Thermal state entanglement entropy on a quantum graph

Verga, Alberto; Elías, Ricardo Gabriel

doi:10.1103/physreve.100.062137

Cited by 6 publications

(2 citation statements)

References 55 publications

(69 reference statements)

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“…A natural continuation of this paper is to study other Euclidean models (such as Landau-Ginzburg model [87][88][89], Gross-Pitaevskii model [90][91][92], Euclidean Schwarzschild and other curved manifolds [93][94][95][96][97]) in order to obtain new elements for the set of DZF-based SPMs and extract out its advanges from its physical consequences. Another continuation is to evalue different phase transitions problems and entanglement networks of quantum systems of interets (such as qubits [98][99][100][101][102] or biological light-harvesting complexes [103][104][105][106][107]). Finally, the objects that we have constructed here can be used to study design, formation, growing, and robustness of real life networks to obtain a depper understanding of their complexity.…”

Section: Discussionmentioning

confidence: 99%

Systemic Performance Measures from Distributional Zeta-Function

Rodríguez-Camargo,

Urquijo-Rodríguez,

Mojica-Nava

2020

Preprint

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We propose the use of the Distributional Zeta-Function (DZF) for constructing a new set of Systemic Performance Measures (SPM). SPM have been proposed to investigate network synthesis problems such as the growing of linear consensus networks. The adoption of the DZF has shown interesting physical consequences that in the usual replica method are still unclarified, i.e., the connection between the spontaneous symmetry breaking mechanism and the structure of the replica space in the disordered model. We relate topology of the network and the partition function present in the DZF by using the spectral and the Hamiltonian structure of the system. The studied objects are the generalized partition funcion, the DZF, the Expected value of the replica partition function, and the quenched free energy of a field network. We show that with these objects we need few operations to increase the percentage of performance enhancement of a network. Furthermore, we evalue the location of the optimal added links for each new SPM and calculate the performance improvement of the new network for each new SPM via the spectral zeta function, H2-norm, and the communicability between nodes. We present the advantages of this new set of SPM in the network synthesis and we propose other methods for using the DZF to explore some issues such as disorder, critical phenomena, finite-temperature, and finite-size effects on networks. Relevance of the results are discussed.

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Section: Discussionmentioning

confidence: 99%

Systemic Performance Measures from Distributional Zeta-Function

Rodríguez-Camargo,

Urquijo-Rodríguez,

Mojica-Nava

2020

Preprint

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“…At variance to the model of Ref. [64,65] the spins do not interact, are then located on the edges of the graph, and, as a consequence, the particle-spin interaction is independent of the local degree of the graph (which was the case in the node spin model). The interaction of the walker with the geometry gives rise to an extension of the usual model of a quantum walk to an interacting one.…”

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confidence: 97%

Quantum walk on a graph of spins: magnetism and entanglement

Sellapillay,

Verga

2020

Preprint

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We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a one dimensional lattice, to investigate its magnetic and entanglement properties. In the continuum limit, we recover a Landau-Lifshitz equation that describes the precession of spins. A rich dynamics is observed, with regimes of particle propagation and localization, together with spin oscillations and relaxation. Entanglement of the asymptotic states follows a volume law for most parameters (the coin rotation angle and the particle-spin coupling).

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Asymptotic entropy of the Gibbs state of complex networks

Glos

Krawiec

Pawela

2021

Sci Rep

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In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erdős–Rényi, Watts–Strogatz, Barabási–Albert and Chung–Lu graph models and a few real-world graphs. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random Erdős–Rényi graphs.

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Thermal state entanglement entropy on a quantum graph

Abstract: A particle jumps between the nodes of a graph interacting with local spins. We show that the entanglement entropy of the particle with the spin network is related to the length of the minimum cycle basis. The structure of the thermal state is reminiscent to the string-net of spin liquids.

Cited by 6 publications

References 55 publications

Systemic Performance Measures from Distributional Zeta-Function

Systemic Performance Measures from Distributional Zeta-Function

Quantum walk on a graph of spins: magnetism and entanglement

Asymptotic entropy of the Gibbs state of complex networks

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