Condensed Matter Seminar, Nicolas Regnault, Princeton University,"Matrix Product States and the Fractional Quantum Hall Effect"

Mon, Dec 8, 2014, 1:15 pm to 2:30 pm
PCTS Seminar Room
: 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. We will also show the direct characterization of the Read-Rezayi quasihole excitations from their MPS description.