Vertex and Edge Orbits of Fibonacci and Lucas Cubes

Ашрафи, Али Реза; Azarija, Jernej; Fathalikhani, Khadijeh; Klavžar, Sandi; Petkovšek, Marko

doi:10.1007/s00026-016-0318-9

Cited by 7 publications

(3 citation statements)

References 17 publications

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“…These are integer sequences of system size and can be found in the OEIS as A000358 and A129526 respectively. 89,90 The ordinary generating functions of these sequences are known to be…”

Section: Periodic Chainmentioning

confidence: 99%

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

et al. 2018

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Recent realization of a kinetically-constrained chain of Rydberg atoms by Bernien et al. [Nature 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work, Turner et al. [arXiv:1711.03528], such dynamics was attributed to the existence of "quantum scarred" eigenstates in the many-body spectrum of the experimentally realized model. Here we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify non-ergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit sub-thermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum-scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of "canonical" thermalization. arXiv:1806.10933v2 [cond-mat.quant-gas]

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“…These are integer sequences of system size and can be found in the OEIS as A000358 and A129526 respectively. 89,90 The ordinary generating functions of these sequences are known to be…”

Section: Periodic Chainmentioning

confidence: 99%

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

et al. 2018

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“…Note 2M + K is the number of translation orbits and M + K is the number of orbits of the combined dihedral symmetry of translation and inversion symmetry. These are integer sequences of system size and can be found in the OEIS as A000358 and A129526, respectively [89,90]. The ordinary generating functions of these sequences are known to be…”

Section: Periodic Chainmentioning

confidence: 99%

Cold Atoms Bear a Quantum Scar

Robinson

2018

Physics

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Recent realization of a kinetically constrained chain of Rydberg atoms by Bernien et al., [Nature (London) 551, 579 (2017)] resulted in the observation of unusual revivals in the many-body quantum dynamics. In our previous work [C. J. Turner et al., Nat. Phys. 14, 745 (2018)], such dynamics was attributed to the existence of "quantum scarred" eigenstates in the many-body spectrum of the experimentally realized model. Here, we present a detailed study of the eigenstate properties of the same model. We find that the majority of the eigenstates exhibit anomalous thermalization: the observable expectation values converge to their Gibbs ensemble values, but parametrically slower compared to the predictions of the eigenstate thermalization hypothesis (ETH). Amidst the thermalizing spectrum, we identify nonergodic eigenstates that strongly violate the ETH, whose number grows polynomially with system size. Previously, the same eigenstates were identified via large overlaps with certain product states, and were used to explain the revivals observed in experiment. Here, we find that these eigenstates, in addition to highly atypical expectation values of local observables, also exhibit subthermal entanglement entropy that scales logarithmically with the system size. Moreover, we identify an additional class of quantum scarred eigenstates, and discuss their manifestations in the dynamics starting from initial product states. We use forward scattering approximation to describe the structure and physical properties of quantum scarred eigenstates. Finally, we discuss the stability of quantum scars to various perturbations. We observe that quantum scars remain robust when the introduced perturbation is compatible with the forward scattering approximation. In contrast, the perturbations which most efficiently destroy quantum scars also lead to the restoration of "canonical" thermalization.

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“…Their usage in theoretical chemistry and some results on the structure of Fibonacci cubes, including representations, recursive construction, hamiltonicity, the nature of the degree sequence and some enumeration results are presented in [3]. Characterization of induced hypercubes in Γ n are considered in [4][5][6][7][8] and many additional new properties of Fibonacci cubes are given in the literature, see for example [9][10][11]. Furthermore, the domination number (see, Section 2) of Γ n is first considered in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Upper Bounds on the Domination and Total Domination Number of Fibonacci Cubes

Saygı

2017

SDÜ Fen Bil Enst Der

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Abstract:One of the basic model for interconnection networks is the n-dimensional hypercube graph Q n and the vertices of Q n are represented by all binary strings of length n. The Fibonacci cube Γ n of dimension n is a subgraph of Q n , where the vertices correspond to those without two consecutive 1s in their string representation. In this paper, we deal with the domination number and the total domination number of Fibonacci cubes. First we obtain upper bounds on the domination number of Γ n for n ≥ 13. Then using these result we obtain upper bounds on the total domination number of Γ n for n ≥ 14 and we see that these upper bounds improve the bounds given in [1].

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Vertex and Edge Orbits of Fibonacci and Lucas Cubes

Cited by 7 publications

References 17 publications

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

Quantum scarred eigenstates in a Rydberg atom chain: Entanglement, breakdown of thermalization, and stability to perturbations

Cold Atoms Bear a Quantum Scar

Upper Bounds on the Domination and Total Domination Number of Fibonacci Cubes

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