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• Remarks on the large-$N$ ${\mathbb C}P^{N-1}$ model

  Antonino Flachi

  2019年12月

  　概要を見る

  In this paper we consider the ${\mathbb C}P^{N-1}$ model confined to an
  interval of finite size at finite temperature and chemical potential. We
  compute, in the large-$N$ approximation, the one-loop effective action of the
  order parameter associated with the effective mass of the quantum fluctuations.
  To discuss some generic features of the ground state of the model, we work out
  a mixed-gradient expansion and obtain an expression for the thermodynamic
  potential density as a functional of the order parameter, generalizing previous
  calculations to arbitrarily large order and to the case of small finite
  density. The technique used here relies on analytic regularization and provides
  an efficient scheme to extract the coefficients of the expansion. These
  coefficients are then used to deduce some generic properties of the ground
  state as a function of external conditions. For vanishing chemical potential
  and intervals of any size, we show that inhomogeneous phases are not
  energetically favored, but we find evidence that they may become energetically
  favored for large enough values of the chemical potential. We also show that
  there can be no transition to a massless phase for any value of the external
  conditions and clarify a seemingly important point regarding the regularization
  of the effective action connected to the appearance of logarithmic divergences
  and to the Mermin-Wagner-Hoenberg-Coleman theorem.
  

• Casimir force for the CP^N−1 model

  Flachi A., Nitta M., Takada S., Yoshii R.

  Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics （Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics）  798 2019年11月

  ISSN  03702693

  　概要を見る

  © 2019 In this work, we derive exact self-consistent solutions to the gap equations of the CPN−1 model on a finite interval with Dirichlet boundary conditions in the large-N approximation. The solution reproduces the confining phase in the infinite system by taking the appropriate limit. We compute the vacuum energy and the Casimir force and observe that the sign of the force is always attractive.

  • Access to Document (DOI)

• Ground state modulations in the CPN-1 model

  Flachi A., Fucci G., Nitta M., Takada S., Yoshii R.

  Physical Review D （Physical Review D）  100 （ 8 ）  2019年10月

  ISSN  24700010

  　概要を見る

  © 2019 authors. Published by the American Physical Society. In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional CPN-1 model, restricted to an interval and at finite temperature. We develop a method to obtain the bulk and boundary parts of the one-loop effective action as a function of the effective mass of the fluctuations. The formalism has the advantage of allowing for a systematic analysis of a large class of boundary conditions and to model the (adiabatic) response of the ground state to changes in the boundary conditions. In the case of periodic boundary conditions, we find that inhomogeneous phases are disfavored for intervals of large size. Away from periodic boundary conditions, our numerical results show that the ground state has a generic crystal-like structure that can be modulated by variations of the boundary conditions. The results presented here could be relevant for experimental implementations of nonlinear sigma models and could be tested by lattice numerical simulations.

  • Access to Document (DOI)

• Cosmic strings, deformed lattices and spontaneous symmetry breaking

  Flachi A., Vitagliano V.

  Journal of Physics: Conference Series （Journal of Physics: Conference Series）  1275 （ 1 ）  2019年09月

  ISSN  17426588

  　概要を見る

  © Published under licence by IOP Publishing Ltd. External conditions have a dramatic impact on the way dynamical symmetry breaking occurs. In a curved background, the natural expectation is that curvature works toward the restoration of the internal symmetry. We show instead that, for topological defects, the competing action of the locally induced curvature and boundary conditions generated by the non-trivial topology allows configurations where symmetries can be spontaneously broken close to the core. Inspired by the effect of geometrical deformations on 2D lattices, we then propose a novel mechanism to induce a superconducting phase by triggering condensation along cosmic strings.

  • Access to Document (DOI)

• Symmetry breaking and lattice kirigami: Finite temperature effects

  Flachi A., Vitagliano V.

  Physical Review D （Physical Review D）  99 （ 12 ）  2019年06月

  ISSN  24700010

  　概要を見る

  © 2019 authors. Published by the American Physical Society. Recent work has analyzed how deformations due to the insertion of a defect in a flat hexagonal lattice affect the ground state structure of an interacting fermion field theory. Such modifications result in an increase of the order parameter in the vicinity of the defect and can be explained by a kirigami effect, that is the combined effect of the curvature, locally introduced by the deformation in the lattice tessellation, and of a synthetic gauge field induced by the boundary conditions along the cut, performed to introduce the defect. In this work, we extend the formalism and previous results to include finite temperature effects.

  • Access to Document (DOI)

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• Quantum field theory in curved space : general relativity : numerical methods : machine learning

  Flachi, Antonino

  学事振興資金研究成果実績報告書 （慶應義塾大学）  2022年

• Quantum vacuum effects, symmetry breaking and gravity

  Flachi, Antonino

  科学研究費補助金研究成果報告書 2021年

• Quantum field theory and statistical mechanics of bubble nucleation on surfaces

  Flachi, Antonino

  学事振興資金研究成果実績報告書 （慶應義塾大学）  2021年

• Quantum field theory in stationary backgrounds

  Flachi, Antonino

  学事振興資金研究成果実績報告書 （慶應義塾大学）  2020年

• Forces of the quantum vacuum and Casimir physics

  Flachi, Antonino

  学事振興資金研究成果実績報告書 （慶應義塾大学）  2018年

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• Phase nucleation in curved space

  2021年04月

  -

  2025年03月

  文部科学省・日本学術振興会, 科学研究費助成事業, フラキ アントニノ, 基盤研究(C), 補助金,  研究代表者

• Quantum vacuum effects, symmetry breaking and gravity

  2018年04月

  -

  2021年03月

  文部科学省・日本学術振興会, 科学研究費助成事業, フラキ，　アントニノ, 基盤研究(C), 補助金,  研究代表者

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• 科学と環境Ⅱ

  2025年度

• 科学と環境Ⅰ

  2025年度

• 料理と科学Ⅱ

  2025年度

• 料理と科学Ⅰ

  2025年度

• 自然科学概論

  2025年度

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