@article { WOS:000688493300002,
title = {Z(2) topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry},
journal = {Phys. Rev. B},
volume = {104},
number = {8},
year = {2021},
month = {AUG 24},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We study a generalization of the two-dimensional transverse-field Ising model, combining both ferromagnetic and antiferromagnetic two-body interactions, that hosts exact global and local Z(2) gauge symmetries. Using exact diagonalization and stochastic series expansion quantum Monte Carlo methods, we confirm the existence of the topological phase in line with previous theoretical predictions. Our simulation results show that the transition between the confined topological phase and the deconfined paramagnetic phase is of first order, in contrast to the conventional Z(2) lattice gauge model in which the transition maps onto that of the standard Ising model and is continuous. We further generalize the model by replacing the transverse field on the gauge spins with a ferromagnetic XX interaction while keeping the local gauge symmetry intact. We find that the Z(2) topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first order. For both models, we discuss the low-energy spinon and vison excitations of the topological phase and their avoided level crossings associated with the first-order quantum phase transitions.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.104.085145},
author = {Wu, Kai-Hsin and Yang, Zhi-Cheng and Green, Dmitry and Sandvik, Anders W. and Chamon, Claudio}
}
@article { WOS:000685127300001,
title = {Z(3) Quantum Double in a Superconducting Wire Array},
journal = {PRX Quantum},
volume = {2},
number = {3},
year = {2021},
month = {AUG 13},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We show that a Z(3) quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the interwire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry-a local Z(3) symmetry involving permutations and shifts by +/- 2 pi/3 of the superconducting phases. The sign of the star potential resulting from the Josephson energy is inverted in this physical realization, leading to a massive degeneracy in the nonzero flux sectors. A dimerization pattern encoded in the capacitances of the array lifts up these degeneracies, resulting in a Z(3) topologically ordered state. Moreover, this dimerization pattern leads to a larger effective vison gap as compared to the canonical case with the usual (uninverted) star term. We further show that our model maps to a quantum three-state Potts model under a duality transformation. We argue, using a combination of bosonization and mean field theory, that altering the dimerization pattern of the capacitances leads to a transition from the Z(3) topological phase into a quantum XY-ordered phase. Our work highlights that combinatorial gauge symmetry can serve as a design principle to build quantum double models using systems with realistic interactions.},
doi = {10.1103/PRXQuantum.2.030327},
author = {Yang, Zhi-Cheng and Green, Dmitry and Yu, Hongji and Chamon, Claudio}
}
@article { ISI:000565826800008,
title = {Braiding photonic topological zero modes},
journal = {Nat. Phys.},
volume = {16},
number = {9},
year = {2020},
month = {SEP},
pages = {989+},
publisher = {NATURE PUBLISHING GROUP},
type = {Article},
abstract = {A remarkable property of quantum mechanics in two-dimensional space is its ability to support {\textquoteleft}anyons{\textquoteright}, particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can exist as bound states confined near topological defects, such as Majorana zero modes trapped in vortices in topological superconductors. Intriguingly, in the simplest cases the non-trivial phase that arises when such defects are {\textquoteleft}braided{\textquoteright} around one another is not intrinsically quantum mechanical; instead, it can be viewed as a manifestation of the geometric (Pancharatnam-Berry) phase in wave mechanics, which makes possible the simulation of such phenomena in classical systems. Here, we report the experimental measurement of the geometric phase owing to such a braiding process. These measurements are obtained with an interferometer constructed from highly tunable two-dimensional arrays of photonic waveguides. Our results introduce photonic lattices as a versatile platform for the experimental study of topological defects and their braiding, and complement ongoing efforts in the study of solid-state systems and cold atomic gases. The non-zero geometric phase acquired by the braiding of vortex modes in photonic waveguide lattices demonstrates their potential to serve as a platform for the study of both Abelian and non-Abelian braiding in bosonic systems.},
issn = {1745-2473},
doi = {10.1038/s41567-020-1007-5},},
author = {Noh, Jiho and Schuster, Thomas and Iadecola, Thomas and Huang, Sheng and Wang, Mohan and Chen, Kevin P. and Chamon, Claudio and Rechtsman, Mikael C.}
}
@article {ISI:000473018400004,
title = {Ground-state degeneracy of non-Abelian topological phases from coupled wires},
journal = {Phys. Rev. B},
volume = {99},
number = {24},
year = {2019},
month = {JUN 20},
pages = {245138},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic su(2)(2) Moore-Read state, but the approach we outline here can be extended to general bosonic su(2)(k) topological phases described by non-Abelian Chern-Simons theories. We also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.99.245138},
author = {Iadecola, Thomas and Neupert, Titus and Chamon, Claudio and Mudry, Christopher}
}
@article {ISI:000465163400005,
title = {Hierarchical Majoranas in a programmable nanowire network},
journal = {Phys. Rev. B},
volume = {99},
number = {15},
year = {2019},
month = {APR 19},
pages = {155138},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {We propose a hierarchical architecture for building {\textquoteleft}{\textquoteleft}logical{{\textquoteright}{\textquoteright}} Majorana zero modes using {\textquoteleft}{\textquoteleft}physical{{\textquoteright}{\textquoteright}} Majorana zero modes at the Y-junctions of a hexagonal network of semiconductor nanowires. Each Y-junction contains three {\textquoteleft}{\textquoteleft}physical{{\textquoteright}{\textquoteright}} Majoranas, which hybridize when placed in close proximity, yielding a single effective Majorana mode near zero energy. The hybridization of effective Majorana modes on neighboring Y-junctions is controlled by applied gate voltages on the links of the honeycomb network. This gives rise to a tunable tight-binding model of effective Majorana modes. We show that selecting the gate voltages that generate a Kekule vortex pattern in the set of hybridization amplitudes yields an emergent {\textquoteleft}{\textquoteleft}logical{{\textquoteright}{\textquoteright}} Majorana zero mode bound to the vortex core. The position of a logical Majorana can be tuned adiabatically, without moving any of the {\textquoteleft}{\textquoteleft}physical{{\textquoteright}{\textquoteright}} Majoranas or closing any energy gaps, by programming the values of the gate voltages to change as functions of time. A nanowire network supporting multiple such {\textquoteleft}{\textquoteleft}logical{{\textquoteright}{\textquoteright}} Majorana zero modes provides a physical platform for performing adiabatic non-Abelian braiding operations in a fully controllable manner.},
issn = {2469-9950},
doi = {10.1103/PhysRevB.99.155138},
author = {Yang, Zhi-Cheng and Iadecola, Thomas and Chamon, Claudio and Mudry, Christopher}
}