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:
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Get familiar with quantum spin chains and the methods for studying equilibrium properties of those.
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Implement a QMC code to study these.
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Investigate ways of studying heat transport in the linear response regime so that it can be calculated using correlation functions in thermal equilibrium.
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Calculate thermal transport in spin chains.