Matrix Product States and the Fractional Quantum Hall Effect

Nicolas Regnault (1, 2)

1 LPA - Laboratoire Pierre Aigrain
2 DPPU - Department of Physics, Princeton University

he understanding and simulation of quantum many-body states in one space dimension has experienced revolutionary progress with the advent of the density matrix renormalization g roup. 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 system s such as the fractional quantum Hall effect are harder to simulate by MPS. Two recent articles[1,2] have proposed an exact MPS representation of a large series of fractional quantum Hall states in various geometries. The model states include all paired $k=2$ Jack polynomials, such as the Moore-Read and Gaffnian states, as well as the Read-Rezayi $k=3$ state. We will discuss how a controlled truncation can be performed on this r epresentation and we will give a natural interpretation from the entanglement spectrum perspective. We will discuss the numerical accuracy of this truncated prescription for vari ous geometries. [1] M.P. Zaletel and R.S. K. Mong, Phys. Rev. B 86, 245305 (2012). [2] B. Estienne, Z. Papic, N. Regnault, B. A. Bernevig, arXiv:1211.3353.

Domaines: Autre [cond-mat.other]

Nicolas Regnault. Matrix Product States and the Fractional Quantum Hall Effect. APS March Meeting, Mar 2013, Baltimore, United States. ⟨hal-00967780⟩