Parity Symmetry Breaking Research Articles

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.

Complete classification of one-dimensional gapped quantum phases in interacting spin systems

Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site unitary symmetry has been given for 1D spin systems in [X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B \textbf{83}, 035107 (2011); arXiv:1008.3745]. It was found that, such symmetry protected topological (SPT) phases are labeled by the projective representations of the symmetry group which can be viewed as a symmetry fractionalization. In this paper, we extend the classification of 1D gapped phases by considering SPT phases with combined time reversal, parity, and/or on-site unitary symmetries and also the possibility of symmetry breaking. We clarify how symmetry fractionalizes with combined symmetries and also how symmetry fractionalization coexists with symmetry breaking. In this way, we obtain a complete classification of gapped quantum phases in 1D spin systems. We find that in general, symmetry fractionalization, symmetry breaking and long range entanglement(present in 2 or higher dimensions) represent three main mechanisms to generate a very rich set of gapped quantum phases. As an application of our classification, we study the possible SPT phases in 1D fermionic systems, which can be mapped to spin systems by Jordan-Wigner transformation.

Parity symmetry in QED3

Schwinger-Dyson equations are used to study spontaneous chiral and parity symmetry breaking of three-dimensional quantum electrodynamics with two-component fermions. This theory admits a topological photon mass that explicitly breaks parity symmetry and generates a fermion mass. We show for the first time that it is possible to spontaneously break both parity and chiral symmetry. We also find that chiral symmetry is restored at a critical number of fermion flavors in our truncation scheme. Finally, the Coleman-Hill theorem is used to demonstrate that the results are reasonably accurate.

Dynamical R-parity breaking at the LHC

In a class of extensions of the minimal supersymmetric standard model with (B-L)/left-right symmetry that explains the neutrino masses, breaking R-parity symmetry is an essential and dynamical requirement for successful gauge symmetry breaking. Two consequences of these models are: (i) a new kind of R-parity breaking interaction that protects proton stability but adds new contributions to neutrinoless double beta decay and (ii) an upper bound on the extra gauge and parity symmetry breaking scale which is within the large hadron collider (LHC) energy range. We point out that an important prediction of such theories is a potentially large mixing between the right-handed charged lepton ($e^c$) and the superpartner of the right-handed gauge boson ($\widetilde W_R^+$), which leads to a brand new class of R-parity violating interactions of type $\widetilde{\mu^c}^\dagger\nu_\mu^c e^c$ and $\widetilde{d^c}^\dagger\u^c e^c$. We analyze the relevant constraints on the sparticle mass spectrum and the LHC signatures for the case with smuon/stau NLSP and gravitino LSP. We note the "smoking gun" signals for such models to be lepton flavor/number violating processes: $pp\to \mu^\pm\mu^\pm e^+e^-jj$ (or $\tau^\pm\tau^\pm e^+e^-jj$) and $pp\to\mu^\pm e^\pm b \bar{b} jj$ (or $\tau^\pm e^\pm b \bar{b} jj$) without significant missing energy. The predicted multi-lepton final states and the flavor structure make the model be distinguishable even in the early running of the LHC.

Computing K and D meson masses with [formula omitted] twisted mass lattice QCD

We discuss the computation of the mass of the K and D mesons within the framework of N f = 2 + 1 + 1 twisted mass lattice QCD from a technical point of view. These quantities are essential, already at the level of generating gauge configurations, being obvious candidates to tune the strange and charm quark masses to their physical values. In particular, we address the problems related to the twisted mass flavor and parity symmetry breaking, which arise when considering a non-degenerate ( c , s ) doublet. We propose and verify the consistency of three methods to extract the K and D meson masses in this framework.

Chiral and parity symmetry breaking for planar fermions: Effects of a heat bath and uniform external magnetic field

We study chiral symmetry breaking for relativistic fermions, described by a parity violating Lagrangian in 2+1-dimensions, in the presence of a heat bath and a uniform external magnetic field. Working within their four-component formalism allows for the inclusion of both parity-even and -odd mass terms. Therefore, we can define two types of fermion anti-fermion condensates. For a given value of the magnetic field, there exist two different critical temperatures which would render one of these condensates identically zero, while the other would survive. Our analysis is completely general: it requires no particular simplifying hierarchy among the energy scales involved, namely, bare masses, field strength and temperature. However, we do reproduce some earlier results, obtained or anticipated in literature, corresponding to special kinematical regimes for the parity conserving case. Relating the chiral condensate to the one-loop effective Lagrangian, we also obtain the magnetization and the pair production rate for different fermion species in a uniform electric field through the replacement $B\to-iE$.

Distinguishing left- and right-handed molecules using two-step coherent pulses

Chiral molecules with broken parity symmetries can be modelled as quantum systems with cyclic-transition structures. By using these novel properties, we design two-step laser pulses to distinguish left- and right-handed molecules from the enantiomers. After the applied pulse drivings, one kind of chiral molecule is trapped in a coherent population trapping state, while the other is pumped to the highest states for ionization. Then the different chiral molecules can be separated.

Gains without inversion in quantum systems with broken parities

For a quantum system with broken parity symmetry, selection rules can not hold and cyclic transition structures are generated. With these loop-transitions we discuss how to achieve inversionless gain of the probe field by properly setting the control and auxiliary fields. Possible implementations of our generic proposal with specific physical objects with broken parities, e.g., superconducting circuits and chiral molecules, are also discussed.

Towards the detection of parity symmetry breaking in chiral molecules

We propose an optical rotation experiment to detect the electroweak parity-violating energy difference (PVED) between the two enantiomers of a chiral molecule. For some chiral molecules, it is shown theoretically that at low enough temperature, in the range from mK to few K, the competition between the PVED, tunneling between the two enantiomers and thermal effects leads to an enantiomeric excess in the thermodynamic equilibrium which is able to produce an optical rotation measurable by state-of-the-art ultrasensitive polarimeters. By means of mechanisms inhibiting tunneling, the sample would keep the enantiomeric excess at higher temperatures. Suitable chiral molecules are pointed out.

Vortex nucleation in a mesoscopic Bose superfluid and breaking of the parity symmetry

We analyze vortex nucleation in mesoscopic two-dimensional Bose superfluid in a rotating trap. We explicitly include a weakly anisotropic stirring potential, breaking thus explicitly the axial symmetry. As the rotation frequency passes the critical value ${\ensuremath{\Omega}}_{c}$, the system undergoes an extra symmetry change or breaking. Well below ${\ensuremath{\Omega}}_{c}$, the ground state is properly described by the mean-field theory with an even condensate wave function. Well above ${\ensuremath{\Omega}}_{c}$, the mean-field solution works also well, but the order parameter becomes odd. This phenomenon involves therefore a discrete parity symmetry breaking. In the critical region, the mean-field solutions exhibit dynamical instability. The true many-body state is a strongly correlated entangled state involving two macroscopically occupied modes (eigenstates of the single-particle density operator). We characterize this state in various aspects: (i) the eligibility for adiabatic evolution, (ii) its analytical approximation given by the maximally entangled combination of two single modes, and finally (iii) its appearance in particle detection measurements.

Landau description for an atomic screened system: the charge symmetry breaking effect

We have examined the presence of a charge symmetry breaking in a screened system. Using a Thomas-Fermi-type potential and a simple mathematical model, we show that screening on the nuclear charge α induces a charge parametrization α→(α,β) in which appears a new dual charge β in the system. Considering this method, the binding energy of electron becomes invariant under parity symmetry for an order parameter ρ=β-α. We find nontrivial solutions for ρ at the minimum of energy which leads to the broken parity symmetry. The equations obtained for this new screening approach is very similar to the Landau theory of phase transition.

Integrable spin chain of superconformal U(M) × $\overline{\mathop{\rm U}(N)}$ Chern-Simons theory

N=6 superconformal Chern-Simons theory with gauge group U(M)xU(N)} is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C4/Zk orbifold singularity. We show that, much like its regular counterpart of M=N, the theory at planar limit have integrability structure in the conformal dimension spectrum of single trace operators. We first revisit the Yang-Baxter equation for a spin chain system associated with the single trace operators. We show that the integrability by itself does not preclude parity symmetry breaking. We construct two-parameter family of parity non-invariant, alternating spin chain Hamiltonian involving three-site interactions between 4 and 4* of SU(4). At weak `t Hooft coupling, we study the Chern-Simons theory perturbatively and calculate anomalous dimension of single trace operators up to two loops. The computation is essentially parallel to the regular case M=N. We find that resulting spin chain Hamiltonian matches with the Hamiltonian derived from Yang-Baxter equation, but to the one preserving parity symmetry. We give several intuitive explanations why the parity symmetry breaking is not detected in the Chern-Simons spin chain Hamiltonian at perturbative level. We suggest that open spin chain, associated with open string excitations on giant gravitons or dibaryons, can detect discrete flat holonomy and hence parity symmetry breaking through boundary field.

Truncated photonic crystal cavities with optimized mode confinement

Optimization of a truncated, dielectric photonic crystal cavity leads to configurations that are far from truncated crystal cavities, and which have significantly better radiation confinement. Starting from a two-dimensional truncated photonic crystal cavity with optimal Q-factor, moving the rods from the lattice positions can increase the Q-factor by orders of magnitude, e.g., from 130 to 11 000 for a cavity constructed from 18 rods. In the process, parity symmetry breaking occurs. Achieving the same Q-factor with a regular lattice requires 60 rods. Therefore, using optimized irregular structures for photonic cavities can greatly reduce material requirements and device size.

Analysis of spin pumping in asymmetric ring conductors with the Aharonov-Casher effect

We investigated the spin pumping behavior in a ring conductor with the Aharonov-Casher effect. The Rashba spin-orbit interaction is the sole oscillating parameter in the proposed spin pump. Our analysis is based on the Floquet scattering matrix formula, where the infinite Floquet channels can provide alternative channels for spin transport. A finite spin current at zero dc bias is obtained in a ring conductor with broken parity symmetry, while the charge current is always zero. The motion of pumped spin is tuned by adjusting the pumping parameters. These results may be useful in simplifying the experimental realization of a spin pump with the Aharonov-Casher effect.

Enhancement of Pairwise Entanglement viaZ2Symmetry Breaking

We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition. This results in an order-induced enhancement of entanglement, and we report on two examples where this takes place.

Parity anomaly in a $$\mathcal{P}\mathcal{T}$$ -symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian \(\mathcal{P}\mathcal{T}\)-symmetric wrong-sign quartic Hamiltonian H = (1/2m)p2 − gx4 is exactly equivalent to the conventional Hermitian Hamiltonian \(\tilde H = ({1 \mathord{\left/ {\vphantom {1 {2m}}} \right. \kern-\nulldelimiterspace} {2m}})p^2 + 4gx^4 - \hbar ({{2g} \mathord{\left/ {\vphantom {{2g} m}} \right. \kern-\nulldelimiterspace} m})^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} x\). First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian \(\tilde H\) is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian \(\mathcal{P}\mathcal{T}\)-symmetric Hamiltonian. The anomaly term in \(\tilde H\) remains unchanged if an x2 term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in \(\tilde H\) are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.

Fermion generations, masses and mixing angles from extra dimensions

We discuss a toy model in six dimensions that predicts two fermion generations, natural mass hierarchy and intergenerational mixing. Matter is described by vector-like six-dimensional fermions, one per each irreducible standard model representation. Two fermion generations arise from the compactification mechanism, through orbifold projection. They are localized in different regions of the compact space by a six-dimensional mass term. Flavour symmetry is broken via Yukawa couplings, with a Higgs vacuum expectation value not constant in the extra space. A hierarchical spectrum is obtained from order one dimensionless parameters of the six-dimensional theory. The Cabibbo angle arises from the soft breaking of six-dimensional parity symmetry. We also briefly discuss how the present model could be extended to cover the realistic case.

Non BPS noncommutative vortices

We construct exact vortex solutions to the equations of motion of the Abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point. We show that our solutions behave as smooth deformations of vortices in ordinary space time except for parity symmetry breaking effects induced by the non commutative parameter $\theta$.

Spontaneous symmetry breaking and exotic quantum orders in integer quantum Hall systems under a tilted magnetic field

We use the microscopic Hartree-Fock approximation to investigate various quantum phase transitions associated with possible spontaneous symmetry breaking induced by a tilted magnetic field in the integral quantum Hall regime of wide parabolic wells and zero width double well (bilayer) systems. We propose a general class of variational wavefunctions that describe several types of parity, spin, and translational symmetry breaking, including spin and charge density wave phases. Zero temperature quantum phase diagrams for these systems are calculated in the parameter regime of experimental interest. We discuss the symmetry properties of our predicted quantum phase diagrams and give a unified picture of these novel many-body phases. A conceptually new aspect of our theory is the predicted possibility for the spontaneous breaking of parity symmetry, which indicates a ``ferroelectric'' quantum order in integer quantum Hall systems and has not been considered in the literature before.