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CAMP Seminar: Matrix Product States and the Fractional Quantum Hall Effect

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Nicolas Regnault, Ecole Normale Superieure and Princeton University
When
21 January 2014 from 3:30 PM to 4:30 PM
Where
339 Davey Laboratory
Contact Name
Contact Phone
814-574-7497
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The understanding and simulation of quantum many-body states in
one space dimension has experienced revolutionary progress with the advent
of the density matrix renormalization group. In modern language, this
method can be viewed as a variational optimization over the set of matrix
product states (MPS). Due to their perimeter law entanglement, 2-D systems
such as the fractional quantum Hall effect are harder to simulate by MPS.

We will show that many fractional quantum Hall states have an exact
infinite MPS representation. We will discuss how a controlled truncation
can be performed on this representation and we will give a natural
interpretation from the entanglement spectrum perspective. Through the
MPS, We will give evidences why certain model states (related to
non-unitary conformal field theories) are pathological.

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