Exact Symmetry Research Articles

An equivariant Bayesian convolutional network predicts recombination hotspots and accurately resolves binding motifs.

MotivationConvolutional neural networks (CNNs) have been tremendously successful in many contexts, particularly where training data are abundant and signal-to-noise ratios are large. However, when predicting noisily observed phenotypes from DNA sequence, each training instance is only weakly informative, and the amount of training data is often fundamentally limited, emphasizing the need for methods that make optimal use of training data and any structure inherent in the process.ResultsHere we show how to combine equivariant networks, a general mathematical framework for handling exact symmetries in CNNs, with Bayesian dropout, a version of Monte Carlo dropout suggested by a reinterpretation of dropout as a variational Bayesian approximation, to develop a model that exhibits exact reverse-complement symmetry and is more resistant to overtraining. We find that this model combines improved prediction consistency with better predictive accuracy compared to standard CNN implementations and state-of-art motif finders. We use our network to predict recombination hotspots from sequence, and identify binding motifs for the recombination–initiation protein PRDM9 previously unobserved in this data, which were recently validated by high-resolution assays. The network achieves a predictive accuracy comparable to that attainable by a direct assay of the H3K4me3 histone mark, a proxy for PRDM9 binding.Availability and implementation https://github.com/luntergroup/EquivariantNetworks Supplementary information Supplementary data are available at Bioinformatics online.

Consequences of μ−τ reflection symmetry at DUNE

We consider minimal type-I seesaw framework to realize $ \mu-\tau $ reflection symmetry in the low-energy neutrino mass matrix, $ M_{\nu} $. Considering DUNE experiment, we scrutinize its potential to measure the precision of 2-3 mixing angle, $ \theta_{23} $ and the Dirac CP-phase, $ \delta $ for the given symmetry. Later, we examine the precision of these two parameters considering NuFit-3.2 data as one of the important true points. To study the low-energy phenomenology, we further discuss various breaking patterns of such an exact symmetry. Moreover, for each breaking scenario we perform the capability test of DUNE for the determination of $ \theta_{23} $ and to establish the phenomenon of CP violation considering the true benchmark point arising from the breaking of $ \mu-\tau $ reflection symmetry. We also make remarks on the potential of DUNE to rule out maximal CP-violation or CP-conservation hypothesis at a certain confidence level for different scenarios.

Flux-stabilized Majorana zero modes in coupled one-dimensional Fermi wires

One promising avenue to study one-dimensional ($1$D) topological phases is to realize them in synthetic materials such as cold atomic gases. Intriguingly, it is possible to realize Majorana boundary modes in a $1$D number-conserving system consisting of two fermionic chains coupled only by pair-hopping processes. It is commonly believed that significant interchain single-particle tunneling necessarily destroys these Majorana modes, as it spoils the $\mathbb{Z}_2$ fermion parity symmetry that protects them. In this Letter, we present a new mechanism to overcome this obstacle, by piercing a (synthetic) magnetic $\pi$-flux through each plaquette of the Fermi ladder. Using bosonization, we show that in this case there exists an exact leg-interchange symmetry that is robust to interchain hopping, and acts as fermion parity at long wavelengths. We utilize density matrix renormalization group and exact diagonalization to verify that the resulting model exhibits Majorana boundary modes up to large single-particle tunnelings, comparable to the intrachain hopping strength. Our work highlights the unusual impacts of different topologically trivial band structures on these interaction-driven topological phases, and identifies a distinct route to stabilizing Majorana boundary modes in $1$D fermionic ladders.

Charged lepton flavor violation and electric dipole moments in the inert Zee model

The inert Zee model is an extension of the Zee model for neutrino masses to allow for a solution to the dark matter problem that involves two vector-like fields, a doublet and a singlet of SU(2)L, and two scalars, also a doublet and a singlet of SU(2)L, all of them being odd under an exact Z2 symmetry. The introduction of the Z2 guarantees one-loop neutrino masses, forbids tree-level Higgs-mediated flavor changing neutral currents and ensures the stability of the dark matter candidate. Due to the natural breaking of lepton numbers in the inert Zee model and encouraged by the ambitious experimental program designed to look for charged lepton flavor violation signals and the electron electric dipole moment, we study the phenomenology of the processes leading to these kind of signals, and establish which are the most promising experimental perspectives on that matter.

Models of exotic interferometer cross-correlations in emergent space-time

A Lorentz invariant framework is developed to model the cross spectrum of two interferometers in a space-time that emerges from a Planck scale quantum system with exact causal symmetry and holographic spacelike rotational correlations. Space-time relationships between world lines are generated by entanglement of geometrical states on causal diamonds. The entanglement is tied to a unique observable signature: an exotic imaginary broad band cross spectrum, with a frequency structure determined by the layout of the interferometers. The models will be used to interpret data from the reconfigured Fermilab Holometer, and for conceptual design of future experiments.

Dark matter assisted Dirac leptogenesis and neutrino mass

We propose an extension of the standard model with U(1)B–L×Z2 symmetry. In this model by assuming that the neutrinos are Dirac (i.e.B–L is an exact symmetry), we found a simultaneous solution for non zero neutrino masses and dark matter content of the universe. The observed baryon asymmetry of the universe is also explained using Dirac Leptogenesis, which is assisted by a dark sector, gauged under a U(1)D symmetry. The latter symmetry of the dark sector is broken at a TeV scale and thereby giving mass to a neutral gauge boson ZD. The standard model Z-boson mixes with the gauge boson ZD at one loop level and paves a way to detect the dark matter through spin independent elastic scattering at terrestrial laboratories.

Hidden charge-conjugation, parity, and time-reversal symmetries and massive Goldstone (Higgs) modes in superconductors

A massive Goldstone (MG) mode, often referred to as a Higgs amplitude mode, is a collective excitation that arises in a system involving spontaneous breaking of a continuous symmetry, along with a gapless Nambu-Goldstone mode. It has been known in the previous studies that a pure amplitude MG mode emerges in superconductors if the dispersion of fermions exhibits the particle-hole (p-h) symmetry. However, clear understanding of the relation between the symmetry of the Hamiltonian and the MG modes has not been reached. Here we reveal the fundamental connection between the discrete symmetry of the Hamiltonian and the emergence of pure amplitude MG modes. To this end, we introduce nontrivial charge-conjugation ($\mathcal C$), parity ($\mathcal P$), and time-reversal ($\mathcal T$) operations that involve the swapping of pairs of wave vectors symmetrical with respect to the Fermi surface. The product of $\mathcal{CPT}$ (or its permutations) represents an exact symmetry analogous to the CPT theorem in the relativistic field theory. It is shown that a fermionic Hamiltonian with a p-h symmetric dispersion exhibits the discrete symmetries under $\mathcal C$, $\mathcal P$, $\mathcal T$, and $\mathcal{CPT}$. We find that in the superconducting ground state, $\mathcal T$ and $\mathcal P$ are spontaneously broken simultaneously with the U(1) symmetry. Moreover, we rigorously show that amplitude and phase fluctuations of the gap function are uncoupled due to the unbroken $\mathcal C$. In the normal phase, the MG and NG modes become degenerate, and they have opposite parity under $\mathcal T$. Therefore, we conclude that the lifting of the degeneracy in the superconducting phase and the resulting emergence of the pure amplitude MG mode can be identified as a consequence of the the spontaneous breaking of $\mathcal T$ symmetry but not of $\mathcal P$ or U(1).

Dual simulation of the 2d U(1) gauge Higgs model at topological angle θ = π: Critical endpoint behavior

We simulate the 2d U(1) gauge Higgs model on the lattice with a topological angle θ. The corresponding complex action problem is overcome by using a dual representation based on the Villain action appropriately endowed with a θ-term. The Villain action is interpreted as a non-compact gauge theory whose center symmetry is gauged and has the advantage that the topological term is correctly quantized so that 2π periodicity in θ is intact. Because of this the θ=π theory has an exact Z2 charge-conjugation symmetry C, which is spontaneously broken when the mass-squared of the scalars is large and positive. Lowering the mass squared the symmetry becomes restored in a second order phase transition. Simulating the system at θ=π in its dual form we determine the corresponding critical endpoint as a function of the mass parameter. Using a finite size scaling analysis we determine the critical exponents and show that the transition is in the 2d Ising universality class, as expected.

Nth-Order Approximate Lagrangians Induced by Perturbative Geometries

A family of perturbative Lagrangians that describe approximate and multidimensional Klein-Gordon equations are studied. We probe the existence of approximate Noether symmetries via generalized geometric conditions for a perturbation of any order. The knowledge of the geometric conditions uncovers that unlike exact symmetries, the approximate Noether symmetries of the Lagrangian which describes the motion of a particle in n-dimensional space under the action of an autonomous force, is inequivalent to the Noether symmetries admitted by the Klein-Gordon Lagrangian in general.

Berry phase of the composite-fermion Fermi sea: Effect of Landau-level mixing

We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low energy excitations following a recently developed approach [Pu, Wu and Jain, Phys. Rev. B 96, 195302 (2018)] and demonstrate them to be very accurate representations of the Coulomb eigenstates. We further ask how the Berry phase associated with a closed loop around the Fermi circle, predicted to be $\pi$ in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)], is affected by Landau level mixing. For this purpose, we consider a simple model wherein we determine the variational ground state as a function of Landau level mixing within the space spanned by two basis functions: the lowest-Landau-level projected and the unprojected composite-fermion Fermi sea wave functions. We evaluate Berry phase for a path around the Fermi circle within this model following a recent prescription, and find that it rotates rapidly as a function of Landau level mixing. We also consider the effect of a particle-hole symmetry breaking three-body interaction on the Berry phase while confining the Hilbert space to the lowest Landau level. Our study deepens the connection between the $\pi$ Berry phase and the exact particle-hole symmetry in the lowest Landau level.

Threshold effects and the line shape of the X(3872) in effective field theory

Latest measurements suggest that the X(3872) mass lies less than 200 keV away from the D0-Dbar0* threshold, reenforcing its interpretation as a loosely-bound mesonic molecule. This observation implies that in processes like D0-Dbar0-pi0 production, threshold effects could disguise the actual pole position of the X(3872). We propose a new effective field theory with D0, Dbar0 and pi0 degrees of freedom for the X(3872), considering Galilean invariance to be an exact symmetry. The D0* enters as a D0-pi0 p-wave resonance, allowing for a comprehensive study of the influence of pion interactions on the X(3872) width. We calculate relations between the mass of the X(3872), its width, and its line shape in D0-Dbar0-pi0 production up to next-to-leading order. Our results provide a tool for the extraction of the X(3872) pole position from the experimental data near threshold.

Broken mirror symmetry in S36 and Ca36

Shape coexistence is an ubiquitous phenomenon in the neutron-rich nuclei belonging to (or sitting at the shores of) the $N=20$ Island of Inversion (IoI). Exact isospin symmetry predicts the same behaviour for their mirrors and the existence of a proton-rich IoI around $Z=20$, centred in the (surely unbound) nucleus $^{32}$Ca. In this article we show that in $^{36}$Ca and $^{36}$S, Coulomb effects break dramatically the mirror symmetry in the excitation energies, due to the different structures of the intruder and normal states. The Mirror Energy Difference (MED) of their 2$^+$ states is known to be very large at -246 keV. We reproduce this value and predict the first excited state in $^{36}$Ca to be a 0$^+$ at 2.7 MeV, 250 keV below the first 2$^+$. In its mirror $^{36}$S the 0$^+$ lies at 55 keV above the 2$^+$ measured at 3.291 MeV. Our calculations predict a huge MED of -720 keV, that we dub "Colossal" Mirror Energy Difference (CMED). A possible reaction mechanism to access the 0$^+_2$ in $^{36}$Ca will be discussed. In addition, we theoretically address the MED's of the $A=34$ $T=3$ and $A=32$ $T=4$ mirrors.

Exploiting Identical Generators in Unit Commitment

We present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually nondominated solutions. We study the impact of aggregation on two large-scale UC instances: one from the academic literature and the other based on real-world operator data. Our computational tests demonstrate that, when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Furthermore, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.

Using mixed many-body particle states to generate exact -symmetry in a time-dependent four-well system

Bose–Einstein condensates with balanced gain and loss in a double-well potential have been shown to exhibit -symmetric states. As proposed by Kreibich (2013 Phys. Rev. A 87 051601), in the mean-field limit the dynamical behaviour of this system, especially that of the -symmetric states, can be simulated by embedding it into a Hermitian four-well system with time-dependent parameters. In this paper we go beyond the mean-field approximation and investigate many-body effects in this system, which are in lowest order described by the single-particle density matrix. The conditions for symmetry in the single-particle density matrix cannot be completely fulfilled by using pure initial states. Here we show that it is mathematically possible to achieve exact symmetry in the four-well many-body system in the sense of the dynamical behaviour of the single-particle density matrix. In contrast to previous work, for this purpose, we use mixed initial states fulfilling certain constraints and use them to calculate the dynamics.

Spin Momentum–Locked Surface States in Metamaterials without Topological Transition

AbstractThe photonic analogy of the quantum spin Hall Effect, that is, a photonic topological insulator (PTI), is of great relevance to science and technology in optics based on the promise of scattering‐free surface states. The challenges in realizing such scattering‐free surface states in PTIs and other types of symmetry‐protected topological phases are the result of the exact symmetry needed for creating a pair of time reversal pseudo‐spin states or special boundary conditions, wherein the exact symmetry imposes strict requirements on materials or boundary conditions. Here, it is experimentally demonstrated that scattering‐free edge states can be created with neither the aforementioned exact symmetry requirements for materials nor the topological transitions. This system is constructed by simply placing together regular homogeneous metamaterials, which are characterized by highly different bianisotropies. Of the particular surface states, backward reflection would be deeply suppressed, provided that the related evanescent tail into the bulk regions vanishes shortly and that the pseudo‐spin is not flipped by the scatterers. This work gives an example of constructing scattering‐free surface states in classical systems without strict symmetry protections and may potentially stimulate various novel applications in the future.

Gap Symmetry of the Heavy Fermion Superconductor CeCu_{2}Si_{2} at Ambient Pressure.

Recent observations of two nodeless gaps in superconducting CeCu_{2}Si_{2} have raised intensive debates on its exact gap symmetry, while a satisfactory theoretical basis is still lacking. Here we propose a phenomenological approach to calculate the superconducting gap functions, taking into consideration both the realistic Fermi surface topology and the intra- and interband quantum critical scatterings. Our calculations yield a nodeless s^{±}-wave solution in the presence of strong interband pairing interaction, in good agreement with experiments. This provides a possible basis for understanding the superconducting gap symmetry of CeCu_{2}Si_{2} at ambient pressure and indicates the potential importance of multiple Fermi surfaces and interband pairing interaction in understanding heavy fermion superconductivity.

Itinerant quantum multicriticality of two-dimensional Dirac fermions

We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders, which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $O(S_1)$ and $O(S_2)$ symmetries in the ordered phase. Performing a renormalization group analysis by using the $\epsilon=(3-d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an \emph{enlarged} $O(S_1+S_2)$ chiral symmetry. Such a fixed point acts as an exotic quantum multi-critical point (MCP), governing the \emph{continuous} semimetal-insulator as well as insulator-insulator (for example antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either $O(S_1)$ or $O(S_2)$ chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher dimensional Dirac fermions is also outlined.

Topology and strong four fermion interactions in four dimensions

We study massless fermions interacting through a particular four fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms. We determine the structure of the low energy effective action for the auxiliary field needed to generate the four fermion term and find it has an novel structure that admits topologically non-trivial defects with non-zero Hopf invariant. We show that fermions propagating in such a background pick up a mass without breaking symmetries. Furthermore pairs of such defects experience a logarithmic interaction. We argue that a phase transition separates a phase where these defects proliferate from a broken phase where they are bound tightly. We conjecture that by tuning one additional operator the broken phase can be eliminated with a single BKT-like phase transition separating the massless from massive phases.

The effective theory of shift-symmetric cosmologies

A shift symmetry is a ubiquitous ingredient in inflationary models, both in effective constructions and in UV-finite embeddings such as string theory. It has also been proposed to play a key role in certain Dark Energy and Dark Matter models. Despite the crucial role it plays in cosmology, the observable, model independent consequences of a shift symmetry are yet unknown. Here, assuming an exact shift symmetry, we derive these consequences for single-clock cosmologies within the framework of the Effective Field Theory of Inflation. We find an infinite set of relations among the otherwise arbitrary effective coefficients, which relate non-Gaussianity to their time dependence. For example, to leading order in derivatives, these relations reduce the infinitely many free functions in the theory to just a single one. Our Effective Theory of shift-symmetric cosmologies describes, among other systems, perfect and imperfect superfluids coupled to gravity and driven superfluids in the decoupling limit. Our results are the first step to determine observationally whether a shift symmetry is at play in the laws of nature and whether it is broken by quantum gravity effects.

Lifted Generalized Dual Decomposition

Many real-world problems, such as Markov Logic Networks (MLNs) with evidence, can be represented as a highly symmetric graphical model perturbed by additional potentials. In these models, variational inference approaches that exploit exact model symmetries are often forced to ground the entire problem, while methods that exploit approximate symmetries (such as by constructing an over-symmetric approximate model) offer no guarantees on solution quality. In this paper, we present a method based on a lifted variant of the generalized dual decomposition (GenDD) for marginal MAP inference which provides a principled way to exploit symmetric sub-structures in a graphical model. We develop a coarse-to-fine inference procedure that provides any-time upper bounds on the objective. The upper bound property of GenDD provides a principled way to guide the refinement process, providing good any-time performance and eventually arriving at the ground optimal solution.