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This paper advances the theoretical understanding of open quantum systems by rigorously analyzing symmetries and anomalies in dissipative Majorana chains using Lindblad dynamics. It establishes a controlled framework for extending concepts like non-invertible symmetries to these environments, which is fundamental for developing robust topological qubits and error-corrected quantum hardware. The work bridges lattice models with conformal field theory, offering new insights into the stability of quantum information against environmental noise.
Dissipative Majorana Chain---Anomalies and Non-Invertible Symmetries
arXiv:2610.12607v1 Announce Type: new Abstract: We study symmetries and anomalies of dissipative Majorana chains described by Lindblad dynamics. Using the operator-state mapping, we represent the Lindbladian as a non-Hermitian operator on a doubled Hilbert space. In this formulation, the ket and bra contours admit strong fermion parities and strong translations, while their diagonal combinations define weak symmetries. For even and odd chain lengths, we diagnose anomalies by comparing symmetry algebras with and without weak fermion-parity defects. These algebras retain the lattice precursor of the modulo-$8$ anomaly of the closed Majorana chain and exhibit projective relations between strong fermion parity and weak translation, as well as between weak fermion parity and strong translation, which are intrinsic to open quantum systems. We establish the IR correspondence between the lattice symmetry algebras and those of the doubled Majorana CFT in four spin sectors, identifying chiral fermion parities emanated from the lattice translations. Finally, we develop the lattice bosonization of the dissipative chain. For even length with collective energy dephasing, combining the defect and no-defect sectors and imposing GSO projections gives rise to an Ising Lindbladian with non-invertible Kramers--Wannier symmetries descending from the anomalous strong translation and fermion parity of the Majorana chain. For odd length, constructing mutually commuting ket- and bra-sector spin operators instead yields an Ising Lindbladian with a Kramers--Wannier duality defect. Our results provide a controlled framework for extending lattice anomalies and non-invertible symmetries to open quantum systems.
Abstract:We study symmetries and anomalies of dissipative Majorana chains described by Lindblad dynamics. Using the operator-state mapping, we represent the Lindbladian as a non-Hermitian operator on a doubled Hilbert space. In this formulation, the ket and bra contours admit strong fermion parities and strong translations, while their diagonal combinations define weak symmetries. For even and odd chain lengths, we diagnose anomalies by comparing symmetry algebras with and without weak fermion-parity defects. These algebras retain the lattice precursor of the modulo-$8$ anomaly of the closed Majorana chain and exhibit projective relations between strong fermion parity and weak translation, as well as between weak fermion parity and strong translation, which are intrinsic to open quantum systems. We establish the IR correspondence between the lattice symmetry algebras and those of the doubled Majorana CFT in four spin sectors, identifying chiral fermion parities emanated from the lattice translations. Finally, we develop the lattice bosonization of the dissipative chain. For even length with collective energy dephasing, combining the defect and no-defect sectors and imposing GSO projections gives rise to an Ising Lindbladian with non-invertible Kramers--Wannier symmetries descending from the anomalous strong translation and fermion parity of the Majorana chain. For odd length, constructing mutually commuting ket- and bra-sector spin operators instead yields an Ising Lindbladian with a Kramers--Wannier duality defect. Our results provide a controlled framework for extending lattice anomalies and non-invertible symmetries to open quantum systems.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th)
arXiv:2610.12607 [quant-ph]
(or arXiv:2610.12607v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.12607 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 263 words
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