Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.
Unpaired Majorana fermions in quantum wires
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abstract
Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length $L$ possesses two ground states with an energy difference proportional to $\exp(-L/l_0)$ and different fermionic parities. Such systems can be used as qubits since they are intrinsically immune to decoherence. The property of a system to have boundary Majorana fermions is expressed as a condition on the bulk electron spectrum. The condition is satisfied in the presence of an arbitrary small energy gap induced by proximity of a 3-dimensional p-wave superconductor, provided that the normal spectrum has an odd number of Fermi points in each half of the Brillouin zone (each spin component counts separately).
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A matrix product operator construction using link-enhanced MPOs enables infinite-lattice simulations of (1+1)D gauge theories with manifest translation invariance and symmetry.
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Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions
Z_k symmetries from Pythagorean triples in two free Weyl fermions yield non-invertible defects that generate all U(1)^2-preserving boundaries for two Dirac fermions.
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Infinite matrix product states for $(1+1)$-dimensional gauge theories
A matrix product operator construction using link-enhanced MPOs enables infinite-lattice simulations of (1+1)D gauge theories with manifest translation invariance and symmetry.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.