrix product states. We also analyse which states have a continuum limit after a finite number of a coarse-graining renormalization steps. We give several examples of states with and without the different kinds of continuum limits.Comment: 7 pages, 2 figures. New version: somewhat expanded, some explanations added. Close to published versio