Transport in random spin chains

Author(s)

Luiz Filipe Campos Faria

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin
• Defense date: 2019-09-20

Examining board members

Eduardo Miranda; José Antonio Brum; Ricardo Luís Doretto; Tobias Micklitz; André de Pinho Vieira

• Advisor: Eduardo Miranda

Abstract

Interaction effects are notoriously difficult to take into account, especially when there is disorder in the problem. To address this kind of problem we need to resort to reliable methods and, in one dimension, the Strong Disorder Renormalization Group (SDRG) has been quite successful in describing the phenomena. In this work we use the SDRG to obtain spin transport properties in disordered spin chains. In the literature there are results regarding the conducting properties of some disordered spin chains. More specifically, there are published claims that the spin conductivity of the disordered XX model is metallic. This system, however, is exactly mapped onto a model of non-interacting spinless fermions with off-diagonal disorder only. The latter system is known to be localized although the wave functions are anomalous, with a stretched exponential behavior, rather than the more usual exponential form. This localized nature of the wave functions is in apparent contradiction with the claimed metallic behavior. We resolve this apparent paradox by working with the same method and showing that the adequate quantity to characterize the conducting properties is the typical (most probable or geometric average) value of the conductivity, rather than its arithmetic average: whereas the latter is metallic, the former is indeed insulating. The discrepancy between these two quantities is well known in one-dimensional systems. Their widely different values are a hallmark of strongly disordered systems. We confirm these features within the SDRG framework. We extended this study to $SU(2)$ symmetric spin 1 chains. We show that the same anomalous behavior is seen and the typical value is the most indicated quantity to characterize the transport properties of the model. We then study the heat transport properties of the $XX$ model. For this case, the arithmetic mean of thermal conductivity already indicates an insulating behavior and its values are not so discrepant from the typical ones. This suggests that the localization is faster. When we look at the distributions, they are not as wide as in the spin transport case (AU)

• FAPESP's process: 15/01966-1 - Study of disordered strongly interacting fermionic systems
• Grantee: Luiz Filipe Campos Faria
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)