Parity Symmetry Breaking Research Articles

Realistic quantum critical point in one-dimensional two-impurity models

We show that the two-impurity Anderson model exhibits an additional quantum critical point at infinitely many specific distances between both impurities for an inversion symmetric one-dimensional dispersion. Unlike the quantum critical point previously established, it is robust against particle-hole or parity symmetry breaking. The quantum critical point separates a spin doublet from a spin singlet ground state and is, therefore, protected. A finite single-particle tunneling $t$ or an applied uniform gate voltage will drive the system across the quantum critical point. The discriminative magnetic properties of the different phases cause a jump in the spectral functions at low temperature, which might be useful for future spintronics devices. A local parity conservation will prevent the spin-spin correlation function from decaying to its equilibrium value after spin manipulations.

Parity-symmetry breaking and topological phases in a superfluid ring

We study analytically the superfluid flow of a Bose-Einstein condensate in a ring geometry in presence of a rotating barrier. We show that a phase transition breaking a parity symmetry among two topological phases occurs at a critical value of the height of the barrier. Furthermore, a discontinuous (accompanied by hysteresis) phase transition is observed in the ordered phase when changing the angular velocity of the barrier. At the critical point where the hysteresis area vanishes, chemical potential of the ground state develops a cusp (a discontinuity in the first derivative). Along this path, the jump between the two corresponding states having a different winding number shows strict analogies with a topological phase transition. We finally study the current-phase relation of the system and compare some of our calculations with published experimental results.

Signatures of broken parity and time-reversal symmetry in generalized string-net models

We study indicators of broken time-reversal and parity symmetries in gapped topological phases of matter. We focus on phases realized by Levin-Wen string-net models, and generalize the string-net model to describe phases which break parity and time-reversal symmetries. We do this by introducing an extra degree of freedom into the string-net graphical calculus, which takes the form of a branch cut located at each vertex of the underlying string-net lattice. We also work with string-net graphs defined on arbitrary (non-trivalent) graphs, which reveals otherwise hidden information about certain configurations of anyons in the string-net graph. Most significantly, we show that objects known as higher Frobenius-Schur indicators can provide several efficient ways to detect whether or not a given topological phase breaks parity or time-reversal symmetry.

Effect of two-dimensional parity symmetry breaking in Aharonov-Bohm interference phenomena

ABSTRACTThe quantum-mechanical dephasing effect of a two-dimensional parity symmetry breaking is demonstrated in a solid-state quantum-coherent mesoscopic ring interferometer. The interferometer, fabricated on an InGaAs/InAlAs heterostructure, shows Aharonov-Bohm oscillations under magnetic fields at low temperatures. Under asymmetric bias voltage on side-gates, a weakening of the Aharonov-Bohm oscillations is observed. The weakening corresponds to an effective dephasing under two-dimensional parity symmetry breaking by the applied electric field, and is interpreted as a counterpart to the weakening observed under time-reversal symmetry breaking by a magnetic field.

Manipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking.

One-way transmission and negative refraction are the exotic wave properties founded in photonic crystals which attract a great attention due to their promising applications in photonic devices. How to integrate such two phenomena in one material or device is interesting and valuable. In this work, we theoretically and experimentally demonstrate that one-way electromagnetic space wave can be realized by means of two-dimensional magnetic photonic crystals. Simultaneously breaking the time-reversal and parity symmetries of the magnetic photonic crystals designed, we observe oblique incident space wave propagating one-way in the magnetic photonic crystals with positive or negative refraction occurring at interfaces, which can be manipulated upon the incident angle and operating frequency. Our work may offer a potential platform to realize some exotic photoelectronic and microwave devices such as one-way imaging and one-way cloaking.

Dynamics of Localized Structures in Systems with Broken Parity Symmetry.

A great variety of nonlinear dissipative systems are known to host structures having a correlation range much shorter than the size of the system. The dynamics of these localized structures (LSs) has been investigated so far in situations featuring parity symmetry. In this Letter we extend this analysis to systems lacking this property. We show that the LS drifting speed in a parameter varying landscape is not simply proportional to the parameter gradient, as found in parity preserving situations. The symmetry breaking implies a new contribution to the velocity field which is a function of the parameter value, thus leading to a new paradigm for LSs manipulation. We illustrate this general concept by studying the trajectories of the LSs found in a passively mode-locked laser operated in the localization regime. Moreover, the lack of parity affects significantly LSs interactions which are governed by asymmetrical repulsive forces.

Axial Current Generation by P-Odd Domains in QCD Matter.

The dynamics of topological domains which break parity (P) and charge-parity (CP) symmetry of QCD are studied. We derive in a general setting that those local domains will generate an axial current and quantify the strength of the induced axial current. Our findings are verified in a top-down holographic model. The relation between the real time dynamics of those local domains and the chiral magnetic field is also elucidated. We finally argue that such an induced axial current would be phenomenologically important in a heavy-ion collisions experiment.

Parity Symmetry and Parity Breaking in the Super-Ohmic Spin-Boson Model

The parity symmetry and parity breaking in the super-Ohmic spin-boson model (SBM) is studied by using the coherent-state approach. We show that the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias, and then it can be restored by involving an additional spin into the SBM to couple with the original spin by an Ising interaction. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom.

Magnetoelectric effect in bilayer graphene controlled by valley-isospin density

We show that bilayer graphene exhibits magneto-electric effects that are formally similar to those commonly seen in band insulators with broken inversion and time-reversal symmetries. Three unusual features characterize the magneto-electric responses exhibited by bilayer graphene: (i) unlike most other magneto-electric media, bilayer graphene is a conductor, (ii) bilayer graphene has a non-quantized magneto-electric coupling even though its electronic structure does not break parity and time-reversal symmetry, and (iii) the magnitude of the magneto-electric coupling in bilayer graphene is determined by the valley-isospin density, which can be manipulated experimentally. This last property also enables a purely electric measurement of valley-isospin densities. While our theoretical arguments use bilayer graphene as an example, they are generally valid for any material with similar symmetries.

Generalizations and limitations of string-net models

We ask which topological phases can and can not be realized by exactly soluble string-net models. We answer this question for the simplest class of topological phases, namely, those with Abelian braiding statistics. Specifically, we find that an Abelian topological phase can be realized by a string-net model if and only if (i) it has a vanishing thermal Hall conductance and (ii) it has at least one Lagrangian subgroup, a subset of quasiparticles with particular topological properties. Equivalently, we find that an Abelian topological phase is realizable if and only if it supports a gapped edge. We conjecture that the latter criterion generalizes to the non-Abelian case. We establish these results by systematically constructing all possible Abelian string-net models and analyzing the quasiparticle braiding statistics in each model. We show that the low-energy effective field theories for these models are multicomponent $\text{U}(1)$ Chern-Simons theories, and we derive the $K$-matrix description of each model. An additional feature of this work is that the models we construct are more general than the original string-net models, due to several new ingredients. First, we introduce two new objects $\ensuremath{\gamma},\ensuremath{\alpha}$ into the construction which are related to ${\mathbb{Z}}_{2}$ and ${\mathbb{Z}}_{3}$ Frobenius-Schur indicators. Second, we do not assume parity invariance. As a result, we can realize topological phases that were not accessible to the original construction, including phases that break time-reversal and parity symmetry.

Note on specific chiral ensembles of statistical hydrodynamics: “Order function” for transition of turbulence transfer scenarios

Hydrodynamic helicity signatures the parity symmetry breaking, chirality, of the flow. Statistical hydrodynamics thus respect chirality, as symmetry breaking and restoration are key to its fundamentals, such as the spectral transfer direction and its mechanism. Homochiral sub-system of three-dimensional (3D) Navier-Stokes isotropic turbulence has been numerically realized with helical representation technique to present inverse energy cascade [Biferale et al., Phys. Rev. Lett. 108, 164501 (2012)]. The situation is analogous to 2D turbulence where inverse energy cascade, or more generally energy-enstrophy dual cascade scenario, was argued with the help of a negative temperature state of the absolute equilibrium by Kraichnan. Indeed, if the helicity in such a system is taken to be positive without loss of generality, a corresponding negative temperature state can be identified [Zhu et al., J. Fluid Mech. 739, 479 (2014)]. Here, for some specific chiral ensembles of turbulence, we show with the corresponding absolute equilibria that even if the helicity distribution over wavenumbers is sign definite, different ansatzes of the shape function, defined by the ratio between the specific helicity and energy spectra s(k) = H(k)/E(k), imply distinct transfer directions, and we could have inverse-helicity and forward-energy dual transfers (with, say, s(k) ∝ k−2 resulting in absolute equilibrium modal spectral density of energy \documentclass[12pt]{minimal}\begin{document}$U(k)=\frac{1}{\alpha +\beta k^{-2}}$\end{document}U(k)=1α+βk−2, exactly the enstrophy one of two-dimensional Euler by Kraichan), simultaneous forward transfers (with s(k) = constant), or even no simply-directed transfer (with, say, non-monotonic s(k) ∝ sin 2k), besides the inverse-energy and forward-helicity dual transfers (with, say, s(k) = k as in the homochiral case).

Restricted partition functions and inverse energy cascades in parity symmetry breaking flows

When the symmetries of homogenous isotropic turbulent flows are broken, different sets of modes with different physical roles emerge. In particular, choosing a forcing which puts more weight on one or the other of these sets may result in different statistics for the energy transfers. We use the general method of computing a partition function restricted to a portion of phase space to study analytically these different statistics. We illustrate this method in the case of parity symmetry breaking, measured by helicity. It is shown that when helicity is sign-definite at all scales, an inverse cascade is expected for the energy. When sign-definiteness is lost, even for a small set of modes, this cascade disappears and there is a sharp phase transition to the standard helical equipartition spectra.

Polarization corrections to single-particle energies studied within the energy-density-functional and quasiparticle random-phase approximation approaches

Background: Models based on using perturbative polarization corrections and mean-field blocking approximation give conflicting results for masses of odd nuclei.Purpose: We systematically investigate the polarization and mean-field models, implemented within self-consistent approaches that use identical interactions and model spaces, to find reasons for the conflicts between them.Methods: For density-dependent interactions and with pairing correlations included, we derive and study links between the mean-field and polarization results obtained for energies of odd nuclei. We also identify and discuss differences between the polarization-correction and full particle-vibration-coupling (PVC) models. Numerical calculations are performed for the mean-field ground-state properties of deformed odd nuclei and then compared to the polarization corrections determined using the approach that conserves spherical symmetry.Results: We have identified and numerically evaluated self-interaction (SI) energies that are at the origin of different results obtained within the mean-field and polarization-correction approaches.Conclusions: Mean-field energies of odd nuclei are polluted by the SI energies, and this makes them different from those obtained using polarization-correction methods. A comparison of both approaches allows for the identification and determination of the SI terms, which then can be calculated and removed from the mean-field results, giving the self-interaction-free energies. The simplest deformed mean-field approach that does not break parity symmetry is unable to reproduce full PVC effects.

Gravity effects on thick brane formation from scalar field dynamics

The formation of a thick brane in five-dimen\-sional space-time is investigated when warp geometries of $AdS_5$ type are induced by scalar matter dynamics and triggered by a thin-brane defect. The scalar matter is taken to consist of two fields with $O(2)$ symmetric self interaction and with manifest $O(2)$ symmetry breaking by terms quadratic in fields. One of them serves as a thick brane formation mode around a kink background and another one is of a Higgs-field type which may develop a classical background as well. Scalar matter interacts with gravity in the minimal form and gravity effects on (quasi)localized scalar fluctuations are calculated with usage of gauge invariant variables suitable for perturbation expansion. The calculations are performed in the vicinity of the critical point of spontaneous breaking of the combined parity symmetry where a non-trivial v.e.v. of the Higgs-type scalar field is generated. The nonperturbative discontinuous gravitational effects in the mass spectrum of light localized scalar states are studied in the presence of a thin-brane defect. The thin brane with negative tension happens to be the most curious case when the singular barriers form a potential well with two infinitely tall walls and the discrete spectrum of localized states arises completely isolated from the bulk.

Lehmann effects and rotatoelectricity in liquid crystalline systems made of achiral molecules

We discuss Lehmann effects and rotato-electricity for liquid crystalline phases made of achiral molecules. We point out that for static and dynamic Lehmann effects to exist, it is not necessary to have chiral molecules provided the overall structure has macroscopic chirality. This question is of direct relevance for liquid crystalline phases formed by bent-core molecules provided they have a sufficiently low symmetry. This includes systems which break parity symmetry and have overall C(2) or C(1) symmetry. We point out that for liquid crystalline gels and elastomers one should be able to observe rotato-electricity for systems with macroscopic chirality. Rotatoelectricity is associated with the relative rotations between two subsystems, namely, between the network and the director, in an external electric field. Candidates include gels and even monolayers prepared from bent-core molecules with sufficiently low symmetry.

FULLY TORSION-BASED FORMULATION FOR CURVED MANIFOLDS

We develop a new description of curved manifolds that represent a topological phase for the usual Levi-Civita connection and a dynamical phase for the torsion, being the only part of the connection that generates curvature. The holonomy group structure of such manifolds is studied, and different expressions of the torsion in terms of gauge fields are considered with the purpose to describe different dynamical scenarios. Additionally some models of torsion interacting with fermions are constructed; specifically a four-dimensional model that mimics an usual fermion-gauge fields system is considered; this model undergoes parity symmetry breaking with a dynamical background. Since these manifolds represent new gravitational backgrounds, we speculate on possible applications in the study of qualitative and quantitative aspects of the gauge/gravity duality.

Pomeranchuk-nematic instability in the presence of a weak magnetic field

We analyze a two-dimensional Pomeranchuk-nematic instability, trigger by the Landau parameter ${F}_{2}<0$, in the presence of a small magnetic field. Using Landau Fermi-liquid theory in the isotropic phase, we analyze the collective modes near the quantum critical point ${F}_{2}=\ensuremath{-}1,{\ensuremath{\omega}}_{c}=0$ (where ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency). We focus on the effects of parity symmetry breaking on the Fermi-surface deformation. We show that the linear response approximation of the Landau-Silin equation is not sufficient to study the critical regime and it is necessary to compute corrections at least of order ${\ensuremath{\omega}}_{c}^{2}$. Identifying the slowest oscillation mode in the disordered phase, we compute the phase diagram for the isotropic/nematic phase transition in terms of ${F}_{2}$ and ${\ensuremath{\omega}}_{c}$.

A chiral rhenium complex with predicted high parity violation effects: synthesis, stereochemical characterization by VCD spectroscopy and quantum chemical calculations

With their rich electronic, vibrational, rotational and hyperfine structure, molecular systems have the potential to play a decisive role in precision tests of fundamental physics. For example, electroweak nuclear interactions should cause small energy differences between the two enantiomers of chiral molecules, a signature of parity symmetry breaking. Enantioenriched oxorhenium(VII) complexes S-(-)- and R-(+)-3 bearing a chiral 2-methyl-1-thio-propanol ligand have been prepared as potential candidates for probing molecular parity violation effects via high resolution laser spectroscopy of the Re=O stretching. Although the rhenium atom is not a stereogenic centre in itself, experimental vibrational circular dichroism (VCD) spectra revealed a surrounding chiral environment, evidenced by the Re=O bond stretching mode signal. The calculated VCD spectrum of the R enantiomer confirmed the position of the sulfur atom cis to the methyl, as observed in the solid-state X-ray crystallographic structure, and showed the presence of two conformers of comparable stability. Relativistic quantum chemistry calculations indicate that the vibrational shift between enantiomers due to parity violation is above the target sensitivity of an ultra-high resolution infrared spectroscopy experiment under active preparation.

Strong curvature effects in Neumann wave problems

Waveguide phenomena play a major role in basic sciences and engineering. The Helmholtz equation is the governing equation for the electric field in electromagnetic wave propagation and the acoustic pressure in the study of pressure dynamics. The Schrödinger equation simplifies to the Helmholtz equation for a quantum-mechanical particle confined by infinite barriers relevant in semiconductor physics. With this in mind and the interest to tailor waveguides towards a desired spectrum and modal pattern structure in classical structures and nanostructures, it becomes increasingly important to understand the influence of curvature effects in waveguides. In this work, we demonstrate analytically strong curvature effects for the eigenvalue spectrum of the Helmholtz equation with Neumann boundary conditions in cases where the waveguide cross section is a circular sector. It is found that the linear-in-curvature contribution originates from parity symmetry breaking of eigenstates in circular-sector tori and hence vanishes in a torus with a complete circular cross section. The same strong curvature effect is not present in waveguides subject to Dirichlet boundary conditions where curvature contributions contribute to second-order in the curvature only. We demonstrate this finding by considering wave propagation in a circular-sector torus corresponding to Neumann and Dirichlet boundary conditions, respectively. Results for relative eigenfrequency shifts and modes are determined and compared with three-dimensional finite element method results. Good agreement is found between the present analytical method using a combination of differential geometry with perturbation theory and finite element results for a large range of curvature ratios.

NONRECIPROCAL MULTIFERROIC SUPERLATTICES WITH BROKEN PARITY SYMMETRY

Multiferroic materials are characterized by the coexistence of ferroelectric and ferromagnetic (or antiferromagnetic) orders, the coupling to lattice vibration can be invoked either through piezoelectric or piezomagnetic effects. In this paper, the polaritonic band structures of multiferroic superlattices composed of oppositely polarized domains are investigated using the generalized transfer matrix method. For the primitive cell with broken parity symmetry, the polaritonic band structure is asymmetrical with respect to the forward and backward propagation directions (nonreciprocality). In particular, the band extreme points move away from the Brillouin zone center. This asymmetry in band-gap positions and widths can be used to design compact one-way optical isolators, while the extremely slow light velocities near the asymmetrical upper edges of lower bands includes the essential ingredients for designing slow light devices.