Dulmage-Mendelsohn Percolation: Geometry of Maximally Packed Dimer Models and Topologically Protected Zero Modes on Site-Diluted Bipartite Lattices Article Swipe
Ritesh Bhola
,
Sounak Biswas
,
Md Mursalin Islam
,
Kedar Damle
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1103/physrevx.12.021058
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1103/physrevx.12.021058
The classic combinatorial construct of maximum matchings probes the random geometry of regions with local sublattice imbalance in a site-diluted bipartite lattice. We demonstrate that these regions, which host the monomers of any maximum matching of the lattice, control the localization properties of a zero-energy quantum particle hopping on this lattice. The structure theory of Dulmage and Mendelsohn provides us with a way of identifying a complete and nonoverlapping set of such regions. This motivates our large-scale computational study of the Dulmage-Mendelsohn decomposition of site-diluted bipartite lattices in two and three dimensions. Our computations uncover an interesting universality class of percolation associated with the end-to-end connectivity of such monomer-carrying regions with local sublattice imbalance, which we dub Dulmage-Mendelsohn percolation. Our results imply the existence of a monomer percolation transition in the classical statistical mechanics of the associated maximally packed dimer model and the existence of a phase with area-law entanglement entropy of arbitrary many-body eigenstates of the corresponding quantum dimer model. They also have striking implications for the nature of collective zero-energy Majorana fermion excitations of bipartite networks of Majorana modes localized on sites of diluted lattices, for the character of topologically protected zero-energy wavefunctions of the bipartite random hopping problem on such lattices, and thence for the corresponding quantum percolation problem, and for the nature of low-energy magnetic excitations in bipartite quantum antiferromagnets diluted by a small density of nonmagnetic impurities.
Related Topics
Concepts
MAJORANA
Bipartite graph
Percolation (cognitive psychology)
Lattice (music)
Quantum
Physics
Condensed matter physics
Percolation theory
Zero (linguistics)
Theoretical physics
Quantum mechanics
Superconductivity
Combinatorics
Mathematics
Philosophy
Graph
Neuroscience
Biology
Linguistics
Acoustics
Conductivity
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physrevx.12.021058
- http://link.aps.org/pdf/10.1103/PhysRevX.12.021058
- OA Status
- gold
- Cited By
- 11
- References
- 104
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4282969394
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4282969394Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1103/physrevx.12.021058Digital Object Identifier
- Title
-
Dulmage-Mendelsohn Percolation: Geometry of Maximally Packed Dimer Models and Topologically Protected Zero Modes on Site-Diluted Bipartite LatticesWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-06-15Full publication date if available
- Authors
-
Ritesh Bhola, Sounak Biswas, Md Mursalin Islam, Kedar DamleList of authors in order
- Landing page
-
https://doi.org/10.1103/physrevx.12.021058Publisher landing page
- PDF URL
-
https://link.aps.org/pdf/10.1103/PhysRevX.12.021058Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
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https://link.aps.org/pdf/10.1103/PhysRevX.12.021058Direct OA link when available
- Concepts
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MAJORANA, Bipartite graph, Percolation (cognitive psychology), Lattice (music), Quantum, Physics, Condensed matter physics, Percolation theory, Zero (linguistics), Theoretical physics, Quantum mechanics, Superconductivity, Combinatorics, Mathematics, Philosophy, Graph, Neuroscience, Biology, Linguistics, Acoustics, ConductivityTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
11Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2, 2024: 4, 2023: 2, 2022: 3Per-year citation counts (last 5 years)
- References (count)
-
104Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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