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This research identifies a purely lattice-based mechanism that generates an Andreev-like boundary condition, offering a microscopic interpretation of phenomena in the two-channel Kondo problem and monopole scattering. By utilizing Majorana representations and duality defects within folded lattice models, the study bridges concepts from condensed matter physics with quantum field theory to describe charge-conjugating boundaries without relying on traditional superconducting interfaces.
Emergent Andreev Reflection from a Lattice Duality Defect
arXiv:2606.23684v2 Announce Type: replace-cross Abstract: Andreev reflection converts an incoming fermion into an outgoing hole and is usually tied to a superconducting interface. We show that an analogous charge-conjugating boundary condition emerges from a purely lattice duality defect. Starting from a Majorana representation of the transverse-field Ising chain, we construct a folded lattice model in which a boundary Majorana impurity implements a one-site translation of a staggered Majorana chain. In the continuum, this translation becomes a chiral fermion-parity defect: it flips the sign of the only left-moving Majorana mode while leaving the right-moving mode unchanged. When the two Majorana modes are recombined into a complex fermion in the folded geometry, this sign flip becomes the Andreev-like boundary condition. Our lattice formulation gives a microscopic interpretation of the Emery--Kivelson boundary of the two-channel Kondo problem and of Maldacena--Ludwig monopole scattering, while identifying the boundary as the interface between a Kitaev-chain SPT phase and a gapless chain. The same Majorana translation defect also provides a lattice realization of an axial $U(1)_A$-symmetric charge-flip boundary.
Abstract:Andreev reflection converts an incoming fermion into an outgoing hole and is usually tied to a superconducting interface. We show that an analogous charge-conjugating boundary condition emerges from a purely lattice duality defect. Starting from a Majorana representation of the transverse-field Ising chain, we construct a folded lattice model in which a boundary Majorana impurity implements a one-site translation of a staggered Majorana chain. In the continuum, this translation becomes a chiral fermion-parity defect: it flips the sign of the only left-moving Majorana mode while leaving the right-moving mode unchanged. When the two Majorana modes are recombined into a complex fermion in the folded geometry, this sign flip becomes the Andreev-like boundary condition. Our lattice formulation gives a microscopic interpretation of the Emery--Kivelson boundary of the two-channel Kondo problem and of Maldacena--Ludwig monopole scattering, while identifying the boundary as the interface between a Kitaev-chain SPT phase and a gapless chain. The same Majorana translation defect also provides a lattice realization of an axial $U(1)_A$-symmetric charge-flip boundary.
Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
arXiv:2606.23684 [cond-mat.str-el]
(or arXiv:2606.23684v2 [cond-mat.str-el] for this version)
Full text under the publisher's open licence · 196 words
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