Topological phases with parafermions: theory and blueprints
Annual Review of Condensed Matter Physics Annual Reviews 7:1 (2016) 119-139
Abstract:
We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we generalize the intimate connection between the -symmetric Ising quantum spin chain and Majorana fermions to -symmetric chains and parafermions. In particular, we highlight how parafermion chains host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes—focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators—and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.Critical lines and ordered phases in a Rydberg-blockade ladder
Physical Review B American Physical Society 108:12 (2023) 125135
Abstract:
Arrays of Rydberg atoms in the blockade regime realize a wealth of strongly correlated quantum physics, but theoretical analysis beyond the chain is rather difficult. Here we study a tractable model of Rydberg-blockade atoms on the square ladder with a Z2×Z2 symmetry and at most one excited atom per square. We find D4, Z2, and Z3 density-wave phases separated by critical and first-order quantum phase transitions. A noninvertible remnant of U(1) symmetry applies to our full three-parameter space of couplings, and its presence results in a larger critical region as well as two distinct Z3-broken phases. Along an integrable line of couplings, the model exhibits a self-duality that is spontaneously broken along a first-order transition. Aided by numerical results, perturbation theory, and conformal field theory, we also find critical Ising2 and three-state Potts transitions, and provide good evidence that the latter can be chiral.Stochastic strong zero modes and their dynamical manifestations
Physical Review E American Physical Society 107 (2023) L042104
Abstract:
Strong zero modes (SZMs) are conserved operators localised at the edges of certain quantum spin chains, which give rise to long coherence times of edge spins. Here we define and analyse analogous operators in one-dimensional classical stochastic systems. For concreteness, we focus on chains with single occupancy and nearest-neighbour transitions, in particular particle hopping and pair creation and annihilation. For integrable choices of parameters we find the exact form of the SZM operators. Being in general non-diagonal in the classical basis, the dynamical consequences of stochastic SZMs are very different from those of their quantum counterparts. We show that the presence of a stochastic SZM is manifested through a large class of exact transient relations between time-correlation functions, absent in the same system with periodic boundaries.Topological quantum field theory and polynomial identities for graphs on the torus
Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions European Mathematical Society Publishing House 10:2 (2022) 277-298
Abstract:
We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.Microscopic characterization of Ising conformal field theory in Rydberg chains
Physical Review B: Condensed matter and materials physics American Physical Society 104:23 (2021) 235109