Finite-size corrections in the bosonic algebraic approach to two-dimensional systems

Fernández, Pedro Pérez; Arias, J. M.; García-Ramos, J. E.; Pérez‐Bernal, F.

doi:10.1103/physreva.83.062125

Cited by 16 publications

(19 citation statements)

References 57 publications

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“…In nuclear physics many aspects of QPTs have been studied [1][2][3], both theoretically and experimentally. Also, in other fields such as molecular physics [4,5], quantum optics [6,7], or solid-state physics [8] studies related to relevant QPTs have been recently presented.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of the two-fluid Lipkin model: A “butterfly” catastrophe

et al. 2016

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Background:In the past few decades quantum phase transitions have been of great interest in nuclear physics. In this context, two-fluid algebraic models are ideal systems to study how the concept of quantum phase transition evolves when moving into more complex systems, but the number of publications along this line has been scarce up to now. Purpose: We intend to determine the phase diagram of a two-fluid Lipkin model that resembles the nuclear protonneutron interacting boson model Hamiltonian using both numerical results and analytic tools, i.e., catastrophe theory, and compare the mean-field results with exact diagonalizations for large systems. Method: The mean-field energy surface of a consistent-Q-like two-fluid Lipkin Hamiltonian is studied and compared with exact results coming from a direct diagonalization. The mean-field results are analyzed using the framework of catastrophe theory. Results:The phase diagram of the model is obtained and the order of the different phase-transition lines and surfaces is determined using a catastrophe theory analysis. Conclusions: There are two first-order surfaces in the phase diagram, one separating the spherical and the deformed shapes, while the other separates two different deformed phases. A second-order line, where the later surfaces merge, is found. This line finishes in a transition point with a divergence in the second-order derivative of the energy that corresponds to a tricritical point in the language of the Ginzburg-Landau theory for phase transitions.

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Section: Introductionmentioning

confidence: 99%

Phase diagram of the two-fluid Lipkin model: A “butterfly” catastrophe

et al. 2016

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“…The calculation of finite-size corrections to the mean field limit greatly deepens the knowledge of the model. These corrections are a fundamental help to characterize the QPTs between the different geometric limits of a model and to analytically extract the scaling exponents for the model, as it will be shown for the model under study in a forthcoming publication [21].…”

Section: Discussionmentioning

confidence: 99%

“…As in the previous case, the obtained correction notably improves the mean field result, in particular in the vicinity of the critical control parameter. The results presented are encompassed in an open line of research [21]. We are currently working on computing the BMF correction for other observables, on analytically deriving finitesize scaling exponents for the u(2) − so(3) second order phase transition, and on establishing a connection between Ref.…”

Section: Beyond Mean Field Analytical Correctionsmentioning

confidence: 99%

Novel results from an algebraic approach to molecular bending dynamics

Pérez‐Bernal

Álvarez‐Bajo

Arias

et al. 2011

J. Phys.: Conf. Ser.

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We present a brief review of research topics of current interest that depend on an algebraic approach to molecular bending dynamics. This approach is based on a u(3) spectrum generating algebra. In particular, we briefly present results on three topics: the calculation of finite-size analytical corrections to mean field results, the application of the model to the largeamplitude vibrational bending mode of the NCNCS molecule, and the analysis of the influence of quadratic Casimir operators on excited state quantum phase transitions.

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“…In fact, beyond mean-field corrections for finite N values can be obtained in a systematic way using an expansion in powers of N [49]. However, as we show in the next section, considering parity in the definition of the cat states allows them to reproduce the exact entanglement properties of the coupled 2DVM model.…”

Section: Parity and Schrödinger-cat Statesmentioning

confidence: 98%

“…We shall show that even-cat states provide finitesize N approximations to some N = ∞ quantities like the ground-state energy "per particle" and order parameters like the equilibrium radius. The finite-size corrections obtained with these trial states differ from a systematic expansion of the different observables as a function of system's size, computing the relevant corrections for each power of N [49]. However, the main advantage of including even-cat states as a variational ansatz is that they offer the possibility of capturing, qualitatively and quantitatively, entanglement measures of the exact ground state for finite N values.…”

Section: Introductionmentioning

confidence: 99%

Entanglement in shape phase transitions of coupled molecular benders

Calixto

Pérez‐Bernal

2014

Phys. Rev. A

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We study the entanglement properties of the shape phase transitions between different geometric limits of two coupled equivalent molecular benders modeled with the two-dimensional limit of the vibron model. This system has four possible geometric configurations: linear, cis-bent, trans-bent, and nonplanar. We show how the entanglement, accessed through the calculation of the linear entropy, between benders and between rotational and vibrational degrees of freedom changes sensitively in the critical regions of this two-fluid bosonic model. The numeric calculation is complemented with a variational approach to the ground-state wave function in terms of symmetry-adapted coherent states.

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Finite-size corrections in the bosonic algebraic approach to two-dimensional systems

Cited by 16 publications

References 57 publications

Phase diagram of the two-fluid Lipkin model: A “butterfly” catastrophe

Phase diagram of the two-fluid Lipkin model: A “butterfly” catastrophe

Novel results from an algebraic approach to molecular bending dynamics

Entanglement in shape phase transitions of coupled molecular benders

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