Goal: The goal is to compute the transport coefficients, especially thermal conductivity, as a function of temperature and size of the spin s= {1/2,1,3/2}. If time permits, it will also be interesting to see how an external magnetic field influences the transport properties.
Method:
To start on this project it is essential to first develop a finite-temperature QMC numerical simulation code that can handle quantum spin chains for different values of the spin.
The state-of-the-art Monte Carlo method to study unfrustrated quantum spin systems is the socalled Stochastic Series Expansion (SSE) method which is a finite temperature world-line Monte Carlo algorithm for discrete quantum systems. The candidate will make an implementation of this method tailor-made to one dimensional spin chains. The code must be able to handle different spin magnitudes, and also allow for external magnetic fields and possible also anisotropy in spin space.
The SSE is set in imaginary-time, and so the code should give as outputs imaginary-time correlation functions of currents relevant to the desired transport coefficients.
We aim to calculate transport in the linear response regime employing Kubo formulae, and then extrapolate to zero Matsubara frequency in order to get the DC conductances. Such extrapolations require a small separation between Matsubara frequencies meaning that the method will be best at low temperatures.
We will also be on the outlook for better ways of doing the calculations, especially we will look into the possibility of using extra stochastic sampling in order to get a fast readout of the imaginary-time correlation functions.
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.