aqora

Matrix product state simulations with general non-Abelian symmetries

Miklós Antal Werner, Cătălin Paşcu Moca, Örs Legeza +1 more

Bulletin of the American Physical SocietyMar 15, 20210 citations

General framework of non-Abelian SU(N) symmetries for matrix product states

Andreas Weichselbaum, Jan von Delft

Bulletin of the American Physical SocietyFeb 29, 20120 citations

Matrix product state representation of non-Abelian quasiholes

Yang-Le Wu, Benoit Estienne, Nicolas Regnault +1 more

We provide a detailed explanation of the formalism necessary to construct matrix product states for non-Abelian quasiholes in fractional quantum Hall model states. Our construction yields an efficient representation of the wave functions with conformal-block normalization and monodromy, and complements the matrix product state representation of fractional quantum Hall ground states.

arXiv:1504.06620Physical Review BJul 9, 201521 citations

On the product form of quasi-free states

J. Manuceau, F. Rocca, D. Testard

Communications in Mathematical PhysicsMar 1, 196930 citations

Braiding Non-Abelian Quasiholes in Fractional Quantum Hall States

Yang-Le Wu, Benoit Estienne, Nicolas Regnault +1 more

Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function.Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function.

arXiv:1405.1720Physical Review LettersSep 8, 201456 citations

Various Manifestation of Non -Abelian Statistics in Condensed Matter Systems

Suk Bum Chung

Since fractional statistics of Laughlin states is reflected in its topological degeneracy, it is natural to expect non-Abelian statistics to have some effect on topological degeneracy. To study the topological degeneracy of the Moore-Read nu = 5/2 quantum Hall state on a torus, we construct the wave functions of this state in the presence of two quasiholes [6]. These explicit wave functions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, and this requires a change of parity of the electron number in sonic of the ground states.Since fractional statistics of Laughlin states is reflected in its topological degeneracy, it is natural to expect non-Abelian statistics to have some effect on topological degeneracy. To study the topological degeneracy of the Moore-Read nu = 5/2 quantum Hall state on a torus, we construct the wave functions of this state in the presence of two quasiholes [6]. These explicit wave functions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, and this requires a change of parity of the electron number in sonic of the ground states.

Jan 1, 20080 citations

Matrix Product States for Non-Abelian Quasiholes

Related papers

Matrix Product States for Non-Abelian Quasiholes

Related papers