Delocalization and energy transport in a many-body system with power-law interaction

Seminar
QUEST Center event
No
Speaker
Prof. Alexander Mirlin, University of Karlsruhe, Germany
Date
30/11/2016 - 16:30 - 15:00Add to Calendar 2016-11-30 15:00:00 2016-11-30 16:30:00 Delocalization and energy transport in a many-body system with power-law interaction I will discuss the delocalization in a many-body system due to a power-law interaction. One experimentally relevant realization of this problem is the effect of Coulomb interaction in Anderson insulators. Particle-hole excitations built on localized electron states are viewed as two-level systems (“spins”) randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport and evaluate the spin relaxation rate and the thermal conductivity. For physically relevant cases of two-dimensional and three-dimensional spin systems with 1/r^{3} dipole-dipole interaction (originating from the conventional 1/r Coulomb interaction between electrons), the found thermal conductivity κ scales with temperature as κ ∝ T^{3} and κ ∝ T^{4/3}, respectively. Our results are of relevance also to other realizations of random spin Hamiltonians with long-range interactions. We also determine the delocalization threshold for a finite-size system (“quantum dot” with localized single-particle states and power-law interaction). In this context, I will discuss a connection of this problem with Anderson localization on random regular graphs.   Reznik Building 209 room 210 Department of Physics physics.dept@mail.biu.ac.il Asia/Jerusalem public
Place
Reznik Building 209 room 210
Abstract

I will discuss the delocalization in a many-body system due to a power-law interaction. One experimentally relevant realization of this problem is the effect of Coulomb interaction in Anderson insulators. Particle-hole excitations built on localized electron states are viewed as two-level systems (“spins”) randomly distributed in space and energy and coupled due to electron-electron interaction. A small fraction of these states form resonant pairs that in turn build a complex network allowing for energy propagation. We identify the character of energy transport and evaluate the spin relaxation rate and the thermal conductivity. For physically relevant cases of two-dimensional and three-dimensional spin systems with 1/r^{3} dipole-dipole interaction (originating from the conventional 1/r Coulomb interaction between electrons), the found thermal conductivity κ scales with temperature as κ ∝ T^{3} and κ ∝ T^{4/3}, respectively. Our results are of relevance also to other realizations of random spin Hamiltonians with long-range interactions. We also determine the delocalization threshold for a finite-size system (“quantum dot” with localized single-particle states and power-law interaction). In this context, I will discuss a connection of this problem with Anderson localization on random regular graphs.  

Last Updated Date : 28/11/2016