6,120 research outputs found
Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
We demonstrate the semiclassical nature of symmetry twist defects that differ
from quantum deconfined anyons in a true topological phase by examining
non-abelian crystalline defects in an abelian lattice model. An underlying
non-dynamical ungauged S3-symmetry labels the quasi-extensive defects by group
elements and gives rise to order dependent fusion. A central subgroup of local
Wilson observables distinguishes defect-anyon composites by species, which can
mutate through abelian anyon tunneling by tuning local defect phase parameters.
We compute a complete consistent set of primitive basis transformations, or
F-symbols, and study braiding and exchange between commuting defects. This
suggests a modified spin-statistics theorem for defects and non-modular group
structures unitarily represented by the braiding S and exchange T matrices.
Non-abelian braiding operations in a closed system represent the sphere braid
group projectively by a non-trivial central extension that relates the
underlying symmetry.Comment: 44 pages, 43 figure
Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States
We describe the braiding statistics of topological twist defects in abelian
bosonic bilayer (mmn) fractional quantum Hall (FQH) states, which reduce to the
Z_n toric code when m=0. Twist defects carry non-abelian fractional
Majorana-like characteristics. We propose local statistical measurements that
distinguish the fractional charge, or species, of a defect-quasiparticle
composite. Degenerate ground states and basis transformations of a multi-defect
system are characterized by a consistent set of fusion properties. Non-abelian
unitary exchange operations are determined using half braids between defects,
and projectively represent the sphere braid group in a closed system. Defect
spin statistics are modified by equating exchange with 4\pi rotation. The
braiding S matrix is identified with a Dehn twist (instead of a \pi/2 rotation)
on a torus decorated with a non-trivial twofold branch cut, and represents the
congruent subgroup \Gamma_0(2) of modular transformations.Comment: 6 pages, 3 figure
From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
Weyl and Dirac (semi)metals in three dimensions have robust gapless
electronic band structures. Their massless single-body energy spectra are
protected by symmetries such as lattice translation, (screw) rotation and time
reversal. In this manuscript, we discuss many-body interactions in these
systems. We focus on strong interactions that preserve symmetries and are
outside the single-body mean-field regime. By mapping a Dirac (semi)metal to a
model based on a three dimensional array of coupled Dirac wires, we show (1)
the Dirac (semi)metal can acquire a many-body excitation energy gap without
breaking the relevant symmetries, and (2) interaction can enable an anomalous
Weyl (semi)metallic phase that is otherwise forbidden by symmetries in the
single-body setting and can only be present holographically on the boundary of
a four dimensional weak topological insulator. Both of these topological states
support fractional gapped (gapless) bulk (resp. boundary) quasiparticle
excitations.Comment: 29 pages, 19 figures. This version has an expanded 'Summary of
Results' and 'Conclusion and Discussion' section to make it more accessible
to a broader audienc
Optimized numerical gradient and Hessian estimation for variational quantum algorithms
Sampling noisy intermediate-scale quantum devices is a fundamental step that
converts coherent quantum-circuit outputs to measurement data for running
variational quantum algorithms that utilize gradient and Hessian methods in
cost-function optimization tasks. This step, however, introduces estimation
errors in the resulting gradient or Hessian computations. To minimize these
errors, we discuss tunable numerical estimators, which are the
finite-difference (including their generalized versions) and scaled
parameter-shift estimators [introduced in Phys. Rev. A 103, 012405 (2021)], and
propose operational circuit-averaged methods to optimize them. We show that
these optimized numerical estimators offer estimation errors that drop
exponentially with the number of circuit qubits for a given sampling-copy
number, revealing a direct compatibility with the barren-plateau phenomenon. In
particular, there exists a critical sampling-copy number below which an
optimized difference estimator gives a smaller average estimation error in
contrast to the standard (analytical) parameter-shift estimator, which exactly
computes gradient and Hessian components. Moreover, this critical number grows
exponentially with the circuit-qubit number. Finally, by forsaking analyticity,
we demonstrate that the scaled parameter-shift estimators beat the standard
unscaled ones in estimation accuracy under any situation, with comparable
performances to those of the difference estimators within significant
copy-number ranges, and are the best ones if larger copy numbers are
affordable.Comment: 24 pages, 7 figures (updated Fig. 4, new Fig. 6, new Secs. IV C, V C,
VII and Appendix C5 since last version
Symmetric-Gapped Surface States of Fractional Topological Insulators
We construct the symmetric-gapped surface states of a fractional topological
insulator with electromagnetic -angle and
a discrete gauge field. They are the proper generalizations of
the T-pfaffian state and pfaffian/anti-semion state and feature an extended
periodicity compared with their of "integer" topological band insulators
counterparts. We demonstrate that the surface states have the correct anomalies
associated with time-reversal symmetry and charge conservation.Comment: 5 pages, 33 references and 2 pages of supplemental materia
From orbifolding conformal field theories to gauging topological phases
Topological phases of matter in (2+1) dimensions are commonly equipped with
global symmetries, such as electric-magnetic duality in gauge theories and
bilayer symmetry in fractional quantum Hall states. Gauging these symmetries
into local dynamical ones is one way of obtaining exotic phases from
conventional systems. We study this using the bulk-boundary correspondence and
applying the orbifold construction to the (1+1) dimensional edge described by a
conformal field theory (CFT). Our procedure puts twisted boundary conditions
into the partition function, and predicts the fusion, spin and braiding
behavior of anyonic excitations after gauging. We demonstrate this for the
electric-magnetic self-dual gauge theory, the twofold symmetric
, and the -symmetric Wess-Zumino-Witten theories.Comment: 23 pages, 1 figur
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