Quantum discrete<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>model at finite temperatures

Savkin, V. V.; Rubtsov, A. N.; Janssen, Τ.

doi:10.1103/physrevb.65.214103

Cited by 9 publications

(5 citation statements)

References 27 publications

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“…The theoretical interpretations for structural phase transition and domain wall dynamics have be well established in the framework of Krumhansl-Schrieffer model (also known as φ 4 model). 16,17,18,19 In this model, the particles are subject to anharmonic on-site potentials and harmonic inter-site couplings. The on-site potential is represented as a polynomial form of the order parameter such as polarization, displacement, or elasticity, which displays a substantial change around T c .…”

Section: A Model Hamiltonianmentioning

confidence: 99%

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Quantum Monte Carlo study on speckle variation due to photorelaxation of ferroelectric clusters in paraelectric barium titanate

Jia¹,

Namikawa

Zheng

et al. 2009

Phys. Rev. B

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Time-dependent speckle pattern of paraelectric barium titanate observed in a soft x-ray laser pump-probe measurement is theoretically investigated as a correlated optical response to the pump and probe pulses. The scattering probability is calculated based on a model with coupled soft x-ray photon and ferroelectric phonon mode. It is found that the speckle variation is related with the relaxation dynamics of ferroelectric clusters created by the pump pulse. Additionally, critical slowing down of cluster relaxation arises on decreasing temperature towards the paraelectric-ferroelectric transition temperature. Relation between critical slowing down, local dipole fluctuation and crystal structure are revealed by quantum Monte Carlo simulation.

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Section: A Model Hamiltonianmentioning

confidence: 99%

“…16,17,18,19 In this model, the particles are subject to anharmonic on-site potentials and harmonic inter-site couplings. The on-site potential is represented as a polynomial form of the order parameter such as polarization, displacement, or elasticity, which displays a substantial change around T c .…”

Section: A Model Hamiltonianmentioning

confidence: 99%

Quantum Monte Carlo study on speckle variation due to photorelaxation of ferroelectric clusters in paraelectric barium titanate

Jia¹,

Namikawa

Zheng

et al. 2009

Phys. Rev. B

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“…For making comparison with previous results, we list the mappings from our parametrisation to some others. In the works [20,23] m . This Hamiltonian is particularly useful for exploring the limit of the Ising model (a → ∞), where particles are strongly localized to positions around −1 and 1.…”

Section: Appendix C: Methods Testingmentioning

confidence: 99%

“…Studies of higher dimensional systems found the emergence of classical order-disorder phase transition in the double well chain with finite barrier and a displacive transition at vanishing barrier [23]. Investigations in 1D discrete φ 4 model were done in the limit of large double-well barrier, i.e.…”

Section: Phase Diagram At Non-zero Temperaturementioning

confidence: 99%

“…The finite-temperature phase diagram of the φ 4 model continues to be a field of active research, as it can change considerably from system to system [22]. In higher dimensions, the phase diagram shows the occurrence of classical phase transition, induced by thermal fluctuations, emerging from quantum criticality [23]. However, different regimes surrounding the QCP are not well understood, with the exception of the infinite-barrier limit, which is analogous to the Ising model.…”

Section: Introductionmentioning

confidence: 99%

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Rényi entropy of quantum anharmonic chain at non-zero temperature

Srdinšek¹,

Casula²,

Vuilleumier³

2023

Preprint

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The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the Rényi entropy is a precious tool to characterize the phase diagram of critical systems not only around the QCP but also away from it, thanks to its capability to detect the emergence of local order at finite temperature. For an efficient evaluation of the Rényi entropy, we introduce a new algorithm based on a path integral Langevin dynamics combined with a previously proposed thermodynamic integration method built on regularized paths. We apply this framework to study the critical behavior of a linear chain of anharmonic oscillators, a particular realization of the φ 4 model. We fully resolved its phase diagram, as a function of both temperature and interaction strength. At finite temperature, we find a sequence of three regimes -para, disordered and quasi long-range ordered -, met as the interaction is increased. The Rényi entropy divergence coincides with the crossover between the para and disordered regime, which shows no temperature dependence. The occurrence of quasi long-range order, on the other hand, is temperature dependent. The two crossover lines merge in proximity of the QCP, at zero temperature, where the Rényi entropy is sharply peaked. Via its subsystem-size scaling, we confirm that the transition belongs to the two-dimensional Ising universality class. This phenomenology is expected to happen in all φ 4 -like systems, as well as in the elusive water ice transition across phases VII, VIII and X.

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Analytic results for a phase transition in a planar array of chains

Barsan

2007

Philosophical Magazine

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Quantum discreteφ4model at finite temperatures

Cited by 9 publications

References 27 publications

Quantum Monte Carlo study on speckle variation due to photorelaxation of ferroelectric clusters in paraelectric barium titanate

Quantum Monte Carlo study on speckle variation due to photorelaxation of ferroelectric clusters in paraelectric barium titanate

Rényi entropy of quantum anharmonic chain at non-zero temperature

Analytic results for a phase transition in a planar array of chains

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