Quasilocal conserved quantities and transport in integrable one-dimensional systems

• Grant number: 14/18173-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: November 01, 2014
• End date: November 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Rodrigo Gonçalves Pereira
• Grantee: Rodrigo Gonçalves Pereira
• Visiting researcher: Vincent Pasquier
• Visiting researcher institution: Institut de Physique Théorique (IPhT), France
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Quantum integrable models are usually characterized by a macroscopic number of local conserved quantities. One example is the XXZ model, which describes anisotropic spin-$1/2$ chain materials and Mott-insulating phases of two-component bosons in optical lattices. The nontrivial conservation laws of integrable systems have striking consequences for their dynamical properties. Recently, it was shown that, rather than local conserved quantities, the infinite spin conductivity at high temperatures inside the critical phase of the XXZ model is due to quasilocal conserved quantities --- operators without a local density, yet with an extensive operator norm. In this project, we propose to extend the research on quasilocal operators in several directions, including the study of integrable higher-S spin chains, the calculation of the eigenvalues of two-parameter transfer matrices, and the formulation of quasilocal operators in the integrable field theory appropriate for the low temperature regime of critical spin chains. (AU)