FINITE SIZE EFFECTS IN ENTANGLED RINGS OF QUBITS

We study translationally invariant rings of qubits with a finite number of sites N, and determine the maximal nearest-neighbor entanglement for a fixed z-component of the total spin. For small numbers of sites we present analytical results. We establish a relation between the maximal nearest-neighbor concurrence and the ground state energy of an XXZ spin model. This connection allows us to calculate the concurrence numerically for N≤24. We point out some interesting finite-size effects. Finally, we generalize our results beyond nearest neighbors.

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Unzipping of two random heteropolymers: Ground-state energy and finite-size effects

Physical Review E ◽

10.1103/physreve.78.011903 ◽

2008 ◽

Vol 78 (1) ◽

Cited By ~ 3

Author(s):

M. V. Tamm ◽

S. K. Nechaev

Keyword(s):

Ground State Energy ◽

Ground State ◽

Size Effects ◽

State Energy ◽

Finite Size ◽

Finite Size Effects

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GROUND STATE OF THE 2D EXTENDED HUBBARD MODEL WITH MORE THAN NEAREST-NEIGHBOR INTERACTIONS

International Journal of Modern Physics B ◽

10.1142/s0217979212501561 ◽

2012 ◽

Vol 26 (29) ◽

pp. 1250156 ◽

Cited By ~ 4

Author(s):

S. HARIR ◽

M. BENNAI ◽

Y. BOUGHALEB

Keyword(s):

Phase Diagram ◽

Hubbard Model ◽

Ground State ◽

State Energy ◽

Nearest Neighbor ◽

Finite Size ◽

Square Lattice ◽

Extended Hubbard Model ◽

Eigenvalues And Eigenvectors ◽

Repulsion Energy

We investigate the ground state phase diagram of the two dimensional Extended Hubbard Model (EHM) with more than Nearest-Neighbor (NN) interactions for finite size system at low concentration. This EHM is solved analytically for finite square lattice at one-eighth filling. All eigenvalues and eigenvectors are given as a function of the on-site repulsion energy U and the off-site interaction energy Vij. The behavior of the ground state energy exhibits the emergence of phase diagram. The obtained results clearly underline that interactions exceeding NN distances in range can significantly influence the emergence of the ground state conductor–insulator transition.

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Homogeneous one-dimensional Bose–Einstein condensate in the Bogoliubov’s regime

Modern Physics Letters B ◽

10.1142/s0217984916503073 ◽

2016 ◽

Vol 30 (22) ◽

pp. 1650307 ◽

Cited By ~ 2

Author(s):

Elías Castellanos

Keyword(s):

Ground State ◽

Size Effects ◽

Finite Size ◽

Einstein Condensate ◽

Finite Size Effects ◽

One Dimensional ◽

Bose Einstein Condensate ◽

Ground State Properties ◽

Low Dimensional ◽

Bose Einstein

We analyze the corrections caused by finite size effects upon the ground state properties of a homogeneous one-dimensional (1D) Bose–Einstein condensate. We assume from the very beginning that the Bogoliubov’s formalism is valid and consequently, we show that in order to obtain a well-defined ground state properties, finite size effects of the system must be taken into account. Indeed, the formalism described in the present paper allows to recover the usual properties related to the ground state of a homogeneous 1D Bose–Einstein condensate but corrected by finite size effects of the system. Finally, this scenario allows us to analyze the sensitivity of the system when the Bogoliubov’s regime is valid and when finite size effects are present. These facts open the possibility to apply these ideas to more realistic scenarios, e.g. low-dimensional trapped Bose–Einstein condensates.

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Finite-size effects in exponential random graphs

Journal of Complex Networks ◽

10.1093/comnet/cnaa008 ◽

2020 ◽

Vol 8 (1) ◽

Author(s):

A Gorsky ◽

O Valba

Keyword(s):

Random Graphs ◽

Ground State ◽

Size Effects ◽

Chemical Potential ◽

Network Flows ◽

Finite Size ◽

Critical Value ◽

Star Model ◽

Finite Size Effects ◽

Exponential Random Graphs

Abstract In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density $p<0.5$ or as the single cluster at $p>0.5$. We find that there exists the critical value of number of nodes $N^{*}(p)$ when the ground state undergoes clear-cut crossover. At $N>N^{*}(p),$ the network flows via a cluster evaporation to the state involving the small star in the Erdős–Rényi environment. The similar evaporation of the cluster takes place at $N>N^{*}(p)$ in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.

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