Spontaneous Symmetry Breakdown Research Articles

Griffiths-Type Theorems for Short-Range Spin Glass Models

We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap R1,2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^{1,2}$$\\end{document} implies the non-differentiability of the two-replica free energy with respect to the replica coupling parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}. In Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}_2$$\\end{document} invariant models such as the standard Edwards–Anderson model, the non-differentiability is equivalent to the spin glass order characterized by a nonzero Edwards–Anderson order parameter. This generalization of Griffiths’ theorem is proved for any short-range spin glass models with classical bounded spins. We also prove that the non-differentiability of the two-replica free energy mentioned above implies replica symmetry breaking in the literal sense, i.e., a spontaneous breakdown of the permutation symmetry in the model with three replicas. This is a general result that applies to a large class of random spin models, including long-range models such as the Sherrington-Kirkpatrick model and the random energy model. There is a 25-minute video that explains the main results of the present work:https://youtu.be/BF3hJiY1xvI

The Horizons in Circular Accelerated Motions and Its Consequences

In this work, we study the existence of horizons in circular accelerated motions and its consequences. One particular case is the existence of two horizons in any uniform circular motion. The radiation of the Poincaré invariant vacuum is related to the spontaneous breakdown of the conformal symmetry in Quantum Field Theory The main consequence of the existence of these horizons is the Unruh radiation coming from such horizons. This consequence allows us to study the possible experimental detection of the Unruh radiation in such motions. The radiation of the Poincaré invariant vacuum is related to the spontaneous breakdown of the conformal symmetry in Quantum Field Theory. This radiation is associated with an effective temperature that can be detected using an Unruh–DeWitt detector. In fact, this effective temperature at the relativistic limit depends linearly with respect to the proper acceleration. However, in general, this dependence is not linear, contrary of what happens in the classical Unruh effect. In the relativistic limit and high density case, the uniform circular motion becomes a rotating black hole. This allows for future studies of pre-black hole configurations.

Non-existence of spontaneous symmetry breakdown of time-translation symmetry on general quantum systems: Any macroscopic order parameter moves not!

The Kubo–Martin–Schwinger (KMS) condition is a well-founded general definition of equilibrium states on quantum systems. The time invariance property of equilibrium states is one of its basic consequences. From the time invariance of any equilibrium state it follows that the spontaneous breakdown of time-translation symmetry is impossible. Moreover, triviality of the temporal long-range order is derived from the KMS condition. Therefore, the manifestation of genuine quantum time crystals is impossible as long as the standard notion of spontaneous symmetry breakdown is considered.

Localised surface plasmon resonance inducing cooperative Jahn–Teller effect for crystal phase-change in a nanocrystal

The Jahn–Teller effect, a phase transition phenomenon involving the spontaneous breakdown of symmetry in molecules and crystals, causes important physical and chemical changes that affect various fields of science. In this study, we discovered that localised surface plasmon resonance (LSPR) induced the cooperative Jahn–Teller effect in covellite CuS nanocrystals (NCs), causing metastable displacive ion movements. Electron diffraction measurements under photo illumination, ultrafast time-resolved electron diffraction analyses, and theoretical calculations of semiconductive plasmonic CuS NCs showed that metastable displacive ion movements due to the LSPR-induced cooperative Jahn–Teller effect delayed the relaxation of LSPR in the microsecond region. Furthermore, the displacive ion movements caused photo-switching of the conductivity in CuS NC films at room temperature (22 °C), such as in transparent variable resistance infrared sensors. This study pushes the limits of plasmonics from tentative control of collective oscillation to metastable crystal structure manipulation.

Aspects of spontaneous symmetry breaking in Rindler and anti–de Sitter spacetimes for the O(N) linear sigma model

We investigate aspects of spontaneous breakdown of symmetry for $O(N)$ symmetric linear sigma model in the background of Rindler and Anti-de Sitter spacetimes respectively. In the large $N$ limit, by computing the one-loop effective action, we report that in three dimensional Rindler space, there is a phase transition from the disordered phase to an ordered phase past a certain critical Rindler acceleration parameter `$a$'. Connections with finite temperature field theory results are established, thereby further reinforcing the idea that Rindler space can indeed be a proxy for Minkowski spacetime with finite temperature. We extend our calculations to Anti-de Sitter space in various dimensions and observe that symmetry is broken in three dimensions, but not in four dimensions. We discuss the implications of our results.

Extension of the Goldstone and the Englert-Brout-Higgs mechanisms to non-Hermitian theories

We discuss the extension of the Goldstone and Englert-Brout-Higgs mechanisms to non-Hermitian Hamiltonians that possess an antilinear PT symmetry. We study a model due to Alexandre, Ellis, Millington and Seynaeve and show that for the spontaneous breakdown of a continuous global symmetry we obtain a massless Goldstone boson in all three of the antilinear symmetry realizations: eigenvalues real, eigenvalues in complex conjugate pairs, and eigenvalues real but eigenvectors incomplete. In this last case we show that it is possible for the Goldstone boson mode to be a zero-norm state. For the breakdown of a continuous local symmetry the gauge boson acquires a non-zero mass by the Englert-Brout-Higgs mechanism in all realizations of the antilinear symmetry, except the one where the Goldstone boson itself has zero norm, in which case, and despite the fact that the continuous local symmetry has been spontaneously broken, the gauge boson remains massless.

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing Nature. The origin of scales, such as the Higgs vacuum expectation value (vev), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales like the QCD confinement radius are generated by the dilaton vev. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.

Weak Universality Induced by Q=±2e Charges at the Deconfinement Transition of a (2+1)-Dimensional U(1) Lattice Gauge Theory.

Matter-free lattice gauge theories (LGTs) provide an ideal setting to understand confinement to deconfinement transitions at finite temperatures, which is typically due to the spontaneous breakdown (at large temperatures) of the center symmetry associated with the gauge group. Close to the transition, the relevant degrees of freedom (Polyakov loop) transform under these center symmetries, and the effective theory depends on only the Polyakov loop and its fluctuations. As shown first by Svetitsky and Yaffe, and subsequently verified numerically, for the U(1) LGT in (2+1) dimensions, the transition is in the 2D XY universality class, while for the Z_{2} LGT, it is in the 2D Ising universality class. We extend this classic scenario by adding higher charged matter fields and show that the critical exponents γ and ν can change continuously as a coupling is varied, while their ratio is fixed to the 2D Ising value. While such weak universality is well known for spin models, we demonstrate this for LGTs for the first time. Using an efficient cluster algorithm, we show that the finite temperature phase transition of the U(1) quantum link LGT in the spin S=1/2 representation is in the 2D XY universality class, as expected. On the addition of Q=±2e charges distributed thermally, we demonstrate the occurrence of weak universality.

Prediction of time-reversal-symmetry breaking fermionic quadrupling condensate in twisted bilayer graphene

Recent mean-field calculations suggest that the superconducting state of twisted bilayer graphene exhibits either a nematic order or a spontaneous breakdown of the time-reversal symmetry. The two-dimensional character of the material and the large critical temperature relative to the Fermi energy dictate that the material should have significant fluctuations. We study the effects of these fluctuations using Monte Carlo simulations. We show that in a model proposed earlier for twisted bilayer graphene there is a fluctuation-induced phase with quadrupling fermionic order for all considered parameters. This four-electron condensate, instead of superconductivity, shows a spontaneous breaking of time-reversal symmetry. Our results suggest that twisted bilayer graphene is an especially promising platform to study different types of condensates, beyond the pair-condensate paradigm.

BRST formalism of Weyl conformal gravity

We present the BRST formalism of a Weyl conformal gravity in Weyl geometry. Choosing the extended de Donder gauge-fixing condition (or harmonic gauge condition) for the general coordinate invariance and the new scalar gauge-fixing for the Weyl invariance we find that there is a Poincar${\rm{\acute{e}}}$-like $\IOSp(10|10)$ supersymmetry as in a Weyl invariant scalar-tensor gravity in Riemann geometry. We also point out that there is a gravitational conformal symmetry in quantum gravity although there is a massive Weyl gauge field as a result of spontaneous symmetry breakdown of Weyl gauge symmetry and account for how the gravitational conformal symmetry is spontaneously broken to the Poincar\'e symmetry. The corresponding massless Nambu-Goldstone bosons are the graviton and the dilaton. We also prove the unitarity of the physical S-matrix on the basis of the BRST quartet mechanism.

Emergent time crystals from phase-space noncommutative quantum mechanics

It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our point is that such effects do emerge from position (qˆi) and/or momentum (pˆi) noncommutativity, i.e., from [qˆi,qˆj]≠0 and/or [pˆi,pˆj]≠0 (for i≠j). In such a context, a predictive analysis is carried out for the 2-dim noncommutative quantum harmonic oscillator through a procedure supported by the Weyl-Wigner-Groenewold-Moyal framework. This allows for the understanding of how the phase-space noncommutativity drives the amplitude of periodic oscillations identified as time crystals. A natural extension of our analysis also shows how the spontaneous formation of time quasi-crystals can arise.

Three-dimensional imaging of ferroaxial domains using circularly polarized second harmonic generation microscopy

The spontaneous symmetry breakdown of matter is one of the most important concepts in materials physics and leads to a phase transition into an ordered phase and domain formation in its consequence. The so-called ‘ferroaxial order’ characterized by a rotational structural distortion with an axial vector symmetry has gained growing interest as a new class of ordered state. However, the observation of ferroaxial domain states, that is, clockwise and counterclockwise rotational states, is not straightforward and has been little investigated. Here, we propose that the circular intensity difference in second harmonic generation (CID-SHG) offers an experimental technique to investigate ferroaxial order and its domain states through the transition process of higher-order multipoles such as magnetic-dipole and electric-quadrupole. By using CID-SHG microscopy, we successfully visualize three-dimensional images of ferroaxial domain structures in NiTiO3. Our results indicate that CID-SHG is a sensitive probe of ferroaxial order and opens possibilities for the use of ferroaxial materials in nonlinear optical manipulations.

Semiclassics with ’t Hooft flux background for QCD with 2-index quarks

We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small ℝ2× T2 with a suitable magnetic flux. We first discuss the ’t Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The T2 compactification with the magnetic flux preserves the ’t Hooft anomaly, and the 2d effective theory is constrained by the same anomaly of 4d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the ’t Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large-N orientifold equivalence between QCD(Sym/ASym) and mathcal{N} = 1 supersymmetric SU(N) Yang-Mills theory.

Scale invariance and dilaton mass

We consider a generic scale invariant scalar quantum field theory and its symmetry breakdown. Based on the dimension counting identity, we give a concise proof that dilaton is exactly massless at the classical level if scale invariance is broken spontaneously. On the other hand, on the basis of the generalized dimension counting identity, we prove that the dilaton becomes massive at the quantum level if scale invariance is explicitly broken by quantum anomaly. It is pointed out that a subtlety occurs when scale invariance is spontaneously broken through a scale invariant regularization method where the renormalization scale is replaced with the dilaton field. In this case, the dilaton remains massless even at the quantum level after spontaneous symmetry breakdown of scale symmetry, but when the massless dilaton couples non-minimally to the Einstein-Hilbert term and is applied for cosmology, it is phenomenologically ruled out by solar system tests unless its coupling to matters is much suppressed compared to the gravitational interaction.

Fractals, metamorphoses and symmetries in quantum field theory

The mechanism of spontaneous breakdown of symmetry in quantum field theory is reviewed, the Goldstone theorem derived and the formation of ordered patterns is discussed. Metamorphoses and fractal self-similarity are described in terms of the dynamical rearrangement of symmetry in spontaneously broken symmetry theories. The isomorphism between fractal self-similarity and deformed coherent states is exhibited. It is also discussed how the missing of infrared terms in physical observations is responsible of the metamorphosis processes. The dynamical generation of squeezed, entangled coherent states plays a crucial role in the formation of ordered patterns (morphogenesis). The discussion on metamorphoses and other results extend to condensed matter physics, elementary particles, biological systems and brain studies.

4 × 4-matrix transformation for systems with spontaneous symmetry breakdown and self-consistent renormalization in nonequilibrium Thermo Field Dynamics

This study aims to construct a theoretical formulation of a nonequilibrium process for a system of Bose–Einstein condensate associated with a spontaneous symmetry breakdown. For this, Thermo Field Dynamics is used. We then describe the most general forms of a 4 × 4-matrix transformation and an unperturbed Hamiltonian. After calculating the 4 × 4-matrix self-energy and identifying its on-shell, we impose the renormalization condition in which the entire on-shell self-energy should vanish. This condition provides a sufficient number of independent equations to determine all of the parameters in an unperturbed Hamiltonian, among which the quantum transport equations for normal and anomalous number distributions are included.

Strong first-order phase transition and B-violation in the compact 341 model

Baryogenesis in the context of the compact [Formula: see text] model is investigated. Using the finite temperature effective potential approach together with unitarity, stability and no ghost masses constraints, the existence of a strong first-order electroweak phase transition (EWPT) was shown and checked numerically during all steps of the spontaneous breakdown of the gauge symmetry of the model. Higgs masses regions fulfilling the EWPT criteria are also discussed. Moreover, and as a byproduct of our study, the [Formula: see text]-violation via sphaleron was also emphasized.

Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

Insights on the peak in the speed of sound of ultradense matter

In this work we investigate the minimal physical requirements needed for generating a speed of sound that surpasses its asymptotic conformal limit. It is shown that a peak in the speed of sound of homogeneous matter naturally emerges in the transition from a phase with broken chiral symmetry to one with a gapped Fermi surface. We argue that this could be relevant for understanding the peak in the speed of sound displayed by some of the current models for cold ultradense matter. A minimal model implementation of this mechanism is presented, based on the spontaneous breakdown of an approximate particle-antiparticle symmetry, and its thermodynamic properties are determined.

Quantum criticality of the Ohmic spin-boson model in a high dense spectrum: Symmetries, quantum fluctuations and correlations

Study of dissipative quantum phase transitions in the Ohmic spin-boson model is numerically challenging in a dense limit of environmental modes. In this work, large-scale numerical simulations are carried out based on the variational principle. The validity of variational calculations, spontaneous breakdown of symmetries, and quantum fluctuations and correlations in the Ohmic bath are carefully analyzed, and the critical coupling as well as exponents are accurately determined in the weak tunneling and continuum limits. In addition, quantum criticality of the Ohmic bath is uncovered both in the delocalized phase and at the transition point.