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What is a particle-conserving Topological Superfluid? The fate of Majorana modes beyond mean-field theory
We investigate Majorana modes of number-conserving fermionic superfluids from both basic physics principles, and concrete models perspectives. After reviewing a criterion for establishing topological superfluidity in interacting systems, based on many-body fermionic parity switches, we reveal the emergence of zero-energy modes anticommuting with fermionic parity. Those many-body Majorana modes are constructed as coherent superpositions of states with different number of fermions. While realization of Majorana modes beyond mean field is plausible, we show that the challenge to quantum-control them is compounded by particle-conservation, and more realistic protocols will have to balance engineering needs with astringent constraints coming from superselection rules. Majorana modes in number-conserving systems are the result of a peculiar interplay between quantum statistics, fermionic parity, and an unusual form of spontaneous symmetry breaking. We test these ideas on the Richardson–Gaudin–Kitaev chain, a number-conserving model solvable by way of the algebraic Bethe ansatz, and equivalent in mean field to a long-range Kitaev chain.
Gauged baryon and lepton number in MSSM{sub 4} brane worlds
A recent D-brane model designed to accommodate a phenomenologically acceptable fourth generation of chiral fermions was noted to produce an unexpected additional unbroken nonanomalous U(1) gauge group at the string scale. We show that the corresponding charges acting on minimal supersymmetric standard model fields count baryon and lepton numbers. If broken spontaneously at lower scales, these U(1){sub B} and U(1){sub L} symmetries provide potential avenues for preserving baryogenesis while nonetheless explaining the suppression of proton decay (without the need for R parity), as well as the smallness of right-handed neutrino Majorana masses compared to the string scale.
Neutrinoless double- β decay in effective field theory: The light-Majorana neutrino-exchange mechanism
Not Available
Neutrino Masses from Generalized Symmetry Breaking
We explore generalized global symmetries in theories of physics beyond the standard model. Theories of Z ′ bosons generically contain “noninvertible” chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well motivated U ( 1 ) L μ − L τ , there is a noninvertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g., U ( 1 ) L μ − L τ ⊂ SU ( 3 ) H , where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas, e.g., y ν ∼ y τ exp ( − S inst ) . These theories require no bevy of new fields nor additional global symmetries but are instead simple, natural, and predictive: The discovery of a lepton family Z ′ at low energies will reveal the scale at which L μ − L τ emerges from a larger gauge symmetry. Published by the American Physical Society 2024
Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising interlayer interactions, deriving effective models via perturbation theory and performing Majorana mean-field theory calculations. We show that a diverse array of magnetic and topological phase transitions occur, depending on the direction of the interlayer Ising interaction and the relative sign of Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite signs of the Kitaev interaction, we observe a notable weakening of magnetic ordering tendencies and the Kitaev spin liquid survives up to a remarkably larger interlayer exchange. Our mean-field analysis suggests the emergence of an intermediate gapped ℤ 2 spin-liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated 120° compass model. We furthermore use perturbation theory to study the model with the Ising axis pointing along the $\hat{z}$ axis or lying in the 𝑥𝑦 plane. In both cases, our analysis reveals the formation of one-dimensional Ising chains, which remain decoupled in perturbation theory, resulting in a subextensive ground-state degeneracy. Our results highlight the interplay between topological order and magnetic ordering tendencies in bilayer quantum spin liquids.
Majorana path integral for nonequilibrium dynamics of two-level systems
We present a new field-theoretic approach to analyze nonequilibrium dynamics of two-level systems (TLS), which is based on a correspondence between a driven TLS and a Majorana fermion field theory coupled to bosonic fields. This approach allows us to calculate analytically properties of nonlinear TLS dynamics with an arbitrary accuracy. We apply our method to analyze specific TLS dynamics under a monochromatic periodic drive that is relevant to the problem of decoherence in Josephson junction qubits. It is demonstrated that the method gives the precise positions of the resonance peaks in the nonlinear dielectric response function that are in agreement with numerical simulations.
Path from Lattice QCD to the Short-Distance Contribution to 0 ν β β Decay with a Light Majorana Neutrino
Not Available
Classification of (2 + 1) D invertible fermionic topological phases with symmetry
Here we provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups G f and general values of the chiral central charge c - . Here G f is a central extension of a bosonic symmetry group G b by fermion parity, (-1) F , specified by a second cohomology class [ω 2 ]∈ $\mathscr{H}^2$(Gb,$\mathbb{Z}_2$). Our approach proceeds by gauging fermion parity and classifying the resulting G b symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c - ) 1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c - = 0. We show how the tenfold way classification of topological insulators and superconductors fits into our scheme, along with general nonperturbative constraints due to certain choices of c - and G f . Mathematically, our results also suggest an explicit general parametrization of deformation classes of (2 + 1)D invertible topological quantum field theories with G f symmetry.
The contribution of light Majorana neutrinos to neutrinoless double beta decay and cosmology
Cosmology is making impressive progress and it is producing stringent bounds on the sum of the neutrino masses Σ, a parameter of great importance for the current laboratory experiments. In this letter, we exploit the potential relevance of the analysis of Palanque-Delabrouille et al. to the neutrinoless double beta decay (0νββ) search. This analysis indicates small values for the lightest neutrino mass, since the authors find Σ<84 meV at 1σ C.L., and provides a 1σ preference for the normal hierarchy. The allowed values for the Majorana effective mass, probed by 0νββ, turn out to be <75 meV at 3σ C.L. and lower down to less than 20 meV at 1σ C.L. . If this indication is confirmed, the impact on the 0νββ experiments will be tremendous since the possibility of detecting a signal will be out of the reach of the next generation of experiments.
Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
We study the geometric measure of entanglement (GM) of pure symmetric states related to rank 1 positive-operator-valued measures (POVMs) and establish a general connection with quantum state estimation theory, especially the maximum likelihood principle. Based on this connection, we provide a method for computing the GM of these states and demonstrate its additivity property under certain conditions. In particular, we prove the additivity of the GM of pure symmetric multiqubit states whose Majorana points under Majorana representation are distributed within a half sphere, including all pure symmetric three-qubit states. We then introduce a family of symmetric states that are generated from mutually unbiased bases and derive an analytical formula for their GM. These states include Dicke states as special cases, which have already been realized in experiments. We also derive the GM of symmetric states generated from symmetric informationally complete POVMs (SIC POVMs) and use it to characterize all inequivalent SIC POVMs in three-dimensional Hilbert space that are covariant with respect to the Heisenberg-Weyl group. Finally, we describe an experimental scheme for creating the symmetric multiqubit states studied in this article and a possible scheme for measuring the permanence of the related Gram matrix.
Structure of the Majorana Clifford group
In quantum information science, Clifford operators and stabilizer codes play a central role for systems of qubits (or qudits). In this study, we study their analogs for systems composed of Majorana fermions. In this case, a crucial role is played by fermion parity symmetry, which is an unbreakable symmetry present in any system with fundamentally fermionic degrees of freedom. We prove that the subgroup of parity-preserving Majorana Cliffords can be represented by the orthogonal group over the binary field 𝔽 2 , and we show how it can be generated by braiding operators and used to construct any (even-parity) Majorana stabilizer code. We also analyze the frame potential for this so-called p-Clifford group when acting on a fixed-parity sector of the Hilbert space, proving that it is equivalent to the frame potential of the ordinary Clifford group acting on the same sector.
Multichannel Topological Kondo Effect
A Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group SO(M). The impurity spin stems from the nonlocal topological ground state degeneracy of the island and thus the effect is known as the topological Kondo effect. We introduce a physically motivated N-channel generalization of the topological Kondo model. Starting from the simplest case N =2, we conjecture a stable intermediate coupling fixed point and evaluate the resulting low-temperature impurity entropy. The impurity entropy indicates that an emergent Fibonacci anyon can be realized in the N =2 model. We also map the case N =2, M =4 to the conventional four-channel Kondo model and find the conductance at the intermediate fixed point. By using the perturbative renormalization group, we also analyze the large-N limit, where the fixed point moves to weak coupling. In the isotropic limit, we find an intermediate stable fixed point, which is stable to “exchange” coupling anisotropies, but unstable to channel anisotropy. We evaluate the fixed point impurity entropy and conductance to obtain experimentally observable signatures of our results. Here, in the large-N limit, we evaluate the full crossover function describing the temperature-dependent conductance.
Topological quantum phase transitions in the spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings
We examine the topological properties of a spin–singlet superconductor with Rashba and Dresselhaus (110) spin–orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov–de Gennes (BdG) Hamiltonian by symmetry analysis. In particular, the Pfaffian invariant P for the particle–hole symmetry can be used to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, an edge index, namely the Pfaffian invariant P(k{sub y}) or the winding number W(k{sub y}), is needed to make them topologically stable. These edge indices can also be used in determining the location of the Majorana flat bands. - Highlights: • Majorana fermion can emerge in the spin–orbit coupled singlet superconductor. • Pfaffian invariant and 1D winding number can be used to identify the nontrivial topological phase where Majorana flat band exists. • All the possible phase diagrams in the spin–orbit coupled singlet superconductor are demonstrated. • Majorana flat band only exists in the y direction in our model. • Majorana flat band has a significant experimental signature in the tunneling conductance measurement.
The expanding search for Majorana particles
The reports in this issue about half-quantum vortices in strontium ruthenate (page 17) and about spin-orbit coupling in a nanowire (page 19) both involve a system in which theorists have proposed that one might find an elusive Majorana particle. A system of Majorana particles might be a good candidate for a topological quantum computer.
Low radioactivity CaF{sub 2} scintillator crystals for CANDLES
CANDLES is the project to search for neutrinoless double beta (0{nu}{beta}{beta}) decay of {sup 48}Ca by using CaF{sub 2} scintillators. The observation of 0{nu}{beta}{beta} decay will prove the existence of massive Majorana neutrinos. Expected performances and current status of the CANDLES system are described.
Low Radioactive Techniques in SuperNEMO: Status of the Radon R and D
Radon is a well-known source of background with respect to the search for neutrinoless double beta decay (0{nu}{beta}{beta}), due to the high Q{sub {beta}} value of one of its daughter nucleus {sup 214}Bi. Radon has been observed and reduced down to 6.5 mBq/m{sup 3} in the NEMO-3 experiment which is looking for the 0{nu}{beta}{beta} process in {sup 100}Mo and in six other isotopes. The SuperNEMO project, a next-generation double beta decay experiment which will also use a tracko-calorimeter technique, has been in an R and D phase since 2006. The goal is to reach a sensitivity of T{sub 1/2}(0{nu})>10{sup 26} y corresponding to an effective Majorana neutrino mass of 0.05-0.1 eV with 100 kg of {sup 82}Se. Such a sensitivity requires in particular to improve the radon radiopurity down to 0.1 mBq/m{sup 3} in the tracking chamber.
Status of the Majorana Demonstrator experiment
The Majorana Demonstrator neutrinoless double beta-decay experiment is currently under construction at the Sanford Underground Research Facility in South Dakota, USA. An overview and status of the experiment are given.