Original Symmetry Research Articles

Conservation Laws and Stability of Field Theories of Derived Type

We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time gives rise to the series of symmetries of action functional. If the wave operator is given by n-th-order polynomial then this series includes n independent entries, which can be explicitly constructed. The Noether theorem is then used to construct an n-parameter set of second-rank conserved tensors. The canonical energy-momentum tensor is included in the series, while the other entries define independent integrals of motion. The Lagrange anchor concept is applied to connect the general conserved tensor in the series with the original space-time translation symmetry. This result is interpreted as existence of multiple energy-momentum tensors in the class of derived systems. To study stability we seek for bounded-conserved quantities that are connected with the time translations. We observe that the derived theory is stable if its wave operator is defined by a polynomial with simple and real roots. The general constructions are illustrated by the examples of the Pais–Uhlenbeck oscillator, higher-derivative scalar field, and extended Chern–Simons theory.

Fermion Propagator in QED - Landau-Khalatnikov-Fradkin Transformations

Gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD) describe the physical world accurately at the level of fundamental particles. They possess gauge symmetry reflected in terms of several identities and transformation laws which impose tight constraints on all conceivable Green functions which define the theory. In this article, we describe and summarize the role played by the Landau-Khalatnikov-Fradkin (LKF) transformations in this context. Within the set of covariant gauges, these transformations tell us how to construct a Green function in an arbitrary gauge, starting from its explicit expression in a particular gauge. In perturbation theory, these transformations are satisfied at every order of approximation. A non-perturbative description of QED and QCD in the continuum is provided by the Schwinger-Dyson Equations (SDEs). These are the fundamental equations of motion encoding the dynamics of Green functions. These equations provide a unified description of weak and strong coupling regimes and are thus increasingly employed to study strongly interacting theories and their transition to the perturbative limit. As these equations are an infinite set of coupled non-linear equations, a truncation is essential to reduce them to a solvable number. LKF transformations provide a stringent constraint on the acceptable truncations which preserve the original symmetries of the gauge theory involved. Most of these truncations consist in cleverly constructing an Anstaz for the electron-photon vertex in QED and the quark-gluon vertex in QCD. In this article, we review the LKF transformations for the fermion propagator. Very importantly, they imply the gauge invariance of the chiral fermion condensate and the pole mass of a fermion. We provide the first demonstration of the latter in this article. Moreover, we also describe how the LKF transformations of the fermion propagator provide gauge-symmetry constraints on a non-perturbative construction of the three-point fermion-boson vertex.

Nonmagnetic Substitution in Pyrochlore Iridate Y2(Ir1–xTix)2O7: Structure, Magnetism, and Electronic Properties

Tuning of spin-orbit coupling and electron correlation effects in pyrochlore iridates is considered for many interesting phenomena. We have investigated the temperature evolution of structural, magnetic and electronic properties in doped Y$_2$(Ir$_{1-x}$Ti$_{x}$)$_2$O$_7$ ($x$ = 0.0, 0.02, 0.05, 0.10 and 0.15) where the substitution of nonmagnetic Ti$^{4+}$ (3$d^0$) for Ir$^{4+}$ (5$d^5$) amounts to dilution of magnetic network and tuning of these parameters in opposite way. The system retains its original structural symmetry but local structural parameters show an evolution with Ti content. While the magnetic transition temperature is not largely influenced, both magnetic moment and magnetic frustration decreases with Ti doping. Magnetic relaxation measurement shows the parent compound Y$_2$Ir$_2$O$_7$ as well as its Ti doped analogues are in nonequilibrium magnetic state where the magnetic relaxation rate increases with Ti. Temperature dependent Raman measurements indicate no changes in structural symmetry, however, across the magnetic transition temperature an anomaly in A$_{1g}$ Raman mode is observed. Temperature dependent x-ray diffraction data also support the Raman spectroscopy data, however, an evolution of lattice parameters with temperature is observed. The electrical resistivity data of Y$_2$(Ir$_{1-x}$Ti$_{x}$)$_2$O$_7$ series exhibits insulating behavior throughout the temperature range, however, the resistivity decreases with Ti doping. The nature of charge conduction is found to follow power-law behavior in whole series but the validity of this model varies with temperature. A negative magnetoresistance has been observed at low temperature in present series which is explained with weak localized mechanism. Similar to other Ir based oxides, a crossover from negative to positive MR has been observed in present system.

Alloy theory with atomic resolution for Rashba or topological systems

Interest in substitutional disordered alloys has recently reemerged with focus on the symmetry-sensitive properties in the alloy such as topological insulation and Rashba effect. A substitutional random alloy manifests a distribution of local environments, creating a polymorphous network. While the macroscopic average (monomorphous) structure may have the original high symmetry of the constituent compounds, many observable physical properties are sensitive to local symmetry, and are hence $<P(S_i)>$ rather than $P(S_0)$=$P(<S_i>)$. The fundamental difference between polymorphous $<P(S_i)>$ and monomorphous $P(S_0)$ led to the often-diverging results and the missing the atomic-scale resolution needed to discern symmetry-related physics. A natural approach capturing the polymorphous aspect is supercell model, which however suffers the difficulty of band folding ('spaghetti bands'), rendering the E vs k dispersion needed in topology and Rashba physics and seen in experiments, practically inaccessible. A solution that retains the polymorphous nature but restores the E vs k relation is to unfold the supercell bands. This yields alloy Effective Band Structure (EBS), providing a 3D picture of spectral density consisting of E- and k-dependent spectral weight with coherent and incoherent features, all created naturally by the polymorphous distribution of many local environments. We illustrate this EBS approach for CdTe-HgTe, PbSe-SnSe and PbS-PbTe alloys. We found properties that are critical for e.g. topological phase transition and Rashba splitting but totally absent in conventional monomorphous approaches, including (1) co-existing, wavevector- and energy-dependent coherent band splitting and incoherent band broadening, (2) coherent-incoherent transition along different k space directions, and (3) Rashba-like band splitting having both coherent and incoherent features.

Elastic constants of β-Ti15Mo

Elastic constants of single crystals of metastable β-titanium Ti15Mo alloy (in wt. %), grown in an optical floating zone furnace, were measured by resonant ultrasound spectroscopy with the aim to study the dependence of these constants on formation of isothermal ω particles. Samples with different heat treatment (isothermal/anisothermal ageing at different temperatures) were studied. Ultrasonic measurements were complemented by characterization of the samples by transmission electron microscopy. The results proved that isothermal ω particles always exactly follow the original cubic symmetry of the β matrix and that the evolution of the elastic constants of the β-ω multi-phase crystals and the volume fraction of ω phase can be reliably approximated using Hill's homogenizing procedure, assuming cubic elastic constants of the β phase and isotropic elastic constants representing ω particles. It was shown that ultrasonic methods can be used for the study of the evolution of microstructure of metastable β-titanium alloys due to the high contrast in elastic moduli of the β and ω phases.

Interaction behavior between solitons and (2+1)-dimensional CDGKS waves

Starting from the Darboux transformation (DT) related nonlocal symmetry of the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) equation, the original symmetry is localized by introducing four field quantities. On the basis of the local symmetry, some novel group invariant solutions are derived by utilizing the classical symmetry reduction method. The result shows that the essential and unique role of the DT is to add an additional soliton to the fifth order nonlinear wave, which is the basic reduction of the (2+1)-dimensional CDGKS equation. As an illustration, the interactions between solitons and fifth order nonlinear waves expressed by Jacobi elliptic functions and incomplete elliptic integrals of the third kind are exhibited, and some of their dynamical properties are analyzed.

An integrable Lorentz-breaking deformation of two-dimensional CFTs

It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator T \bar TTT‾, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that possess a conserved U(1)U(1) current, JJ. The deformation takes the schematic form J \bar TJT‾ and is interesting because it preserves an SL(2,\mathbb{R}) \times U(1)SL(2,ℝ)×U(1) subgroup of the original global conformal symmetries. For the case of a purely (anti)chiral current, we find the finite-size spectrum of the deformed theory and study its thermodynamic properties. We test our predictions in a simple example involving deformed free fermions.

Typology of M. G. Aranovsky musical thinking and symmetry

Typology of M. G. Aranovsky musical thinking and symmetry

Unified origin of axion and monopole dark matter, and solution to the domain-wall problem

We propose a scenario where the spontaneous breakdown of the Peccei-Quinn symmetry leads to monopole production. Both the axion and the monopole contribute to dark matter, and the Witten effect on the axion mass is a built-in feature. In the KSVZ-type axion model, seemingly different vacua are actually connected by the hidden gauge symmetry, which makes the axionic string unstable and separate into two Alice strings. The Alice string is attached to a single domain wall due to the QCD instanton effect, solving the domain-wall problem. This is in the same spirit of the Lazarides-Shafi mechanism, although the discrete Peccei-Quinn symmetry is not embedded into the center of the original gauge symmetry. In the DFSZ-type axion model, the domain-wall problem is avoided by the Witten effect. If the Peccei-Quinn symmetry is explicitly broken by a small amount, monopoles acquire a tiny electric charge and become mini-charged dark matter. Interestingly, the quality of the Peccei-Quinn symmetry is closely tied to darkness of dark matter.

Magnetic states in a three-dimensional topological Kondo insulator

We theoretically study the magnetic phase diagram of a three-dimensional topological Kondo insulator by means of real-space dynamical mean field theory. We find that ferromagnetically ordered states become stable upon hole doping. Besides a wide ferromagnetic phase, we observe surface magnetism close to half-filling, which corresponds to an A-type antiferromagnetic state. We further study the impact of the magnetism on the symmetry protected surface states and find that depending on the surface and the magnetization direction, surface states are still protected by reflection symmetry present in our model. The symmetry protected surface states are shifted away by the magnetization from their original high symmetry momenta in the Brillouin zone. Remarkably, due to the magnetization, the surface states are deformed, resulting in the appearance of arcs in the momentum resolved spectrum.

Origin of symmetry breaking in the seed-mediated growth of bi-metal nano-heterostructures

Seed-mediated growth is the most general way to controllably synthesize bimetal nano-heterostructures. Despite successful instances through trial and error were reported, the way for second metal depositing on the seed, namely whether the symmetry of resulted nano-heterostructure follows the original crystal symmetry of seed metal, remains an unpredictable issue to date. In this work, we propose that the thermodynamic factor, i.e., the difference of equilibrium electrochemical potentials (corresponding to their Fermi levels) of two metals in the growth solution, plays a key role for the symmetry breaking of bimetal nano-heterostructures during the seed-mediated growth. As a proof-of-principle experiment, by reversing the relative position of Fermi levels of the Pd nanocube seeds and the second metal Au with changing the concentration of reductant (L-ascorbic acid) in the growth solution, the structure of as-prepared products successfully evolved from centrosymmetric Pd@Au core-shell trisoctahedra to asymmetric Pd-Au hetero-dimers. The idea was further demonstrated by the growth of Ag on the Pd seeds. The present work intends to reveal the origin of symmetry breaking in the seed-mediated growth of nano-heterostructures from the viewpoint of thermodynamics, and these new insights will in turn help to achieve rational construction of bimetal nano-heterostructures with specific functions.

Universal description of pattern formation in optical oscillators under bichromatic injection

We study pattern formation in a complex Swift–Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems submitted to a bichromatic injection when the instability is toward long (transverse) wavelengths. Applications include two-level lasers and photorefractive oscillators. Under such an injection, the original continuous phase symmetry of the system is replaced by a discrete one and phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures, such as phase domains and dark-ring (phase) cavity solitons. The stability of the homogeneous solutions is studied, and numerical simulations are made covering all the dynamical regimes of the model, which turn out to be very rich. Derivations of the rocked complex Swift–Hohenberg equation, using multiple scale techniques, are given for the two-level laser and the photorefractive oscillator.

Dynamical Symmetry Breaking in Geometrodynamics

Using a first-order perturbative formulation, we analyze the local loss of symmetry when a source of electromagnetic and gravitational fields interacts with an agent that perturbs the original geometry associated with the source. We had proved that the local gauge groups are isomorphic to local groups of transformations of special tetrads. These tetrads define two orthogonal planes at every point in space–time such that every vector in these local planes is an eigenvector of the Einstein–Maxwell stress–energy tensor. Because the local gauge symmetry in Abelian or even non-Abelian field structures in four-dimensional Lorentzian space–times is manifested by the existence of local planes of symmetry, the loss of symmetry is manifested by a tilt of these planes under the influence of an external agent. In this strict sense, the original local symmetry is lost. We thus prove that the new planes at the same point after the tilting generated by the perturbation correspond to a new symmetry. Our goal here is to show that the geometric manifestation of local gauge symmetries is dynamical. Although the original local symmetries are lost, new symmetries arise. This is evidence for a dynamical evolution of local symmetries. We formulate a new theorem on dynamical symmetry evolution. The proposed new classical model can be useful for better understanding anomalies in quantum field theories.

Seeking fixed points in multiple coupling scalar theories in the \u03b5 expansion

Fixed points for scalar theories in 4 − ε, 6 − ε and 3 − ε dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings. The original maximal symmetry, O(N), is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the a-theorem are used to help classify potential fixed points. At lowest order in the ε-expansion it is shown that at fixed points there is a lower bound for a which is saturated at bifurcation points.

All-optical transistor based on Rydberg atom-assisted optomechanical system

We study the optical response of a double optomechanical cavity system assisted by two Rydberg atoms. The target atom is only coupled with one side cavity by a single cavity mode, and gate one is outside the cavities. It has been realized that a long-range manipulation of optical properties of a hybrid system, by controlling the Rydberg atom decoupled with the optomechanical cavity. Switching on the coupling between atoms and cavity mode, the original spatial inversion symmetry of the double cavity structure has been broken. Combining the controllable optical non-reciprocity with the coherent perfect absorption/transmission/synthesis effect (CPA/CPT/CPS reported by [ X.-B.Yan Opt. Express 22, 4886 (2014)], we put forward the theoretical schemes of an all-optical transistor which contains functions such as a controllable diode, rectifier, and amplifier by controlling a single gate photon.

On finite symmetries and their gauging in two dimensions

It is well-known that if we gauge a ℤn symmetry in two dimensions, a dual ℤn symmetry appears, such that re-gauging this dual ℤn symmetry leads back to the original theory. We describe how this can be generalized to non-Abelian groups, by enlarging the concept of symmetries from those defined by groups to those defined by unitary fusion categories. We will see that this generalization is also useful when studying what happens when a non-anomalous subgroup of an anomalous finite group is gauged: for example, the gauged theory can have non-Abelian group symmetry even when the original symmetry is an Abelian group. We then discuss the axiomatization of two-dimensional topological quantum field theories whose symmetry is given by a category. We see explicitly that the gauged version is a topological quantum field theory with a new symmetry given by a dual category.

Dirac field and gravity in NC SO(2,3)_star model

Action for the Dirac spinor field coupled to gravity on noncommutative (NC) Moyal-Weyl spacetime is obtained without prior knowledge of the metric tensor. We emphasize gauge origins of gravity and its interaction with fermions by demonstrating that a classical action invariant under SO(2, 3) gauge transformations can be exactly reduced to the Dirac action in curved spacetime after breaking the original symmetry down to the local Lorentz SO(1, 3) symmetry. The commutative SO(2, 3) invariant action can be straightforwardly deformed via Moyal-Weyl star -product to its NC SO(2,3)_star invariant version which can be expanded perturbatively in powers of the deformation parameter using the Seiberg-Witten map. The NC gravity-matter couplings in the expansion arise as an effect of the gauge symmetry breaking. We calculate in detail the first order NC correction to the classical Dirac action in curved spacetime and show that it does not vanish. Moreover, linear NC effects are apparent even in flat spacetime. We analyse NC deformation of the Dirac equation, Feynman propagator and dispersion relation for electrons in Minkowski spacetime and conclude that constant NC background acts as a birefringent medium for electrons propagating in it.

Impact of thickness variation on structural, dielectric and piezoelectric properties of (Ba,Ca)(Ti,Zr)O3 epitaxial thin films

It is shown that the dielectric and piezoelectric properties of Ba(Ti0.8Zr0.2)O3-x(Ba0.7Ca0.3)TiO3 (x = 0.45) (BCTZ 45) epitaxial thin films have a nontrivial dependence on film thickness. BCTZ 45 epitaxial films with different thicknesses (up to 400 nm) have been deposited on SrTiO3 by pulsed laser deposition and investigated by different combined techniques: conventional and off-axis X-ray diffraction, high resolution transmission electron microscopy and dielectric and piezoforce microscopy. The changes occurring in epitaxial films when their thickness increases have been attributed to a partial relaxation of misfit strain, driving the induced tetragonal symmetry in very thin films to the original rhombohedral symmetry of the bulk material in the thickest film, which influences directly and indirectly the dielectric and piezoelectric properties.

Effect of Al presence and synthesis method on phase composition of the hydrogen absorbing La–Mg–Ni-based compounds

Results for (La,Mg)Ni3.5 and (La,Mg)(Ni,Al)3.5 systems synthesized by metallurgical and mechanochemical techniques are reported. Powder X-ray and neutron diffraction combined with Rietveld refinements and profile analysis show that depending on the applied synthesis method various structurally related phases can be obtained for the same nominal composition. The hexagonal A2B7-type structure incorporating aluminum, with the refined composition La0.77Mg0.23Ni3.41Al0.09, has been identified. Al atoms occupy 12% of the 6h site within the LaNi5 slabs. This intermetallic phase absorbs hydrogen (deuterium) when exposed to 10 bar of H2 (D2) gas at room temperature. The H(D)-containing phase expands isotropically and retains the original symmetry of the parent compound.

Effect ofCu2+substitution in spin-orbit coupledSr2Ir1−xCuxO4: Structure, magnetism, and electronic properties

Sr$_2$IrO$_4$ is an extensively studied spin-orbit coupling induced insulator with antiferromagnetic ground state. The delicate balance between competing energy scales plays crucial role for its low temperature phase, and the route of chemical substitution has often been used to tune these different energy scales. Here, we report an evolution of structural, magnetic and electronic properties in doped Sr$_2$Ir$_{1-x}$Cu$_x$O$_4$ ($x$ $\leq$ 0.2). The substitution of Cu$^{2+}$ (3$d^9$) for Ir$^{4+}$ (5$d^5$) acts for electron doping, though it tunes the related parameters such as, spin-orbit coupling, electron correlation and Ir charge state. Moreover, both Ir$^{4+}$ and Cu$^{2+}$ has single unpaired spin though it occupies different $d$-orbitals. With Cu substitution, system retains its original structural symmetry but the structural parameters show systematic changes. X-ray photoemission spectroscopy measurements show Ir$^{4+}$ equivalently converts to Ir$^{5+}$ and a significant enhancement in the density of states has been observed at the Fermi level due to the contribution from the Cu 3$d$ orbitals, which supports the observed decrease in the resistivity with Cu substitution. While the long-range magnetic ordering is much weakened and the highest doped sample shows almost paramagnetic-like behavior the overall system remains insulator. Analysis of resistivity data shows mode of charge conduction in whole series follows 2-dimensional variable-range-hopping model but the range of validity varies with temperature. Whole series of samples exhibit negative magnetoresistance at low temperature which is considered to be a signature of weak localization effect in spin-orbit coupled system, and its evolution with Cu appears to follow the variation of resistivity with $x$.