Showing papers on "Explicit symmetry breaking published in 2013"
TL;DR: In this paper, it was shown that the boundary excitations of SPT phases can be described by a nonlocal Lagrangian term that generalizes the Wess-Zumino-Witten term for continuous nonlinear σ models.
Abstract: Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain is the first example of SPT phases which is protected by SO(3) spin rotation symmetry. The topological insulator is another example of SPT phases which are protected by U(1) and time-reversal symmetries. In this paper, we show that interacting bosonic SPT phases can be systematically described by group cohomology theory: Distinct d-dimensional bosonic SPT phases with on-site symmetry G (which may contain antiunitary time-reversal symmetry) can be labeled by the elements in H^(1+d)[G,UT(1)], the Borel (1+d)-group-cohomology classes of G over the G module UT(1). Our theory, which leads to explicit ground-state wave functions and commuting projector Hamiltonians, is based on a new type of topological term that generalizes the topological θ term in continuous nonlinear σ models to lattice nonlinear σ models. The boundary excitations of the nontrivial SPT phases are described by lattice nonlinear σ models with a nonlocal Lagrangian term that generalizes the Wess-Zumino-Witten term for continuous nonlinear σ models. As a result, the symmetry G must be realized as a non-on-site symmetry for the low-energy boundary excitations, and those boundary states must be gapless or degenerate. As an application of our result, we can use H^(1+d)[U(1)⋊ Z^(T)_(2),U_T(1)] to obtain interacting bosonic topological insulators (protected by time reversal Z2T and boson number conservation), which contain one nontrivial phase in one-dimensional (1D) or 2D and three in 3D. We also obtain interacting bosonic topological superconductors (protected by time-reversal symmetry only), in term of H^(1+d)[Z^(T)_(2),U_T(1)], which contain one nontrivial phase in odd spatial dimensions and none for even dimensions. Our result is much more general than the above two examples, since it is for any symmetry group. For example, we can use H1+d[U(1)×Z2T,UT(1)] to construct the SPT phases of integer spin systems with time-reversal and U(1) spin rotation symmetry, which contain three nontrivial SPT phases in 1D, none in 2D, and seven in 3D. Even more generally, we find that the different bosonic symmetry breaking short-range-entangled phases are labeled by the following three mathematical objects: (G_H,G_Ψ,H^(1+d)[G_Ψ,U_T(1)]), where G_H is the symmetry group of the Hamiltonian and G_Ψ the symmetry group of the ground states.
1,001 citations
TL;DR: In this paper, electric fields can break the structural inversion symmetry in bilayer 2D materials, providing a way of tuning the magnetic moment and Berry curvature of bilayer materials.
Abstract: Electric fields can break the structural inversion symmetry in bilayer 2D materials, providing a way of tuning the magnetic moment and Berry curvature. This effect can be probed directly in bilayer MoS2 using optical measurements.
555 citations
TL;DR: In this paper, the Kibble-Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition, and the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential is observed.
Abstract: Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, topological defects can form. The Kibble-Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition. Owing to its ubiquitous nature, this theory finds application in a wide field of systems ranging from cosmology to condensed matter. Here we present the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential, and observe an enhanced power law scaling in accordance with numerical simulations and recent predictions. This simple system with well-defined critical exponents opens up ways to investigate the physics of non-equilibrium dynamics from the classical to the quantum regime.
219 citations
TL;DR: It is demonstrated that a nonlinear global coupling can induce this symmetry breaking, and a novel mechanism for the formation of chimera states is reported, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators.
Abstract: We report a novel mechanism for the formation of chimera states, a peculiar spatiotemporal pattern with coexisting synchronized and incoherent domains found in ensembles of identical oscillators. Considering Stuart-Landau oscillators we demonstrate that a nonlinear global coupling can induce this symmetry breaking. We find chimera states also in a spatially extended system, a modified complex Ginzburg-Landau equation. This theoretical prediction is validated with an oscillatory electrochemical system, the electrooxidation of silicon, where the spontaneous formation of chimeras is observed without any external feedback control.
200 citations
TL;DR: In this paper, the cosmological constraints on axion models where the domain wall number is greater than one were investigated, and the existence of long-lived domain walls led to the overproduction of cold dark matter axions, while the density of gravitational waves is too small to observe at the present time.
Abstract: We investigate the cosmological constraints on axion models where the domain wall number is greater than one. In these models, multiple domain walls attached to strings are formed, and they survive for a long time. Their annihilation occurs due to the effects of explicit symmetry breaking term which might be raised by Planck-scale physics. We perform three-dimensional lattice simulations and compute the spectra of axions and gravitational waves produced by long-lived domain walls. Using the numerical results, we estimated relic density of axions and gravitational waves. We find that the existence of long-lived domain walls leads to the overproduction of cold dark matter axions, while the density of gravitational waves is too small to observe at the present time. Combining the results with other observational constraints, we find that the whole parameter region of models are excluded unless an unacceptable fine-tuning exists.
144 citations
TL;DR: In this paper, a model with a combined breaking of conformal and electroweak symmetry by a strongly coupled hidden sector was proposed, where dark matter candidates were detected in the form of dark pions, whose stability was guaranteed by the flavor symmetry of hidden quark sector.
Abstract: The LHC and other experiments show so far no sign of new physics and long-held beliefs about naturalness should be critically reexamined. We discuss therefore in this paper a model with a combined breaking of conformal and electroweak symmetry by a strongly coupled hidden sector. Even though the conformal symmetry is anomalous, this may still provide an explanation of the smallness of electroweak scale compared to the Planck scale. Specifically we start from a classically conformal model, in which a strongly coupled hidden sector undergoes spontaneous chiral symmetry breaking. A coupling via a real scalar field transmits the breaking scale to the Standard Model Higgs and triggers electroweak symmetry breaking. The model contains dark matter candidates in the form of dark pions, whose stability is being guaranteed by the flavor symmetry of hidden quark sector. We study its relic abundance and direct detection prospects with the Nambu-Jona-Lasinio method and discuss the phase transition in the dark sector as well as in the electroweak sector.
138 citations
TL;DR: It is found that suspended graphene is in the conducting phase with unbroken chiral symmetry, which suggests that fluctuations of chirality and nonperturbative effects might still be quite important.
Abstract: We report on the results of the first-principles numerical study of spontaneous breaking of chiral (sublattice) symmetry in suspended monolayer graphene due to electrostatic interaction, which takes into account the screening of Coulomb potential by electrons on $\ensuremath{\sigma}$ orbitals. In contrast to the results of previous numerical simulations with unscreened potential, we find that suspended graphene is in the conducting phase with unbroken chiral symmetry. This finding is in agreement with recent experimental results by the Manchester group [D. C. Elias et al., Nat. Phys. 7, 701 (2011); A. S. Mayorov et al., Nano Lett. 12, 4629 (2012)]. Further, by artificially increasing the interaction strength, we demonstrate that suspended graphene is quite close to the phase transition associated with spontaneous chiral symmetry breaking, which suggests that fluctuations of chirality and nonperturbative effects might still be quite important.
129 citations
TL;DR: In this article, it was shown that corrections to the form of dilaton interactions arising from conformal symmetry violating effects are suppressed by the square of the ratio of the dilaton mass to the strong coupling scale and are under good theoretical control.
Abstract: We consider scenarios where strong conformal dynamics constitutes the ultraviolet completion of the physics that drives electroweak symmetry breaking. We show that in theories where the operator responsible for the breaking of conformal symmetry is close to marginal at the breaking scale, the dilaton mass can naturally lie below the scale of the strong dynamics. However, in general, this condition is not satisfied in the scenarios of interest for electroweak symmetry breaking, and so the presence of a light dilaton in these theories is associated with mild tuning. We construct the effective theory of the light dilaton in this framework and determine the form of its couplings to Standard Model states. We show that corrections to the form of the dilaton interactions arising from conformal symmetry violating effects are suppressed by the square of the ratio of the dilaton mass to the strong coupling scale and are under good theoretical control. These corrections are generally subleading, except in the case of dilaton couplings to marginal operators, when symmetry violating effects can sometimes dominate. We investigate the phenomenological implications of these results for models of technicolor, and for models of the Higgs as a pseudo-Nambu-Goldstone boson, that involve strong conformal dynamics in the ultraviolet.
129 citations
TL;DR: In this paper, the authors proposed a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM).
Abstract: Symmetries play a crucial role in electroweak symmetry breaking models with non-minimal Higgs content. Within each class of these models, it is desirable to know which symmetry groups can be implemented via the scalar sector. In N-Higgs-doublet models, this classification problem was solved only for N=2 doublets. Very recently, we suggested a method to classify all realizable finite symmetry groups of Higgs-family transformations in the three-Higgs-doublet model (3HDM). Here, we present this classification in all detail together with an introduction to the theory of solvable groups, which play the key role in our derivation. We also consider generalized-CP symmetries, and discuss the interplay between Higgs-family symmetries and CP-conservation. In particular, we prove that presence of the ℤ4 symmetry guarantees the explicit CP-conservation of the potential. This work completes classification of finite reparametrization symmetry groups in 3HDM.
104 citations
TL;DR: A simple model is presented that exhibits a temporal analogue of superconducting crystalline ordering, with a time-dependent order parameter, based on time translation symmetry (τ) invariant dynamics, exploiting weak links (Josephson effects).
Abstract: I present a simple model that exhibits a temporal analogue of superconducting crystalline (Larkin-Ovchinnikov-Ferrell-Fulde) ordering, with a time-dependent order parameter. I sketch designs for minimally dissipative ac circuits, all based on time translation symmetry ($\ensuremath{\tau}$) invariant dynamics, exploiting weak links (Josephson effects). These systems violate $\ensuremath{\tau}$ spontaneously. I also discuss effective theories of that phenomenon, and space-time generalizations.
93 citations
TL;DR: In this paper, a review of symmetry breaking and symmetry transformations in finite quantum systems is presented, with an emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems.
Abstract: The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose-Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.
TL;DR: The axion solution to the strong $CP$ problem calls for an explanation as to why the Lagrangian should be invariant under the global Peccei-Quinn (PQ) symmetry to such a high degree of accuracy.
Abstract: The axion solution to the strong $CP$ problem calls for an explanation as to why the Lagrangian should be invariant under the global Peccei-Quinn (PQ) symmetry, $U(1{)}_{\mathrm{PQ}}$, to such a high degree of accuracy. In this paper, we point out that the $U(1{)}_{\mathrm{PQ}}$ can indeed survive as an accidental symmetry in the low-energy effective theory, if the standard model gauge group is supplemented by a gauged and discrete $R$ symmetry, ${Z}_{N}^{R}$, forbidding all dangerous operators that explicitly break the Peccei-Quinn symmetry. In contrast to similar approaches, the requirement that the ${Z}_{N}^{R}$ symmetry be anomaly-free forces us, in general, to extend the supersymmetric standard model by new matter multiplets. Surprisingly, we find a large landscape of viable scenarios that all individually fulfill the current experimental constraints on the QCD vacuum angle as well as on the axion decay constant. In particular, choosing the number of additional multiplets appropriately, the order $N$ of the ${Z}_{N}^{R}$ symmetry can take any integer value larger than 2. This has interesting consequences with respect to possible solutions of the $\ensuremath{\mu}$ problem, collider searches for vectorlike quarks and axion dark matter.
TL;DR: In this article, the authors considered the minimal extension of the Standard Model with U ( 1 ) B − L gauge symmetry for generating the Higgs potential radiatively and showed that there is a reasonable parameter space that is consistent with a correct electroweak symmetry breaking and the observed Higgs mass.
TL;DR: In this article, a model based on a larger symmetry was proposed to obtain the Higgs mass in the vicinity of 126 GeV, which was shown to be the scalar field necessary to obtain Higgs in the standard model.
Abstract: In the context of the spectral action and the noncommutative geometry approach to the standard model, we build a model based on a larger symmetry. With this "grand symmetry" it is natural to have the scalar field necessary to obtain the Higgs mass in the vicinity of 126 GeV. This larger symmetry mixes gauge and spin degrees of freedom without introducing extra fermions. Requiring the noncommutative space to be an almost commutative geometry (i.e. the product of manifold by a finite dimensional internal space) gives conditions for the breaking of this grand symmetry to the standard model.
TL;DR: In this paper, it was shown that certain relativistic theories at finite density can exhibit an unconventional spectrum of Goldstone excitations, with gapped Goldstones whose gap is exactly calculable in terms of the symmetry algebra.
Abstract: It was recently argued that certain relativistic theories at finite density can exhibit an unconventional spectrum of Goldstone excitations, with gapped Goldstones whose gap is exactly calculable in terms of the symmetry algebra. We confirm this result as well as previous ones concerning gapless Goldstones for non-relativistic systems via a coset construction of the low-energy effective field theory. Moreover, our analysis unveils additional gapped Goldstones, naturally as light as the others, but this time with a model-dependent gap. Their exact number cannot be inferred solely from the symmetry breaking pattern either, but rather depends on the details of the symmetry breaking mechanism--a statement that we explicitly verify with a number of examples. Along the way we provide what we believe to be a particularly transparent interpretation of the so-called inverse-Higgs constraints for spontaneously broken spacetime symmetries.
TL;DR: In this article, the authors construct concrete examples of symmetry-enriched topological phases with global symmetries and demonstrate how the interplay between the global symmetry and the fusion algebra of the anyons of a topologically ordered system determines the existence of gapless edge modes protected by the symmetry and that a quasi-group structure can be defined among these phases.
Abstract: We construct in the $K$ matrix formalism concrete examples of symmetry-enriched topological phases, namely intrinsically topological phases with global symmetries. We focus on the Abelian and nonchiral topological phases and demonstrate by our examples how the interplay between the global symmetry and the fusion algebra of the anyons of a topologically ordered system determines the existence of gapless edge modes protected by the symmetry and that a (quasi)group structure can be defined among these phases. Our examples include phases that display charge fractionalization and more exotic nonlocal anyon exchange under global symmetry that correspond to general group extensions of the global symmetry group.
TL;DR: The modulation instability regime is investigated and the key role of the third-order dispersion on the asymmetry in the spectrum of the dissipative structures is revealed.
Abstract: We study analytically, numerically, and experimentally the nonlinear symmetry breaking induced by broken reflection symmetry in an optical fiber system. In particular, we investigate the modulation instability regime and reveal the key role of the third-order dispersion on the asymmetry in the spectrum of the dissipative structures. Our theory explains early observations, and the predictions are in excellent agreement with our experimental findings.
TL;DR: In this paper, the basic theories of time reversal invariance are provided, and experimental tests of the time reversal symmetry are given, together with a review of the CP symmetry and its relation to time reversal.
Abstract: Time reversal independent of the CP symmetry is reviewed. Experimental tests of time reversal symmetry are given. Basic theories of time reversal invariance are provided.
TL;DR: In this article, the authors explore the possibility that SU(3)_C was not an exact symmetry at all times in the early Universe, using minimal extensions of the standard model that contain a color triplet scalar field and perhaps other fields.
Abstract: We explore the possibility that SU(3)_C was not an exact symmetry at all times in the early Universe, using minimal extensions of the standard model that contain a color triplet scalar field and perhaps other fields We show that, for a range of temperatures, there can exist a phase in which the free energy is minimized when the color triplet scalar has a nonvanishing vacuum expectation value, spontaneously breaking color At very high temperatures and at lower temperatures, color symmetry is restored The breaking of color in this phase is accompanied by the spontaneous breaking of B - L if the color triplet scalar Yukawa couples to quarks and/or leptons We discuss the requirements on the minimal extensions needed for consistency of this scenario with present collider bounds on new colored scalar particles
TL;DR: In this article, the relativistic Landau-He-McKellar-Wilkens quantization and bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects are discussed.
TL;DR: In this paper, the authors investigated the chiral properties of near-zero modes for center vortices in lattice gauge theory and showed that center vortex fluxes contribute to chiral symmetry breaking.
Abstract: We investigate the chiral properties of near-zero modes for thick classical center vortices in $SU(2)$ lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.
TL;DR: In this article, it was shown that the structure of the tree-level vacuum is perturbatively stable against corrections from scalar loops or higher dimensional operators, and the authors gave an explicit illustration in the case of loop corrections by direct computation of the one-loop effective potential of Yukawa fields.
Abstract: The tree level potential for a scalar multiplet of ‘Yukawa fields’ Y for one type of quarks admits the promising vacuum configuration 〈Y〉 ∝ diag(0, 0, 1) that breaks spontaneously SU(3)
L
× SU(3)
R
flavour symmetry. We investigate whether the vanishing entries could be lifted to nonvanishing values by slightly perturbing the potential, thus providing a mechanism to generate the Yukawa hierarchies. For theories where at the lowest order the only massless states are Nambu-Goldstone bosons we find, as a general result, that the structure of the tree-level vacuum is perturbatively stable against corrections from scalar loops or higher dimensional operators. We discuss the reasons for this stability, and give an explicit illustration in the case of loop corrections by direct computation of the one-loop effective potential of Yukawa fields. Nevertheless, a hierarchical configuration 〈Y 〉 ∝ diag(ϵ′, ϵ, 1) (with ϵ′, ϵ ≪ 1) can be generated by enlarging the scalar Yukawa sector. We present a simple model in which spontaneous breaking of the flavour symmetry can give rise to the fermion mass hierarchies.
TL;DR: In this article, the authors investigated spontaneous global symmetry breaking in the absence of Lorentz invariance and studied technical naturalness of Nambu-Goldstone modes for which the dispersion relation exhibits a hierarchy of multicritical phenomena with Lifshitz scaling and dynamical exponents.
Abstract: We investigate spontaneous global symmetry breaking in the absence of Lorentz invariance and study technical naturalness of Nambu-Goldstone modes for which the dispersion relation exhibits a hierarchy of multicritical phenomena with Lifshitz scaling and dynamical exponents $zg1$. For example, we find Nambu-Goldstone modes with a technically natural quadratic dispersion relation which do not break time reversal symmetry and are associated with a single broken symmetry generator, not a pair. The mechanism is protected by an enhanced ``polynomial shift'' symmetry in the free-field limit.
TL;DR: In this article, the second-order terms in isospin asymmetry in both the optical model potential and the symmetry energy decomposition were investigated, and it was shown that the strength of the second order symmetry potential in asymmetric nuclear matter is significant compared to the first order one U sym, 1, especially at high nucleon momentum.
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TL;DR: In this article, the authors present the approach allowing for an arbitrary system without the gravitational anomaly to keep the dilaton massless at all orders in perturbation theory, i.e. to build a theory with conformal symmetry broken spontaneously.
Abstract: The characteristic feature of the spontaneous symmetry breaking is the presence of the Goldstone mode(s). For the conformal symmetry broken spontaneously the corresponding Goldstone boson is the dilaton. Coupling an arbitrary system to the dilaton in a consistent (with quantum corrections) way has certain diculties due to the trace anomaly. In this paper we present the approach allowing for an arbitrary system without the gravitational anomaly to keep the dilaton massless at all orders in perturbation theory, i.e. to build a theory with conformal symmetry broken spontaneously.
TL;DR: In this article, the authors investigated new aspects related to the Abelian gauge-Higgs model with the addition of the Carroll-Field-Jackiw term and showed that new finite and definite Lorentz-breaking terms are induced.
Abstract: We investigate new aspects related to the Abelian gauge-Higgs model with the addition of the Carroll-Field-Jackiw term. We focus on one-loop quantum corrections to the photon and Higgs sectors due to spontaneous breaking of gauge symmetry and show that new finite and definite Lorentz-breaking terms are induced. Specifically in the gauge sector, a $CPT$-even aether term is induced. Besides, aspects of the one-loop renormalization of the background vector-dependent terms are discussed.
TL;DR: While for infinitely large separation (no boundaries), chiral symmetry is broken or restored via a second order phase transition, in the opposite case of small separation the transition becomes first order, rendering effects of finite size, for the present setup, similar to those of a chemical potential.
Abstract: With the intent of exploring how the interplay between boundary effects and chiral symmetry breaking may alter the thermodynamical behavior of a system of strongly interacting fermions, we study the Casimir effect for the setup of two parallel layers using a four-fermion effective field theory at zero density. This system reveals a number of interesting features. While for infinitely large separation (no boundaries), chiral symmetry is broken or restored via a second order phase transition, in the opposite case of small (and, in general, finite) separation the transition becomes first order, rendering effects of finite size, for the present setup, similar to those of a chemical potential. Appropriately moving on the separation-temperature plane, it is possible to generate a peculiar behavior in the temperature dependence of the thermodynamic potential and of the condensate, compensating thermal with geometrical variations. A behavior similar to what we find here has been predicted to occur in bilayer graphene. Chiral symmetry breaking induces different phases (massless and massive) in the Casimir force separated by critical lines.
TL;DR: In this article, parity-time symmetry breaking in non-Hermitian tight-binding lattices with spatially-extended loss-gain regions in the presence of an advective term is investigated.
Abstract: We investigate the onset of parity-time ($\mathcal{PT}$) symmetry breaking in non-Hermitian tight-binding lattices with spatially-extended loss-gain regions in the presence of an advective term. Similarly to the instability properties of hydrodynamic open flows, it is shown that $\mathcal{PT}$ symmetry breaking can be either absolute or convective. In the former case, an initially localized wave packet shows a secular growth with time at any given spatial position, whereas in the latter case the growth is observed in a reference frame moving at some drift velocity while decay occurs at any fixed spatial position. In the convective unstable regime, $\mathcal{PT}$ symmetry is restored when the spatial region of gain or loss in the lattice is limited (rather than extended). We consider specifically a non-Hermitian extension of the Rice-Mele tight-binding lattice model, and show the existence of a transition from absolute to convective symmetry breaking when the advective term is large enough. An extension of the analysis to ac-dc driven lattices is also presented, and an optical implementation of the non-Hermitian Rice-Mele model is suggested, which is based on light transport in an array of evanescently coupled optical waveguides with a periodically bent axis and alternating regions of optical gain and loss.
TL;DR: In this paper, it is shown that without recourse to the Coleman-Weinberg mechanism, the B-L gauge symmetry is broken in the process of spontaneous symmetry breakdown of scale invariance at the tree level.
Abstract: We consider a coupling of dilaton gravity to the classically scale-invariant B-L extended standard model which has been recently proposed as a phenomenologically viable model realizing the Coleman-Weinberg mechanism of breakdown of the electroweak symmetry. It is shown in the present model that without recourse to the Coleman-Weinberg mechanism, the B-L gauge symmetry is broken in the process of spontaneous symmetry breakdown of scale invariance at the tree level and as a result the B-L gauge field becomes massive via the Higgs mechanism. Since the dimensionful parameter is only the Planck mass in our model, one is forced to pick up very small coupling constants if one wishes to realize the breaking of the B-L symmetry at TeV scale.