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The mass–action equivalence emerges naturally as the consequence of Relativistic Heisenberg Uncertainty (RHU). It changes the structure of relativistic energy–momentum equation that has been underpinning the chosen Lagrangian of the Standard Model, i.e., the Lagrangian which the Higgs mechanism works. The transition from the mass–energy to the mass–action equivalence zone occurs at a certain value of the particle’s wave group velocity $$v_{{\text{g}}}$$ indicating the crossing curve between relativistic energy and action. Due to this transition, particles in the Standard Model are not going to gain inertial mass coming from the Higgs mechanism and related Higgs field, but from another mechanism which can break the Lagrangian symmetry of the Standard Model. This mechanism corresponds to Explicit Symmetry Breaking by generating the new type of field, i.e., the X-Higgs-like field and works based on the mass–action equivalence. This field provides the mass for the X Matter as well as Higgs field for Ordinary Matter. The gaining mass of particles due to this mechanism is not related to the form of ordinary relativistic energy, but to the form of relativistic action. It leads us to the new dynamical equation instead of the ordinary Klein–Gordon and Dirac equation. There are two phenomena due to the increasing and decreasing of particle’s velocity in this mechanism. From the lower to the higher velocity, particle gains additional inertial mass from the X Matter, while conversely particle loses its inertial mass. It is reasonable for us to view that the missing inertial mass of particles in the Standard Model is compensated as the Dark Matter. The X-Higgs-like field breaking to be the Dark-Higgs-like and recognized Higgs field can be considered to explain the origin of the Dark and Ordinary Matter from the X Matter.

We study the case of a pseudo-scalar dark matter candidate which emerges from a complex scalar singlet, charged under a global U(1) symmetry, which is broken both explicitly and spontaneously. The pseudo-scalar is naturally stabilized by the presence of a remnant discrete symmetry: dark CP. We study and compare the phenomenology of several simplified models with only one explicit symmetry breaking term. We find that several regions of the parameter space are able to reproduce the observed dark matter abundance while respecting direct detection and invisible Higgs decay limits: in the resonances of the two scalars, featuring the known as forbidden or secluded dark matter, and through non-resonant Higgs-mediated annihilations. In some cases, combining different measurements would allow one to distinguish the breaking pattern of the symmetry. Moreover, this setup admits a light DM candidate at the sub-GeV scale. We also discuss the situation where more than one symmetry breaking term is present. In that case, the dark CP symmetry may be spontaneously broken, thus spoiling the stability of the dark matter candidate. Requiring that this does not happen imposes a constraint on the allowed parameter space. Finally, we consider an effective field theory approach valid in the pseudo-Nambu-Goldstone boson limit and when the U(1) breaking scale is much larger than the electroweak scale., 33 pages, 13 figures, 5 tables, extended discussion on light dark matter, added references, conclusions unchanged; matches published version in JHEP

Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed in a way that the perturbation preserves only some symmetries of the original system. We give a geometric approach to study this phenomenon in the setting of equivariant Hamiltonian systems. A lower bound for the number of orbits of equilibria and orbits of relative equilibria which persist after a small perturbation is given. This bound is given in terms of the equivariant Lyusternik-Schnirelmann category of the group orbit., 25 pages, 4 figures

Medium modification of the quark and gluon condensates in the strongly magnetized symmetric nuclear medium has been calculated using chiral SU(3) model. The explicit symmetry breaking term and the broken scale invariance part of Lagrangian density of the model are exploited to express the quark and gluon condensates in terms of \(\sigma \), \(\zeta \), \(\delta \), and \(\chi \) fields. The density and temperature dependence of these scalar fields, for different magnetic field strength, are evaluated first and subsequently used as input in the expressions of quark and gluon condensates. Our present study on medium modification of quark and gluon condensates can be used further as input in different QCD sum rules. Consequently, this may help to understand the experimental observables arising from various heavy-ion collision experiments whose one of the aim is to explore the in-medium properties of hadrons.

Most of the wisdom on spontaneous symmetry breaking (SSB), especially for elementary particle theory, relies on approximations and/or a perturbative expansion. Since the mechanism of SSB is underlying most of the new developments in theoretical physics, it is worthwhile to try to understand it from a general (non-perturbative) point of view. Most of the popular explanations given in the literature are not satisfactory (if not misleading), since they do not make it clear that the crucial ingredient for the non-symmetrical behaviour of a system described by a symmetric Hamiltonian is the occurrence of infinite degrees of freedom and of inequivalent representations of the algebra of observables. We shall start by recalling a few basic facts.

We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive function of a neural network, designed for phase classification, as a conjugate variable coupled to an external field within the Hamiltonian of a system. Results in the two-dimensional Ising model evidence that the field can induce an order-disorder phase transition by breaking or restoring the symmetry, in contrast with the field of the conventional order parameter which causes explicit symmetry breaking. The critical behavior is then studied by proposing a Hamiltonian-agnostic reweighting approach and forming a renormalization group mapping on quantities derived from the neural network. Accurate estimates of the critical point and of the critical exponents related to the operators that govern the divergence of the correlation length are provided. We conclude by discussing how the method provides an essential step toward bridging machine learning and physics.

This work considers entropy generation and relaxation in quantum quenches in the Ising and $3$-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving R\'enyi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum., Comment: Version 2: minor changes, abstract updated, `Submission to SciPost'; 28 pages, pdflatex, pdf figures. Version 3: clarifications and references added, typos corrected

It has been well established that for symmetry protected topological systems, the non-trivial topology prevents a real space representation using exponentially localized Wannier wavefunctions (WFs) in all directions, unless the protecting symmetry is sacrificed as an on-site transformation. This makes it challenging to determine the symmetry of various physical observables represented using such WFs. In this work, we propose a practical method for overcoming such challenges using the Kane-Mele model as a concrete example. We present a systematic procedure for diagnosing the symmetry of any observables, as well as a method for constructing symmetric operators up to arbitrary truncation accuracy., Comment: 6 pages + 5 figures

We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses ${\mathcal N}=1$ superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-loop computation using a supersymmetric Pauli-Villars regulator. The conformal current multiplet does not exist in the regulated theory because the regulator breaks conformal invariance, R-symmetry and S-supersymmetry explicitly. The minimal massive multiplet is the Ferrara-Zumino (FZ) one and the supersymmetry preserved by the regulator is a specific field dependent combination of Q- and S- supersymmetry of the conformal multiplet. While this supersymmetry is non anomalous, conformal invariance, R-symmetry and the original Q- and S-supersymmetries are explicitly broken by finite contact terms, both in the regulated and renormalized theories. A conformal current multiplet does exist for the renormalized theory and may be obtained from the FZ multiplet by a set of finite local counterterms that eliminate the explicit symmetry breaking, thus restoring superconformal invariance up to anomalies. However, this necessarily renders both Q- and S-supersymmetries anomalous, as is manifest starting at 4-point functions of conformal multiplet currents. The paper contains a detailed discussion of a number of issues and subtleties related to Ward identities that may be useful in a wider context., Comment: 37 pages + 45 pages appendices v2: minor improvements and amendments; v3: minor additions, version to appear in JHEP

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group $G$ are governed by the well-known Wigner-Eckart relations. In the case of infinitely-extended systems, with $G$ spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases., Comment: 12 pages, accepted for publication in Symmetry (MDPI), special issue "Symmetry and Symmetry Breaking: Phase Transitions and Critical Phenomena"

We investigate the properties of a three-dimensional (3D) dipolar Bose–Einstein condensate (BEC) in a double-well potential (DWP). Symmetry breaking and tunneling dynamics phenomena are demonstrated for 164Dy atoms in the 3D DWP using an effective two-mode model. The results show that the symmetry properties of the dynamics are affected markedly by the long-range nature and anisotropy of the dipolar interaction and the isotropic contact interaction.

In this paper we introduce a sort of Lane-Emden system derived from the Klein-Gordon-Fock equation with central symmetry. Point symmetries are obtained and, since the system can be derived as the Euler-Lagrange equation of a certain functional, a Noether symmetry classification is also considered and conservation laws are derived from the point symmetries.

Within the framework of lowest-order constrained variational (LOCV) method using AV18 two-body interaction supplemented by UIX three-body force, equation of state of asymmetric nuclear matter at both zero and finite temperature is studied. Density dependence of the nuclear symmetry energy as well as its partial wave decomposition is also investigated. It is shown that all saturation properties of the cold symmetric nuclear matter, including the symmetry energy and its slope, can be correctly reproduced if the three-body force is used in the LOCV formalism. Furthermore, density and temperature dependence of the symmetry energy and symmetry free energy in hot neutron rich matter is studied. An opposite temperature dependence for the symmetry energy and symmetry free energy is found.

To further improve the efficiency of the Variational Nodal Method (VNM) for solving the neutron transport equation in hexagonal-z geometry, the nodal response matrix is further block-diagonalized by utilizing the symmetry group theory to decompose the surface basis functions into irreducible components. The block-diagonal property of the nodal response matrix is determined by the symmetry properties of the hexagonal node in geometry, material and basis functions, including both reflection and rotation symmetries. To fully utilize those properties, the symmetry group theory is employed to analyze the symmetry property of the nodal response matrices. It is mathematically proved that the nodal response matrix can be further block-diagonalized into 16 diagonal blocks instead of the current 4 ones by using the symmetry group theory. Numerical comparisons demonstrate that the new approach can reduce the memory storage and computing time by a factor of 2∼3 for P7 angular approximation, compared with the currently employed variables transformation algorithm.

A complete symmetry group classification of a coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is carried out. This system is a natural two-components generalization of the Klein–Gordon–Fock system with central symmetry. Moreover, conservation laws for the system are obtained. Some interesting physical conclusions related to the derived conserved vectors are discussed.

Under investigation in this work is a generalized bidirectional sixth-order Sawada–Kotera equation, which is very important in both nonlinear theory and physical application. The Lie symmetry analysis method is implemented to study the vector fields and optimal systems of the equation. Then its symmetry reductions and group invariant solutions are given by using the resulting optimal system, respectively. Furthermore, the explicit power series solutions of the equation are derived with their convergence analysis. Finally, by using the Bell’s polynomials, a straightforward way is presented to construct its bilinear form, solitary wave solution and periodic wave solution with detailed derivation.

This work aims to discuss the static analysis and reanalysis of near-regular (quasi-symmetric) structures and to develop further the analysis of these structures based on the principle of general connect (coupling) and the group representation theory with symmetry groups C 3v and C 1v . During the analysis, only one-dimensional irreducible representations of different symmetry groups are taken into account, and we investigate the effect of these to the static analysis and to local modification method, as well. For these structures any general load can be decomposed into cyclic and asymmetric load, furthermore at most four symmetry components SSS , AAA (C 3v ) and S , A (C 1v ) ( S – symmetric component, A – antimetric component) are used in this paper. The mentioned methods were applied for static analysis with two perpendicular symmetry planes; this paper examines the effect of three symmetry planes and considers the applicability in case of more-than-three symmetry planes for analysis.

Fermi-Lowdin orbital self-interaction corrected density functional theory (FLO-SIC DFT) is applied to C3H5, NO3-, O3 and CH3. In general our results indicate that FLO-SIC does favour symmetric setups for molecules with non-trivial chemical bonding. Further we discuss two types of possible symmetry breaking. In case of O3 a ground state density that breaks symmetry can be found for the symmetric molecular geometry that may be caused by insufficient treatment of correlation energy. The CH3 radical presents a second type of symmetry breaking were the lowest energy geometry becomes distorted. The latter highlights the importance of further development of approximate DFT functionals as well as further extensions of the FLO-SIC method to overcome such non-physical artifacts.

A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symmetry breaking has been predicted in nonlinear wave propagation, including Bose-Einstein condensates and optics, but it has never been observed. Here, we report the experimental evidence of replica symmetry breaking in optical wave propagation, a phenomenon that emerges from the interplay of disorder and nonlinearity. When mode interaction dominates light dynamics in a disordered optical waveguide, different experimental realizations are found to have an anomalous overlap intensity distribution that signals a transition to an optical glassy phase. The findings demonstrate that nonlinear propagation can manifest features typical of spin-glasses and provide a novel platform for testing so-far unexplored fundamental physical theories for complex systems., Replica symmetry breaking describes identical copies of a randomly interacting system exhibiting different dynamics. Here, Pierangeli et al. observe this critical phenomenon in the optical wave propagation inside a disordered nonlinear waveguide.

A numerical asymptotic model for the breaking of two-dimensional plane relativistic electron oscillations under a small deviation from axial symmetry is developed. The asymptotic theory makes use of the construction of time-uniformly applicable solutions to weakly nonlinear equations. A special finite-difference algorithm on staggered grids is used for numerical simulation. The numerical solutions of axially symmetric one-dimensional relativistic problems yield two-sided estimates for the breaking time. Some of the computations were performed on the “Chebyshev” supercomputer (Moscow State University).

The paper proposes a dynamic method, Recursive Symmetry Breaking During Search (ReSBDS), for efficient partial symmetry breaking. We first demonstrate how Partial Symmetry Breaking During Search (ParSBDS) misses important pruning opportunities when given only a subset of symmetries to break. The investigation pinpoints the culprit and in turn suggests rectification. The main idea is to add extra symmetry breaking constraints during search recursively to prune also symmetric nodes of some pruned subtrees. Thus, ReSBDS can break extra symmetry compositions, but is carefully designed to break only the ones that are easy to identify and inexpensive to break. We present theorems to guarantee the soundness and termination of our approach, and compare our method with popular static and dynamic methods. When the variable (value) heuristic is static, ReSBDS is also complete in eliminating all interchangeable variables (values) given only the generator symmetries. We propose further a light version of ReSBDS method (LReSBDS), which has a slightly weaker pruning power of ReSBDS but with a reduced overhead. We give theoretical characterization on the soundness and termination of LReSBDS, and comparisons on pruning strengths against other symmetry breaking methods including ReSBDS. Extensive experimentations confirm the efficiency of ReSBDS and LReSBDS, when compared against state of the art methods.

Polarity formation in a three-dimensional array of molecules is described as a symmetry breaking effect of a generalized Ising Hamiltonian. Geometrical constraints in conjunction with asymmetric multipole interactions are able to break the spin flip symmetry generating a non-vanishing average local polarization.

We present a general, numerically motivated approach to the construction of symmetry adapted basis functions for solving ro-vibrational Schr\"{o}dinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and hence to reflect the symmetry of the system. The symmetry adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are re-constructed by solving over-determined systems of linear equations related to the transformation properties of the corresponding wavefunctions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to a number of problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems.

We study the temperature of rotating probe D7-branes, dual to the temperature of flavored quarks, in the Kuperstein--Sonnenschein holographic model including the effects of spontaneous breakdown of the conformal and chiral flavor symmetry. The model embeds probe D7-branes into the Klebanov-Witten gravity dual of conformal gauge theory, with the embedding parameter, given by the minimal radial extension of the probe, setting the IR scale of conformal and chiral flavor symmetry breakdown. We show that when the minimal extension is positive definite and additional spin is turned on, the induced world volume metrics on the probe admit thermal horizons and Hawking temperatures despite the absence of black holes in the bulk. We find the scale and behavior of the temperature in flavored quarks are determined notably by the IR scale of symmetry breaking, and by the strength and sort of external fields. We also derive the energy--stress tensor of the rotating probe and study its backreaction and energy dissipation. We show that at the IR scale the backreaction is non-negligible and find the energy can flow from the probe to the bulk, dual to the energy dissipation from the flavor sector into the gauge theory., Comment: 38 pages, Latex

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here we study a specific class of such phase transitions in 1+1 dimensions -- the phase transition between bosonic topological phases protected by $Z_n\times Z_n$. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transition and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D., Comment: 41 pages, 12 figures

We compute the isospin susceptibility in an effective O($n$) scalar field theory (in $d=4$ dimensions), to third order in chiral perturbation theory ($\chi$PT) in the delta--regime using the quantum mechanical rotator picture. This is done in the presence of an additional coupling, involving a parameter $\eta$, describing the effect of a small explicit symmetry breaking term (quark mass). For the chiral limit $\eta=0$ we demonstrate consistency with our previous $\chi$PT computations of the finite-volume mass gap and isospin susceptibility. For the massive case by computing the leading mass effect in the susceptibility using $\chi$PT with dimensional regularization, we determine the $\chi$PT expansion for $\eta$ to third order. The behavior of the shape coefficients for long tube geometry obtained here might be of broader interest. The susceptibility calculated from the rotator approximation differs from the $\chi$PT result in terms vanishing like $1/\ell$ for $\ell=L_t/L_s\to\infty$. We show that this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant., Comment: 34 pages

Recent numerical results of current-driven instabilities at low magnetic Prandtl number and high Hartmann number support the possibility of a saturation state characterized by helicity oscillations. We investigate the underlying mechanism by analyzing this possibility using an higher-order Landau-Ginzburg effective Lagrangian for the weakly non-linear amplitude dynamics, where the magnetic and velocity perturbations are linearly dependent. We find that, if the mirror symmetry between left- and right-handed modes is spontaneously broken, it is impossible to achieve an oscillating helical state. We argue that the result is likely to hold also adding higher-order terms and in the presence of an explicit symmetry breaking. We conclude that an oscillating saturating state for the Tayler instability is unlikely to depend on the interaction of chiral modes.

Symmetry, which defines invariant properties under a group of transformations, provides a frame of generalization uncovering regularities from given quantitative descriptions. Based on the Curie’s symmetry principle, connecting between causality and symmetry, we formulate the intuitive but formal selection rules and apply to determine the excitable resonant modes of a photonic crystal defect cavity, which is an important element for plasmonic applications. Quantitative agreement with the numerical simulations demonstrates the effectiveness of the fundamental principle in finding the critical symmetry conditions for the available localized defect states within photonic crystals. Moreover, the principle facilitates analysis of the higher-order or even forbidden modes in the asymmetric excitation configurations regarding the polarizations or positions of the light source, which typically require heavy computations. Our results may be extended similarly to develop the qualitative selection rules in other physical systems with a geometric symmetry.

In this paper, a symmetry analysis of the modified 2D Burgers vortex equation with a flow parameter is presented. A general form of classical and non-classical symmetries of the equation is derived. These are fundamental tools for obtaining exact solutions to the equation. In several physical cases of the parameter, the specific classical and non-classical symmetries of the equation are then obtained. In addition to rediscovering the existing solutions given by different methods, some new exact solutions are obtained with the symmetry method, showing that the symmetry method is powerful and more general for solving partial differential equations (PDEs).

Broken fourfold rotational (C4) symmetry is observed in the experimental properties of several classes of unconventional superconductors. It has been proposed that this symmetry breaking is important for superconducting pairing in these materials, but in the high-Tc cuprates this broken symmetry has never been observed on the Fermi surface. Here we report a pronounced anisotropy in the angle dependence of the interlayer magnetoresistance of the underdoped high transition temperature (high-Tc) superconductor YBa2Cu3O6.58, directly revealing broken C4 symmetry on the Fermi surface. Moreover, we demonstrate that this Fermi surface has C2 symmetry of the type produced by a uniaxial or anisotropic density-wave phase. This establishes the central role of C4 symmetry breaking in the Fermi surface reconstruction of YBa2Cu3O6+δ , and suggests a striking degree of universality among unconventional superconductors. Observations of broken rotational symmetry in YBa2Cu3O6.58 suggest that it could be a universal feature in unconventional superconductors. The origin of superconductivity in materials that do not conform to conventional Bardeen–Cooper–Schrieffer theory remains an important puzzle for condensed matter physicists; one that could hold the key to designing materials that have no resistance near room temperature. An international team of researchers led by Brad Ramshaw used angle-dependent magnetoresistance measurements to directly reveal a broken rotational symmetry on the Fermi surface of underdoped crystals of the copper oxide-based unconventional superconductor YBa2Cu3O6.58. As this feature has been found in several other classes of unconventional superconductors, the authors suggest that this may be a universal feature, which could play an important role in the unconventional formation of superconducting pairs.

Based on the truncated Painleve method or the Mobious (conformal) invariant form, the nonlocal symmetry for the (1+1)–dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painleve II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.

The properties of the ground state of the hydrogen atom in a spherical vacuum cavity with general boundary “not going out” conditions (i.e., when the probability current through the boundary vanishes) are studied. It is shown that in contrast to the confinement of an atom by a potential barrier, in this case depending on the parameters of the cavity, the atom could be in stable equilibrium at the center of the cavity or shift towards its periphery: spontaneous breaking of spherical symmetry occurs. The phase diagram of the shift and the dependence of the shift value and the binding energy of the ground state of the atom on the cavity parameters are presented. At the same time, the deformation properties of the electron wave function (WF) for an asymmetric distortion are so nontrivial that a non-zero shift occurs even when an electron is repulsed from the cavity boundary.

The Landau theory of phase and phase transition, which describes the state of matter by the spontaneous symmetry breaking, and the Fermi liquid theory of interacting Fermi systems are the two corner stones of contemporary condensed matter physics. They act as our starting points to understand the structure, excitations and phase transitions of any condensed matter system. According to such a Landau paradigm, an interacting Fermi system will behave just as non-interacting Fermi gas system at sufficient low energy, if the interaction is not strong enough to induce a symmetry breaking phase transition in the system. In such a case, the perturbation expansion in the interaction strength is assumed to converge and the low energy excitation can be connected to that of a Fermi gas system adiabatically. In strongly correlated electron systems, such as the high temperature superconductors and quantum antiferromagnets, a pertubative picture on the interaction effect usually fails. The correlation effect between the electrons can induce new forms of order that are beyond the Landau symmetry breaking paradigm. Non-Fermi liquid behavior can emerge in the fully symmetric correlated phases. The Mott insulating phase and the quantum spin liquid phase are the most prominent example of such exotic state of matter. After about three decades of intensive studies, people find that the quantum non-locality effect is at the heart of such new forms of order. The quantum non-locality effect manifests itself in the emergence of gauge degree of freedom in the low energy physics of such strongly correlated system. Such emergent gauge filed is not only important for the characterization and classification of the ground state structure, but is also directly responsible for the non-Fermi liquid behavior of the system. The Landau paradigm should be extended to accommodate such new forms of order and the related new form of excitations and new universal class of phase transitions. Such an extension will elevate our understanding of the structure of matter to the level of quantum wave function. Unlike the conventional symmetry breaking order, which is characterized by the correlation functions between local physical observables, the new form of orders, which are commonly called quantum order (with the topological order as one of its typical example), can be better characterized by the entanglement property in the quantum wave function. From a mathematical point of view, the new form of order is closely related to the projective representation theory of the symmetry group, while the conventional symmetry breaking order is well described by the linear representation theory of the symmetry group.

We propose a new method for uniquely quantizing models of massive non-Abelian gauge fields with spontaneously broken symmetry applicable outside the framework of a perturbation theory in the coupling constant.

Made available in DSpace on 2019-10-04T12:38:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-05-20 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) The relative contributions of explicit and dynamical chiral symmetry breaking in QCD models of the quark-gap equation are studied in dependence of frequently employed Ansatze for the dressed interaction and quark-gluon vertex. The explicit symmetry breaking contributions are defined by a constituent-quark sigma term whereas the combined effects of explicit and dynamical symmetry breaking are described by a Euclidean constituent-mass solution. We extend this study of the gap equation to a quark-gluon vertex beyond the Abelian approximation complemented with numerical gluon- and ghost-dressing functions from lattice QCD. We find that the ratio of the sigma term over the Euclidean mass is largely independent of nonperturbative interaction and vertex models for current-quark masses, m(u,d)(mu)

We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be conveniently studied through previously known tools: (i) it maps the nonlocal mirror symmetry to an onsite $\mathbb{Z}_2$ layer-exchange symmetry after folding the SET along the mirror axis, so that we can gauge the symmetry; (ii) it maps all mirror SET information into the boundary properties of the folded system, so that they can be studied by the anyon condensation theory---a general theory for studying gapped boundaries of topological orders; and (iii) it makes the mirror anomalies explicitly exposed in the boundary properties, i.e., strictly 2D SETs and those that can only live on the surface of a 3D system can be easily distinguished through the folding approach. With the folding approach, we derive a set of physical constraints on data that describes mirror SET, namely mirror permutation and mirror symmetry fractionalization on the anyon excitations in the topological order. We conjecture that these constraints may be complete, in the sense that all solutions are realizable in physical systems. Several examples are discussed to justify this. Previously known general results on the classification and anomalies are also reproduced through our approach., Comment: 73 pages, 5 figures; v2: updated to the published version

The Lipkin-Meshkov-Glick (LMG) model was devised to test the validity of different approximate formalisms to treat many-particle systems. The model was constructed to be exactly solvable and yet non-trivial, in order to capture some of the main features of real physical systems. In the present contribution, we explicitly review the fact that different many-body approximations commonly used in different fields in physics clearly fail to describe the exact LMG solution. With similar assumptions as those adopted for the LMG model, we propose a new Hamiltonian based on a general two-body interaction. The new model (Extended LMG) is not only more general than the original LMG model and, therefore, with a potentially larger spectrum of applicability, but also the physics behind its exact solution can be much better captured by common many-body approximations. At the basis of this improvement lies a new term in the Hamiltonian that depends on the number of constituents and polarizes the system; the associated symmetry breaking is discussed, together with some implications for the study of more realistic systems., Accepted for publication in JPhysG (Letter)

In this paper, nonlocal symmetry of the (2+1) dimensional modified generalized long dispersive wave system and its applications are investigated. The nonlocal symmetry related to the eigenfunctions in Lax pairs is derived, and infinitely many nonlocal symmetries are obtained. By introducing three potentials, the prolongation is found to localize the given nonlocal symmetry. Various finite-and infinite-dimensional integrable models are constructed by using the nonlocal symmetry constraint method. Moreover, applying the general Lie symmetry approach to the enlarged system, the finite symmetry transformation and similarity reductions are computed to give novel exact interaction solutions. In particular, the explicit soliton-cnoidal wave solution is obtained for the modified generalized long dispersive wave system, and it can be reduced to the two-dark-soliton solution in one special case.

We investigate the impact of medium modifications of kaons and antikaons on there rapidity distribution and production ratio using A Multi-Phase transport (AMPT) model. The medium modified masses of kaons and antikaons, which are used as input in AMPT model, are calculated using the chiral SU(3) mean field model. Usually in chiral SU(3) models along with the Weinberg Tomozawa term, the contribution of explicit symmetry breaking term and three range terms are considered to evaluate in-medium masses of kaons and antikaons. In the present work, we have considerd Weinberg Tomozawa term and two range terms to study their impact on the above listed experimental observables. The repulsive contribution to the mass of K + meson from the Weinberg term dominates over the attractive contribution from two range terms. For the K − meson Weinberg term as well as two range terms give attractive contribution. Considering all these features from chiral effective model on properties of K + and K − mesons, we explore the rapidity distributions of kaons and antikaons.

Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry ($Z_3$) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry invariant form of the constituent matrices. In the first one we consider explicit cyclic symmetry in the neutrino sector of the Lagrangian which dictates the emerged effective neutrino mass matrix ($m_\nu$) to be symmetry invariant and hence leads to a degeneracy in masses. We then consider explicit breaking of the symmetry through a dimensionless parameter $\epsilon^{\prime}$ to remove the degeneracy. It is seen that the method doesn't support the current neutrino oscillation global fit data even after considering the correction from cyclic symmetry invariant charged lepton mass matrix ($m_l$) unless the breaking parameter is too large. In the second method, we assume the same forms of the neutrino mass matrices, however, symmetry is broken in the charged lepton sector. All the structures of the mass matrices are now dictated by an effective residual symmetry of some larger symmetry group in the Lagrangian. For illustration, we exemplify a toy model based on softly broken $A_4$ symmetry group which leads to one of the combination of $m_l$, $m_D$, $M_{RS}$ and $\mu$ to generate effective $m_\nu$. All the emerged mass matrices predict a constraint range of the CP violating phases and atmospheric mixing angle along with an inverted hierarchical structure of the neutrino masses. Further, significant predictions on $\beta\beta0\nu$ decay parameter $|m_{11}|$ and the sum of the three light neutrino masses ($\Sigma_im_i$) are also obtained., Comment: 14 pages, 19 figures, 6 tables, To appear in NPB