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Thermal transport in 1D spin chains

Thermal transport is usually associated with photons or electrons. Yet, other types of excitations such as magnons are also able to transfer heat. In fact, it was shown about twenty years ago that one dimensional Heisenberg spin chains are in fact very good thermal conductors. In this project we will investigate one dimensional spin chains using a Quantum Monte Carlo (QMC) technique in order to extend the knowledge of thermal transport in Heisenberg spin chains to other spin chains involving also other interactions. In particular we will investigate noncentrosymmetric spin chains that allows for the Dzhyaloshinski-Moryia (DM) interaction. Such inversion symmetry breaking terms may enhance the heat conduction in one direction only, possibly allowing for materials that can act as heat diodes, transporting heat in only one direction.

To start on this project it is essential to first develop a finite-temperature Quantum Monte Carlo (QMC) numerical simulation code that can handle 1d spin chains with DM-interactions. To do this the student will develop a QMC code tailor-made to 1D spin chains. The inclusion of the DM-term will be the essential new ingredient in this code which distinguishes it from more conventional codes that handle Heisenberg-like Hamiltonians. The QMC method that will be used is the Stochastic Series Expansion technique (SSE) that is known as the state-of-the art QMC method for unfrustrated spin systems.

The inclusion of the DM-term will be done essentially by paying close attention to the signs introduced by modifying the Heisenberg-interactions. Once the QMC code is up and running the challenge will be to find a way to calculate the thermal transport. Thermal transport, even in the linear response regime, is challenging to calculate and it will be a main goal of the project to find and implement a viable way to do so within the SSE QMC framework.

The concrete tasks that must be addressed are:

  • Get familiar with quantum spin chains and the methods for studying equilibrium properties of those.

  • Implement a QMC code to study these.

  • Investigate ways of studying heat transport in the linear response regime so that it can be calculated using correlation functions in thermal equilibrium.

  • Calculate thermal transport in spin chains.

     

Published Jan. 27, 2022 12:03 PM - Last modified Jan. 27, 2022 12:07 PM

Supervisor(s)

Student(s)

  • Peder Lon Hauge

Scope (credits)

60