### The quantum Heisenberg XXZ model and the Brauer algebra

Probability Seminar

4th December 2020, 3:00 pm – 4:00 pm

, online

Several quantum spin systems have probabilistic representations as

interchange processes. Some of these processes can be thought of as

continuous time random walks on the symmetric group, which in turn has

led to study using representation theory. We will in particular

discuss the spin-1/2; quantum Heisenberg XXZ model (and analogous

models in higher spins, which are not the XXZ). This model, in a

similar way to study using the symmetric group for other models, can

be studied using the Brauer algebra. We will introduce this algebra,

and its representation theory. Using this we obtain the free energy of

the system when the underlying graph is the complete graph, which

further lets us determine phase diagrams.

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