PIRSA:13020129

Fractional Quantum Hall States on an infinite cylinder: characterizing topological order and quasiparticle forces using infinite DMRG.

Zaletel, M. (2013). Fractional Quantum Hall States on an infinite cylinder: characterizing topological order and quasiparticle forces using infinite DMRG.. Perimeter Institute. https://pirsa.org/13020129

Zaletel, Michael. Fractional Quantum Hall States on an infinite cylinder: characterizing topological order and quasiparticle forces using infinite DMRG.. Perimeter Institute, Feb. 12, 2013, https://pirsa.org/13020129 

          @misc{ pirsa_PIRSA:13020129,
            doi = {10.48660/13020129},
            url = {https://pirsa.org/13020129},
            author = {Zaletel, Michael},
            keywords = {Condensed Matter},
            language = {en},
            title = {Fractional Quantum Hall States on an infinite cylinder: characterizing topological order and quasiparticle forces using infinite DMRG.},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {feb},
            note = {PIRSA:13020129 see, \url{https://pirsa.org}}
          }

Michael Zaletel

University of California, Berkeley

Talk number
PIRSA:13020129
Collection
Talk Type
Subject
Abstract
The density matrix renormalization group (DMRG), which has proved so successful in one dimension, has been making the push into higher dimensions, with the fractional quantum Hall (FQH) effect an important target. I'll briefly explain how the infinite DMRG algorithm can be adapted to find the degenerate ground states of a microscopic FQH Hamiltonian on an infinitely long cylinder, then focus on two applications. To characterize the topological order of the phase, I'll show that the bipartite entanglement spectrum of the ground state is sufficient to determine the quasiparticle charges, topological spins, quantum dimensions, chiral central charge, and Hall viscosity of the phase. Then I will show how to introduce localized quasiparticles of fixed topological charge. By pinning a pair of quasiparticles and dragging them into contact, we can directly measure the force curve of their interaction.