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Bulletin of the American Physical Society

Laughlin state of hard core bosons on a two-leg ladder

Karyn Le Hur, Alexandru Petrescu, Marie Piraud, Ian P. McCulloch, Guillaume Roux

Published Mar 15, 2017• 0 citations
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Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

Alexandru Petrescu, Marie Piraud, Guillaume Roux +2 more

We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge $c=1$, which is a precursor of the two-dimensional Laughlin state at $\ensuremath{\nu}=1/2$. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.

arXiv:1612.05134•Physical review. B./Physical review. B•Jul 31, 2017•61 citations

Publisher's Note: Precursor of the Laughlin state of hard-core bosons on a two-leg ladder [Phys. Rev. B 96, 014524 (2017)]

Alexandru Petrescu, Marie Piraud, Guillaume Roux +2 more

Received 14 August 2018DOI:https://doi.org/10.1103/PhysRevB.98.059901©2018 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose gasesCold gases in optical latticesFractional quantum Hall effectFractionalizationGeometric & topological phasesJosephson effectQuantum phase transitionsQuasiparticles & collective excitationsSpin-orbit couplingTopological phases of matterAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Physical review. B./Physical review. B•Aug 22, 2018•1 citation
We study hard core bosons on a two-leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the possibility to stabilize a ground state of central charge c=1c=1c=1, which is a precursor of the two-dimensional Laughlin state at $\ensuremath{\nu}=1/2$. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. By using a combination of bosonization and density matrix renormalization group (DMRG) calculations, we construct a phase diagram versus density and flux from local observables and central charge. We delimit the region where the finite-size ground state displays signatures compatible with this precursor to the Laughlin state. We show how bipartite charge fluctuations allow access to the Luttinger parameter for the edge Luttinger liquid corresponding to the precursor Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with an exact-diagonalization calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the precursor Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.