Zero Modes Research Articles

Index theorem on T2/ZN orbifolds

We investigate chiral zero modes and winding numbers at fixed points on $T^2/\mathbb{Z}_N$ orbifolds. It is shown that the Atiyah-Singer index theorem for the chiral zero modes leads to a formula $n_+-n_-=(-V_++V_-)/2N$, where $n_{\pm}$ are the numbers of the $\pm$ chiral zero modes and $V_{\pm}$ are the sums of the winding numbers at the fixed points on $T^2/\mathbb{Z}_N$. This formula is complementary to our zero-mode counting formula on the magnetized orbifolds with non-zero flux background $M \neq 0$, consistently with substituting $M = 0$ for the counting formula $n_+ - n_- = (2M - V_+ + V_-)/2N$.

Thick brane structures in generalized hybrid metric-Palatini gravity

In this work, we study 5-dimensional braneworld scenarios in the scalar-tensor representation of the generalized hybrid metric-Palatini gravitational theory. We start by considering a model for a brane supported purely by the gravitational scalar fields of the theory and then consider other distinct cases where the models are also supported by an additional matter scalar field. We investigate the stability of the gravity sector and show that the models are all robust against small fluctuations of the metric. In particular, in the presence of the additional scalar field, we find that the profile of the gravitational zero mode may be controlled by the parameters of the model, being also capable of developing internal structure.

Zero Modes of Velocity Field and Topological Invariant in Quantum Torus

Zero Modes of Velocity Field and Topological Invariant in Quantum Torus

Fault Zone Location Based on Transient Phase Current and Zero Mode Current

To solve the problems of inaccurate location caused by unsynchronized measurement signals, high impedance grounding, and strong noise interference, in this paper, a novel fault location method based on the relationship between transient zero-mode current and transient phase current is proposed. Through analysis, the zero phenomenon is the main cause of misjudgment. The three-phase current of fault feeder detection point is obtained, the similarity between fault phase current and fault transient zero-mode current is calculated, and the segment location is conducted by using dichotomy method. Numerical simulation results demonstrate the effectiveness of the proposed method. This method can greatly reduce the probability of misjudgment and measurement difficulties, and improve detection efficiency.

On the LHC signatures of SU(5)times U(1)' F-theory motivated models

We study low energy implications of F-theory GUT models based on SU(5) extended by a U(1)' symmetry which couples non-universally to the three families of quarks and leptons. This gauge group arises naturally from the maximal exceptional gauge symmetry of an elliptically fibred internal space, at a single point of enhancement, E_8supset SU(5)times SU(5)'supset SU(5)times U(1)^4. Rank-one fermion mass textures and a tree-level top quark coupling are guaranteed by imposing a Z_2 monodromy group which identifies two abelian factors of the above breaking sequence. The U(1)' factor of the gauge symmetry is an anomaly free linear combination of the three remaining abelian symmetries left over by Z_2. Several classes of models are obtained, distinguished with respect to the U(1)' charges of the representations, and possible extra zero modes coming in vector-like representations. The predictions of these models are investigated and are compared with the LHC results and other related experiments. Particular cases interpreting the B-meson anomalies observed in LHCb and BaBar experiments are also discussed.

Exact one-loop false vacuum decay rate

We discuss an exact false vacuum decay rate at one loop for a real and complex scalar field in a quartic-quartic potential with two tree-level minima. The bounce solution is used to compute the functional determinant from both fluctuations. We obtain the finite product of eigenvalues and remove translational zero modes. The orbital modes are regularized with the zeta function and we end up with a complete renormalized decay rate. We derive simple expansions in the thin and thick wall limits and determine their validity.

Consistency conditions for p-form field localization on codimension two braneworlds

In a recent work (Eur. Phys. J. C 80(5), 432, 2020), the present authors obtained general stringent conditions on the localization of fields in braneworlds by imposing the requirement that its zero mode must satisfy Einstein’s equations (EEs). In this manuscript, we continue this study by considering free p-form fields. These fields present an on-shell equivalency relation between a p-form and a (D-p-2)-form, provided by a Hodge duality (HD) transformation. This symmetry will impose a new consistency condition, namely, confinement of a p-form on the brane must imply the localization of its dual. We apply the above two conditions to 6D braneworld models. With this, we find that in global string-like defects, for example, the 1-form field has a normalizable zero mode. By using the HD as a guide, we show that its bulk dual 3-form field also has a normalizable zero mode, making the confinement consistent with HD. However, these solutions cannot be made consistent with EE, therefore, these fields must be ruled out. In fact, by imposing both conditions, only the scalar field and its dual can be consistently localized in codimension two braneworlds. In this way, all the literature so far in which the free vector field (1-form) is localized in codimension two models should be reviewed. These results also point to the fact that the symmetries of the fields can be used to verify the consistency of their localization and even prohibit it.

Symmetry-Enhanced Boundary Qubits at Infinite Temperature

The Z_{2}×Z_{2} symmetry-protected topological (SPT) phase hosts a robust boundary qubit at zero temperature. At finite energy density, the SPT phase is destroyed and bulk observables equilibrate in finite time. Nevertheless, we predict parametric regimes in which the boundary qubit survives to arbitrarily high temperature, with an exponentially longer coherence time than that of the thermal bulk degrees of freedom. In a dual picture, the persistence of the qubit stems from the inability of the bulk to absorb the virtual Z_{2}×Z_{2} domain walls emitted by the edge during the relaxation process. We confirm the long coherence times via exact diagonalization and connect it to the presence of a pair of conjugate almost strong zero modes. Our results provide a route to experimentally construct long-lived coherent boundary qubits at infinite temperature in disorder-free systems. To this end, we propose and analyze an implementation using a Rydberg optical-tweezer array and demonstrate that the difference between edge- and bulk-spin autocorrelators can be distinguished on timescales significantly shorter than the typical coherence time.

Strong Zero Modes from Geometric Chirality in Quasi-One-Dimensional Mott Insulators.

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include Z_{n} chiral quantum clock models with strong zero modes related to Z_{n} parafermions. Here, we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on n=3 where the Mott insulators are three-leg ladders. We link such ladders to Z_{3} chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the Z_{3} chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature.

Vacuum loops in light-front field theory

We demonstrate that vacuum diagrams in the genuine light front (LF) field theory are non-zero, in spite of simple kinematical counter-arguments (positivity and conservation of the LF momentum p+, absence of Fourier zero mode). Using the light-front Hamiltonian (time-ordered) perturbation theory, the vacuum amplitudes in self-interacting scalar λϕ3(1+1) and λϕ4(1+1) models are obtained as p=0 limit of the associated self-energy diagrams, where p is the external momentum. They behave as Cλ2μ−2 in D=2, with μ being the scalar-field mass, or diverge in D=4, in agreement with the usual “equal-time” form of field theory, and with the same value of the constant C. The simplest vacuum diagram with two internal lines is analyzed in detail displaying the subtle role of the small k+ region and its connection to the p=0 limit. However, the vacuum bubbles in the genuine light-front field theory are nonvanishing not due to the Fourier mode carrying LF momentum k+=0 (as is the case in the LF evaluation of the covariant Feynman diagrams), in full accord with the observation that the LF perturbation theory formula breaks down in the exact zero-mode case. This is made explicit using the DLCQ method - the discretized (finite-volume) version of the theory, where the light-front zero modes are manifestly absent, but the vacuum amplitudes still converge to their continuum-theory values with the increasing “harmonic resolution” K.

Traveling-Wave-Based Fault Location Method for Hybrid Distribution Network Mixed with Three-Phase and Phase to Phase Supply Lines

In China, a hybrid distribution network mixed with three-phase main lines and phase to phase supply lines can be found in many MV distribution networks due to lower cost of using two lines from three-phase main lines as well as lower cost of phase to phase transformer. For such a hybrid distribution network it is a challenge for traditional fault location techniques. This paper presents a traveling wave fault location method based on double-terminal measurement techniques. The proposed method analyses the traveling wave propagation mechanism of both aerial mode and zero mode components for a fault. The method then determines which mode component is used for the fault location according to fault types. The method has been developed and assessed on a typical distribution network using ATP power network simulation tool. The tests were conducted under various fault scenarios. The results show that zero mode component is more effective for a fault on the phase of three-phase main lines which is not linked to the phase to phase supply lines. However for a phase-to-phase fault, aerial mode component is more effective. For the remaining fault types, either aerial or zero mode component can be used.

Three Numerical Eigensolvers for 3-D Cavity Resonators Filled With Anisotropic and Nonconductive Media

This paper mainly investigates the classic resonant cavity problem with anisotropic and nonconductive media, which is a linear vector Maxwell's eigenvalue problem. The finite element method based on edge element of the lowest-order and standard linear element is used to solve this type of 3-D closed cavity problem. In order to eliminate spurious zero modes in the numerical simulation, the divergence-free condition supported by Gauss' law is enforced in a weak sense. After the finite element discretization, the generalized eigenvalue problem with a linear constraint condition needs to be solved. Penalty method, augmented method and projection method are applied to solve this difficult problem in numerical linear algebra. The advantages and disadvantages of these three computational methods are also given in this paper. Furthermore, we prove that the augmented method is free of spurious modes as long as the anisotropic material is not magnetic lossy. The projection method based on singular value decomposition technique can be used to solve the resonant cavity problem. Moreover, the projection method {cannot} introduce any spurious modes. At last, several numerical experiments are carried out to verify our theoretical results.

Ambiguities in the local thermal behavior of the scalar radiation in one-dimensional boxes

This paper reports certain ambiguities in the calculation of the ensemble average $\left<T_\mu{}_\nu\right>$ of the stress-energy-momentum tensor of an arbitrarily coupled massless scalar field in one-dimensional boxes in flat spacetime. The study addresses a box with periodic boundary condition (a circle) and boxes with reflecting edges (with Dirichlet's or Neumann's boundary conditions at the endpoints). The expressions for $\left<T^\mu{}^\nu\right>$ are obtained from finite-temperature Green functions. In an appendix, in order to control divergences typical of two dimensions, these Green functions are calculated for related backgrounds with arbitrary number of dimensions and for scalar fields of arbitrary mass, and specialized in the text to two dimensions and for massless fields. The ambiguities arise due to the presence in $\left<T^\mu{}^\nu\right>$ of double series that are not absolutely convergent. The order in which the two associated summations are evaluated matters, leading to two different thermodynamics for each type of box. In the case of a circle, it is shown that the ambiguity corresponds to the classic controversy in the literature whether or not zero mode contributions should be taken into account in computations of partition functions. In the case of boxes with reflecting edges, it results that one of the thermodynamics corresponds to a total energy (obtained by integrating the non homogeneous energy density over space) that does not depend on the curvature coupling parameter $\xi$ as expected; whereas the other thermodynamics curiously corresponds to a total energy that does depend on $\xi$. Thermodynamic requirements (such as local and global stability) and their restrictions to the values of $\xi$ are considered.

Modular flavor symmetry on a magnetized torus

We study the modular invariance in magnetized torus models. Modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework coupling constants such as Yukawa couplings are also transformed under the flavor symmetry. We show that the low-energy effective theory of magnetized torus models is invariant under a specific subgroup of the modular group. Since Yukawa couplings as well as chiral zero modes transform under the modular group, the above modular subgroup (referred to as modular flavor symmetry) provides a new type of modular invariant flavor models with $D_4 \times \mathbb{Z}_2$, $(\mathbb{Z}_4 \times \mathbb{Z}_2) \rtimes \mathbb{Z}_2$, and $(\mathbb{Z}_8 \times \mathbb{Z}_2) \rtimes \mathbb{Z}_2$. We also find that conventional discrete flavor symmetries which arise in magnetized torus model are non-commutative with the modular flavor symmetry. Combining both two symmetries we obtain a larger flavor symmetry, where the conventional flavor symmetry is a normal subgroup of the whole group.

Untying links through anti-parity-time-symmetric coupling

We reveal how the vector field links are untied under the influence of anti-parity-time-symmetric couplings in a dissipative sublattice-symmetric topological photonic crystal lattice. The topology of the quasi-one-dimensional two-band system is encoded in the geometric topology of the vector fields associated with the Bloch Hamiltonian. The linked vector fields reflect the topology of the nontrivial phase. The topological phase transition occurs concomitantly with the untying of the vector field link at the exceptional points. Counterintuitively, more dissipation constructively creates a nontrivial topology. The linking number predicts the number of topological photonic zero modes.

BTZ one-loop determinants via the Selberg zeta function for general spin

We relate the heat kernel and quasinormal mode methods of computing the 1-loop partition function of arbitrary spin fields on a rotating (Euclidean) BTZ background using the Selberg zeta function associated with ℍ3/ℤ, extending (arXiv:1811.08433) [1]. Previously, Perry and Williams [2] showed for a scalar field that the zeros of the Selberg zeta function coincide with the poles of the associated scattering operator upon a relabeling of integers. We extend the integer relabeling to the case of general spin, and discuss its relationship to the removal of non-square-integrable Euclidean zero modes.

Majorana oscillations and parity crossings in semiconductor nanowire-based transmon qubits

We show that the microwave (MW) spectra in semiconductor-nanowire-based transmon qubits provide a strong signature of the presence of Majorana bound states in the junction. This occurs as an external magnetic field tunes the wire into the topological regime and the energy splitting of the emergent Majorana modes oscillates around zero energy owing to their wave function spatial overlap in finite-length wires. In particular, we discuss how these Majorana oscillations, and the concomitant fermion parity switches in the ground state of the junction, result in distinct spectroscopic features --in the form of an intermitent visibility of absorption lines-- that strongly deviate from standard transmon behavior. In contrast, non-oscillating zero modes, such as topologically trivial Andreev bound states resulting from sufficiently smooth potentials, exhibit an overall standard transmon response. These differences in the MW response could help determine whether the junction contains topological Majoranas or not.

Projective symmetry group classifications of quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices

We perform extensive classifications of $\mathbb{Z}_2$ quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic lattices using a spin-rotation invariant fermionic projective symmetry group approach. Taking into account that all three lattices share the same point group $O_h$, we apply an efficient gauge where the classification for the simple cubic lattice can be partially carried over to the other two lattices. We identify hundreds of projective representations for each of the three lattices, however, when constructing short-range mean-field models for the fermionic partons (spinons) these phases collapse to only very few relevant cases. We self-consistently calculate the corresponding mean-field parameters for frustrated Heisenberg models on all three lattices with up to third neighbor spin interactions and discuss the spinon dispersions, ground state energies and dynamical spin structure factors. Our results indicate that phases with non-uniform spinon hopping or pairing amplitudes are energetically favored. An unusual situation is identified for the fcc lattice where the spinon dispersion minimizing the mean-field energy features a network of symmetry protected line-like zero modes in reciprocal space. We further discuss characteristic fingerprints of these phases in the dynamical spin structure factor which may help to identify and distinguish them in future numerical or experimental studies.

From Andreev to Majorana bound states in hybrid superconductor–semiconductor nanowires

Inhomogeneous superconductors can host electronic excitations, known as Andreev bound states (ABSs), below the superconducting energy gap. With the advent of topological superconductivity, a new kind of zero-energy ABS with exotic qualities, known as a Majorana bound state (MBS), has been discovered. A special property of MBS wavefunctions is their non-locality, which, together with non-Abelian braiding, is the key to their promise in topological quantum computation. We focus on hybrid superconductor–semiconductor nanowires as a flexible and promising experimental platform to realize one-dimensional topological superconductivity and MBSs. We review the main properties of ABSs and MBSs, state-of-the-art techniques for their detection and theoretical progress beyond minimal models, including different types of robust zero modes that may emerge without a band-topological transition.

Squaring the fermion: The threefold way and the fate of zero modes

We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension we establish three fundamental no-go theorems that prove the absence of: parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting non-interacting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of non-interacting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models.