Instantons and Berry’s connections on quantum graph

Inoue, Tomonori; Sakamoto, Makoto; Ueba, Inori

doi:10.1088/1751-8121/ac17a3

Cited by 4 publications

(2 citation statements)

References 31 publications

(46 reference statements)

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“…In fact, the matrix which specifies the boundary conditions is not generally Hermitian in even dimensions if we do not impose any symmetries (see e.g. [19]). The extension of the classification in the other spacetime dimensions is a future task.…”

Section: Summary and Discussionmentioning

confidence: 99%

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Correspondence of topological classification between quantum graph extra dimension and topological matter

Inoue¹,

Sakamoto²,

Sato³

et al. 2022

Preprint

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In this paper, we study a classification of boundary conditions with symmetries for a five-dimensional Dirac fermion on a quantum graph. We find that there is a nontrivial correspondence between the classification of boundary conditions at the vertex on the quantum graph and that of the symmetry-protected topological phases of gapped free-fermion systems, which are classified into ten symmetry classes by the time-reversal symmetry, particle-hole symmetry and chiral symmetry. A Hermitian matrix which specifies the boundary conditions in our model corresponds to a zero-dimensional Hamiltonian in the gapped free-fermion systems. Furthermore, symmetries in our model give the condition that restricts the parameter space of the boundary conditions. These conditions are identical to the ones in the gapped free-fermion systems that the Hamiltonian with the symmetries should satisfy. We also show that the topological number for each symmetry class in our model implies the presence of 4d massless fields localized at the vertex of the quantum graph, like gapless boundary states for the free-fermion systems from the bulk-boundary correspondence.

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Section: Summary and Discussionmentioning

confidence: 99%

“…This graph has been applied to the wide range of research areas, e.g. scattering theory on 1d graphs [3][4][5][6], quantum chaos [7][8][9], anyons [10][11][12], supersymmetric quantum mechanics [13][14][15], Berry's phases [16][17][18][19] and so on.…”

Section: Introductionmentioning

confidence: 99%

Correspondence of topological classification between quantum graph extra dimension and topological matter

Inoue¹,

Sakamoto²,

Sato³

et al. 2022

Preprint

Self Cite

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Exotic Instantons in Eight Dimensions

Loginov

Loginova

2021

Adv. Appl. Clifford Algebras

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Novel quantum phases on graphs using abelian gauge theory

Padmanabhan¹,

Sugino²

2021

J. Stat. Mech.

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Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of an even richer variety than the two-dimensional space. We explore this possibility by building a class of frustration-free and gapped Hamiltonians based on discrete abelian gauge groups. The resulting models have a ground state degeneracy that can be either a topological invariant, an extensive quantity or a mixture of the two. For two basis of the degenerate ground states which are complementary in quantum theory, the entanglement entropy (EE) is exactly computed. The result for one basis has a constant global term, known as the topological EE, implying long-range entanglement. On the other hand, the topological EE vanishes in the result for the other basis. Comparisons are made with similar occurrences in the toric code. We analyze excitations and identify anyon-like excitations that account for the topological EE. An analogy between the ground states of this system and the θ-vacuum for a U(1) gauge theory on a circle is also drawn.

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Instantons and Berry’s connections on quantum graph

Cited by 4 publications

References 31 publications

Correspondence of topological classification between quantum graph extra dimension and topological matter

Correspondence of topological classification between quantum graph extra dimension and topological matter

Exotic Instantons in Eight Dimensions

Novel quantum phases on graphs using abelian gauge theory

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