The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Xiao Gang Wen - One of the best experts on this subject based on the ideXlab platform.
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boundary Degeneracy of topological order
Physical Review B, 2015Co-Authors: J C Wang, Xiao Gang WenAbstract:We introduce the concept of boundary Degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary Degeneracy provides richer information than the bulk Degeneracy. Beyond the bulk-edge correspondence, we find the ground state Degeneracy of the fully gapped edge modes depends on boundary gapping conditions. By associating different types of boundary gapping conditions as different ways of particle or quasiparticle condensations on the boundary, we develop an analytic theory of gapped boundaries. By Chern-Simons theory, this allows us to derive the ground state Degeneracy formula in terms of boundary gapping conditions, which encodes more than the fusion algebra of fractionalized quasiparticles. We apply our theory to Kitaev's toric code and Levin-Wen string-net models. We predict that the $Z_2$ toric code and $Z_2$ double-semion model (more generally, the $Z_k$ gauge theory and the $U(1)_k \times U(1)_{-k}$ non-chiral fractional quantum Hall state at even integer $k$) can be numerically and experimentally distinguished, by measuring their boundary Degeneracy on an annulus or a cylinder.
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boundary Degeneracy of topological order
Physical Review B, 2015Co-Authors: Xiao Gang Wen, Juven WangAbstract:We introduce the concept of boundary Degeneracy, as the ground state Degeneracy of topologically ordered states on a compact orientable spatial manifold with gapped boundaries. We emphasize that the boundary Degeneracy provides richer information than the bulk Degeneracy. Beyond the bulk-edge correspondence, we find the ground state Degeneracy of the fully gapped edge modes depends on boundary gapping conditions. By associating different types of boundary gapping conditions as different ways of particle or quasiparticle condensations on the boundary, we develop an analytic theory of gapped boundaries. By Chern-Simons theory, this allows us to derive the ground state Degeneracy formula in terms of boundary gapping conditions, which encodes more than the fusion algebra of fractionalized quasiparticles. We apply our theory to Kitaev's toric code and Levin-Wen string-net models. We predict that the ${Z}_{2}$ toric code and ${Z}_{2}$ double-semion model [more generally, the ${Z}_{k}$ gauge theory and the $U{(1)}_{k}\ifmmode\times\else\texttimes\fi{}U{(1)}_{\ensuremath{-}k}$ nonchiral fractional quantum Hall state at even integer $k$] can be numerically and experimentally distinguished, by measuring their boundary Degeneracy on an annulus or a cylinder.
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Boundary Degeneracy of Topological Order
Physical Review Letters, 2015Co-Authors: Juven Wang, Xiao Gang WenAbstract:We introduce the notion of boundary Degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that it provides richer information than the bulk Degeneracy. Beyond the bulk-edge correspondence, we find the ground state Degeneracy of fully gapped edge states depends on boundary gapping conditions. We develop a quantitative description of different types of boundary gapping conditions by viewing them as different ways of non-fractionalized particle condensation on the boundary. Via Chern-Simons theory, this allows us to derive the ground state Degeneracy formula in terms of boundary gapping conditions, which reveals more than the fusion algebra of fractionalized quasiparticles. We apply our results to Toric code and Levin-Wen string-net models. By measuring the boundary Degeneracy on a cylinder, we predict Zk gauge theory and U(1)k×U(1)k non-chiral fractional quantum hall state at even integer k can be experimentally distinguished. Our work refines definitions of symmetry protected topological order and intrinsic topological order.
Juven Wang - One of the best experts on this subject based on the ideXlab platform.
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boundary Degeneracy of topological order
Physical Review B, 2015Co-Authors: Xiao Gang Wen, Juven WangAbstract:We introduce the concept of boundary Degeneracy, as the ground state Degeneracy of topologically ordered states on a compact orientable spatial manifold with gapped boundaries. We emphasize that the boundary Degeneracy provides richer information than the bulk Degeneracy. Beyond the bulk-edge correspondence, we find the ground state Degeneracy of the fully gapped edge modes depends on boundary gapping conditions. By associating different types of boundary gapping conditions as different ways of particle or quasiparticle condensations on the boundary, we develop an analytic theory of gapped boundaries. By Chern-Simons theory, this allows us to derive the ground state Degeneracy formula in terms of boundary gapping conditions, which encodes more than the fusion algebra of fractionalized quasiparticles. We apply our theory to Kitaev's toric code and Levin-Wen string-net models. We predict that the ${Z}_{2}$ toric code and ${Z}_{2}$ double-semion model [more generally, the ${Z}_{k}$ gauge theory and the $U{(1)}_{k}\ifmmode\times\else\texttimes\fi{}U{(1)}_{\ensuremath{-}k}$ nonchiral fractional quantum Hall state at even integer $k$] can be numerically and experimentally distinguished, by measuring their boundary Degeneracy on an annulus or a cylinder.
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Boundary Degeneracy of Topological Order
Physical Review Letters, 2015Co-Authors: Juven Wang, Xiao Gang WenAbstract:We introduce the notion of boundary Degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that it provides richer information than the bulk Degeneracy. Beyond the bulk-edge correspondence, we find the ground state Degeneracy of fully gapped edge states depends on boundary gapping conditions. We develop a quantitative description of different types of boundary gapping conditions by viewing them as different ways of non-fractionalized particle condensation on the boundary. Via Chern-Simons theory, this allows us to derive the ground state Degeneracy formula in terms of boundary gapping conditions, which reveals more than the fusion algebra of fractionalized quasiparticles. We apply our results to Toric code and Levin-Wen string-net models. By measuring the boundary Degeneracy on a cylinder, we predict Zk gauge theory and U(1)k×U(1)k non-chiral fractional quantum hall state at even integer k can be experimentally distinguished. Our work refines definitions of symmetry protected topological order and intrinsic topological order.
S Tarucha - One of the best experts on this subject based on the ideXlab platform.
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enhanced kondo effect via tuned orbital Degeneracy in a spin 1 2 artificial atom
Physical Review Letters, 2004Co-Authors: S Sasaki, S Amaha, N Asakawa, Mikio Eto, S TaruchaAbstract:A strong Kondo effect is observed for a vertical quantum dot holding an odd number of electrons and spin $1/2$ when an orbital Degeneracy is induced by magnetic field. The estimated Kondo temperature for this ``doublet-doublet'' Degeneracy is similar to that for the singlet-triplet Degeneracy with an even electron number, indicating that a total of fourfold spin and orbital Degeneracy accounts for the enhancement of the Kondo temperature. The experimental observation is qualitatively reproduced by scaling calculations using an SU(4) model at the orbital Degeneracy.
Frank Pollmann - One of the best experts on this subject based on the ideXlab platform.
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polarization plateaus in hexagonal water ice i h
Physical Review B, 2019Co-Authors: Roderich Moessner, Matthias Gohlke, Frank PollmannAbstract:The protons in water ice are subject to so-called ice rules resulting in an extensive ground-state Degeneracy. We study how an external electric field reduces this ground-state Degeneracy in hexagonal water ice ${I}_{h}$ within a minimal model. We observe polarization plateaus when the field is aligned along the [001] and [010] directions. In each case, one plateau occurs at intermediate polarization with reduced but still extensive Degeneracy. The remaining ground states can be mapped to dimer models on the honeycomb and the square lattice, respectively. Upon tilting the external field, we observe an order-disorder transition of Kasteleyn type into a plateau at saturated polarization and vanishing entropy. This transition is investigated analytically using the Kasteleyn matrix and numerically using a modified directed-loop Monte Carlo simulation. The protons in both cases exhibit algebraically decaying correlations. Moreover, the features of the static structure factor are discussed.
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entanglement spectrum of a topological phase in one dimension
Physical Review B, 2010Co-Authors: Frank Pollmann, Ari Turner, Erez Berg, Masaki OshikawaAbstract:We show that the Haldane phase of $S=1$ chains is characterized by a double Degeneracy of the entanglement spectrum. The Degeneracy is protected by a set of symmetries (either the dihedral group of $\ensuremath{\pi}$ rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, ``topologically trivial,'' phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one-dimensional systems. Physically, the Degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.
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entanglement spectrum of a topological phase in one dimension
Physical Review B, 2010Co-Authors: Frank Pollmann, Ari Turner, Erez Berg, Masaki OshikawaAbstract:We show that the Haldane phase of S=1 chains is characterized by a double Degeneracy of the entanglement spectrum. The Degeneracy is protected by a set of symmetries (either the dihedral group of $\pi$-rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, "topologically trivial", phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one dimensional systems. Physically, the Degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.
Masaki Oshikawa - One of the best experts on this subject based on the ideXlab platform.
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entanglement spectrum of a topological phase in one dimension
Physical Review B, 2010Co-Authors: Frank Pollmann, Ari Turner, Erez Berg, Masaki OshikawaAbstract:We show that the Haldane phase of $S=1$ chains is characterized by a double Degeneracy of the entanglement spectrum. The Degeneracy is protected by a set of symmetries (either the dihedral group of $\ensuremath{\pi}$ rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, ``topologically trivial,'' phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one-dimensional systems. Physically, the Degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.
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entanglement spectrum of a topological phase in one dimension
Physical Review B, 2010Co-Authors: Frank Pollmann, Ari Turner, Erez Berg, Masaki OshikawaAbstract:We show that the Haldane phase of S=1 chains is characterized by a double Degeneracy of the entanglement spectrum. The Degeneracy is protected by a set of symmetries (either the dihedral group of $\pi$-rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, "topologically trivial", phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one dimensional systems. Physically, the Degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.
