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In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons and fermions. Here we show how this fundamental concept can be applied to connect bosonic and fermionic lattice models in the realm of condensed matter physics, e.g., to identify a variety of (bosonic) phonon and magnon lattice models which admit topologically nontrivial free fermion models as superpartners. At the single-particle level, the bosonic and the fermionic models that are generated by the SUSY are isospectral except for zero modes, such as flat bands, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences and discuss further ramifications such as the definition of supersymmetric topological invariants for generic bosonic systems. Notably, a Hermitian form of the supercharge operator, the generator of the SUSY, can itself be interpreted as a hopping Hamiltonian on a bipartite lattice. This allows us to identify a wide class of interconnected lattices whose tight-binding Hamiltonians are superpartners of one another or can be derived via squaring or square-rooting their energy spectra all the while preserving band topology features. We introduce a five-fold way symmetry classification scheme of these SUSY lattice correspondences, including cases with a non-zero Witten index, based on a topological classification of the underlying Hermitian supercharge operator. These concepts are illustrated for various explicit examples including frustrated magnets, Kitaev spin liquids, and topological superconductors.
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Topological zero modes and edge symmetries of metastable Markovian bosonic systems
Tight bosonic analogs of free-fermionic symmetry-protected topological phases, and their associated edgelocalized excitations, have long evaded the grasp of condensed-matter and AMO physics. In this paper, building on our initial exploration [Phys. Rev. Lett. 127, 245701 (2021)], we identify a broad class of quadratic bosonic systems subject to Markovian dissipation that realize tight bosonic analogs of the Majorana and Dirac edge modes characteristic of topological superconductors and insulators, respectively. To this end, we establish a general framework for topological metastability for these systems, by leveraging pseudospectral theory as the appropriate mathematical tool for capturing the nonnormality of the Lindbladian generator. The resulting dynamical paradigm, which is characterized by both a sharp separation between transient and asymptotic dynamics and a nontrivial topological invariant, is shown to host edge-localized modes, which we dub Majorana and Dirac bosons. Generically, such modes consist of one conserved mode and a canonically conjugate generator of an approximate phase-space translation symmetry of the dynamics. The general theory is exemplified through several representative models exhibiting the full range of exotic boundary physics that topologically metastable systems can engender. In particular, we explore the extent to which Noether’s theorem is violated in this dissipative setting and the way in which certain symmetries can nontrivially modify the edge modes. Notably, we also demonstrate the possibility of anomalous parity dynamics for a bosonic cat state prepared in a topologically metastable system, whereby an equal distribution between even and odd parity sectors is sustained over a long transient. For both Majorana and Dirac bosons, observable multitime signatures in the form of anomalously long-lived quantum correlations and divergent zero-frequency power spectral peaks are proposed and discussed in detail. Our results point to a paradigm for symmetry-protected topological physics in free bosons, embedded deeply in the long-lived transient regimes of metastable dynamics.
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- Award ID(s):
- 2013974
- PAR ID:
- 10533973
- Publisher / Repository:
- Physical Review B
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 108
- Issue:
- 21
- ISSN:
- 2469-9950
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/PhysRevB.108.214312
