Symmetry Breaking Research Articles

Moduli spaces in CFT: large charge operators

Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry is also broken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space.

Nonreciprocal transmission in silicon micromechanical resonators via parity-time symmetry breaking

Nonreciprocal transmission in silicon micromechanical resonators via parity-time symmetry breaking

Nonreciprocal Acoustic Devices with Asymmetric Peierls Phases.

Nonreciprocity in acoustics is of paramount importance in many practical applications and has been experimentally realized using nonlinear media, moving fluids, or time modulation, which regrettably suffer from large volumes and high-power consumption, difficulty in integration, and inevitable vibrations or phase noise. In modern Hamiltonian theory, the violation of system's reciprocity can be achieved via asymmetric Peierls phases, which typically involves with non-Hermiticity or time-reversal symmetry breaking. Here, we propose a framework for designing nonreciprocal acoustic devices based on the asymmetric Peierls phases that can be fully controlled via active acoustic components. The fully controlled Peierls phases enable various high-performance acoustic devices, including non-Hermitian extensions of isolators, gyrators, and circulators, which are otherwise impossible in previous approaches that are bound by Hermiticity or passivity. We reveal that the transmission phases in isolators are equivalent to the Peierls phase plus a constant. The nonreciprocal phase delay in gyrators and the unirotational transmission behavior in circulators result from the gauge-invariant Aharonov-Bohm phases determined by Peierls phases. Our work not only uncovers multiple intriguing physics related to Peierls phases but also provides a general approach to compact, integratable, nonreciprocal acoustic devices.

Generalizations of Parisi’s replica symmetry breaking and overlaps in random energy models

Generalizations of Parisi’s replica symmetry breaking and overlaps in random energy models

Future targets for light gauge bosons from cosmic strings

Cosmic strings, theoretical one-dimensional topological defects from the early universe, provide a valuable opportunity for exploring dark matter (DM) production and gravitational wave (GW) emission. Our study investigates the production of gauge bosons and GW emission from cosmic string decay, considering the constraints imposed by cosmological observations. We specifically examine how gauge bosons radiated from strings contribute to DM and dark radiation, with limits set by the observed DM abundance and cosmic microwave background data, respectively. Additionally, we analyze the gravitational wave spectrum of this model across both low and high frequencies. Notably, the spectrum typically follows a f−1/3 pattern at high frequencies, beyond the pivot frequency f∗. We derive an analytical expression for the frequency f∗ and confirm its accuracy through numerical verification. Furthermore, we compare the GW spectrum of this model with the forecasted capabilities of future GW observatories, such as the Einstein Telescope, the Laser Interferometer Space Antenna, the Big Bang Observer, and μAres. Finally, we discuss how these considerations impact the model parameters, specifically the gauge boson mass and the energy scale of U(1) symmetry breaking, providing insights into how cosmic strings could enhance our understanding of DM and GW astronomy.

PT Symmetry Breaking Induced Anomalous Valley Hall Effect in 2D Antiferromagnetic Semiconductor.

Realizing the anomalous valley Hall (AVH) effect in two-dimensional (2D) materials is of crucial importance for information processing and recording technology. While the research in this field mainly focuses on ferromagnetic systems, little is known about antiferromagnetic systems. Here, using k·p model analysis, we report a novel mechanism of realizing the AVH effect in 2D antiferromagnetic materials. This physics is related to the PT symmetry breaking induced by intrinsic staggered sublattice potential, which is introduced by asymmetric magnetic ions located at different sublattices. With reversal of the magnetic orientation on different sublattices, the AVH effect can be reversed. Based on first-principles calculations, we further demonstrate this mechanism in an antiferromagnetic monolayer of NiRuCl6. Intriguingly, due to the d orbital mismatch near the Fermi level, monolayer NiRuCl6 simultaneously owns zero net magnetization and large spin splitting and valley polarizations, which facilitates the observation of the AVH effect. Our findings greatly enrich the research on valley physics in antiferromagnetic systems.

Ultrafast and Coherent Dynamics in a Solvent Switchable "Pink Box" Perylene Diimide Dimer.

Perylene diimide (PDI) dimers and higher aggregates are key components in organic molecular photonics and photovoltaic devices, supporting singlet fission and symmetry breaking charge separation. Detailed understanding of their excited states is thus important. This has proven challenging because interchromophoric coupling is a strong function of dimer architecture. Recently, a macrocyclic PDI dimer was reported in which excitonic coupling could be turned on and off simply by changing the solvent. This presents a useful case where coupling is modified without synthetic changes to tune supramolecular structure. Here we present a detailed study of solvent dependent excited state dynamics in this dimer by means of coherent multidimensional spectroscopy. Spectral analysis resolves the different coupling strengths, which are consistent with solvent dependent changes in dimer conformation. The strongly coupled conformer forms an excimer within 300 fs. The low-frequency Raman active modes recovered from two-dimensional electronic spectra reveal frequencies characteristic of exciton coupling. These are assigned to modes modulating the coupling from the corresponding DFT calculations. Further analysis reveals a time dependent frequency during excimer formation. Analysis of two-dimensional "beatmaps" reveals features in the coupled dimer which are not predicted by the displaced harmonic oscillator model and are assigned to vibronic coupling.

Self-organisation and megaregional transport planning along the North Coast of Java

This article explores the intricate relationship between self-organisation and planning in megaregional transportation dynamics, using the North Coast of Java as a case study. Focusing on circular migration during the Eid holiday season, the study identifies the crucial roles of symmetry breaks, feedback loops and interventions in shaping transportation patterns. Specifically, the article employs qualitative methods, including interviews with key stakeholders and analysis of transportation data, to investigate the dynamics of circular migration. The findings reveal how planning interventions influence outcomes, emphasise the importance of multilevel governance, and offer insights for planning in complex systems. This work enhances our understanding of self-organisation and planning, providing valuable guidance for urban practitioners dealing with complex socio-spatial systems.

Broadband Spin and Orbital Momentum Modulator Using Self‐Assembled Nanostructures

AbstractThe structural symmetry of solids plays an important role in defining their linear and nonlinear optical properties. The quest for versatile, cost‐effective, large‐scale, and defect‐free approaches and materials platforms for tailoring structural and optical properties on demand is underway since decades. A self‐assembled spherulite material comprised of synthesized molecules with large dipole moments aligned azimuthally, forming a vortex polarity with spontaneously broken symmetry, is experimentally demonstrated. This unique self‐assembled structure enables new linear and nonlinear light–matter interactions, including generating optical vortex beams with complex spin states and on‐demand topological charges at the fundamental, doubled, and tripled frequencies. This work will likely enable numerous applications in areas such as high‐dimensional quantum information processing with large capacity and high security, spatiotemporal optical vortices, and a novel optical manipulation and trapping platform.

Nonlinear static behaviors of nonlocal nanobeams incorporating longitudinal linear temperature gradient

The elastic parameters and the coefficient of thermal expansion (CTE) of nanomaterials change with temperature. If the elastic modulus, the CTE, and the longitudinal linear temperature gradient are coupled, the longitudinal symmetry of the mechanical properties of nanobeams is broken. However, researchers have not yet to examine how this symmetry breaking affects the mechanical properties of nanobeams. This paper provides a new analysis of the modified thermoelastic beam model established by the nonlocal stress gradient theory. The present analysis incorporates the coupling of the longitudinal linear temperature gradient, elastic modulus, thermal expansion, and scale effect. Afterward, we apply the Galerkin method to explore the buckling, post-buckling, and transverse bending of a (10,10) single-walled carbon nanotube (SWCNT). The results show that the linear temperature gradient induces the breaking of the nanobeam's longitudinal symmetry and then results in the coupling of the symmetrical and antisymmetrical weight functions of the deformations. While the linear temperature gradient marginally affects the symmetry of nanobeams, it significantly raises the buckling temperature and introduces the complexity of the post-buckling and transverse force bending. In addition, the integration of the linear longitudinal temperature gradient, elastic modulus, and nonlocal effect more significantly affects nanobeams' mechanical properties than individual factors.

A prediction of high temperature magnetic coupling in transition metal phthalocyanines.

In spintronics, a perennial goal has been the generation of organic spin-bearing semiconductor materials with magnetic ordering stable at room temperature. To this end, the class of transition metal phthalocyanines has shown much promise in fulfilling this ambition. In particular, alpha-phase cobalt (II) phthalocyanine (α-CoPc) exhibits strong antiferromagnetic exchange interactions producing a long range order up to ∼100K. However, the underlying mechanism by which this magnetic interaction proceeds is not well understood. In this report, a simple mechanism has been proposed based on the Hubbard Hamiltonian, which elucidates the exchange coupling in α-CoPc. The mechanism provides stipulations for increasing the magnetic coupling, and this directs to a proposal that substitution of the central cobalt ion for rhodium will lead to a significant increase in coupling strength. The strength of this exchange interaction has been evaluated using broken symmetry hybrid exchange density functional theory and indicates that the novel rhodium (II) phthalocyanine system is indeed predicted to exhibit significantly stronger magnetic ordering. This study, therefore, identifies the coupling mechanism in α-CoPc as primarily attributable to kinetic exchange, explains its previously reported strong coupling relative to its first-row transition metal counterparts, and suggests that rhodium (II) phthalocyanine is likely to exhibit stable magnetic ordering at room temperature.

Optical orbital angular momentum analogy to the Stern-Gerlach experiment.

Symmetry breaking has been shown to reveal interesting phenomena in physical systems. A notable example is the fundamental work of Otto Stern and Walther Gerlach [Stern and Zerlach, Z. Physik9, 349 (1922)10.1007/BF01326983] nearly 100 years ago demonstrating a spin angular momentum (SAM) deflection that differed from classical theory. Here we use non-separable states of SAM and orbital angular momentum (OAM), known as vector vortex modes, to demonstrate how a classical optics analogy can be used to reveal this non-separability, reminiscent of the work carried out by Stern and Gerlach. We show that by implementing a polarization insensitive device to measure the OAM, the SAM states can be deflected to spatially resolved positions.

Cosmological scaling of precursor domain walls

Domain wall (DW) networks have a large impact on cosmology and present interesting dynamics that can be controlled by various scaling regimes. In the first stage after spontaneous breaking of the discrete symmetry, the network is seeded with “DW precursors,” the zeros of a tachyonic field. At sufficiently weak coupling, this stage can be quite long. The network is then driven to a nonrelativistic scaling regime; in flat spacetime the correlation length grows like L∼tκ with κ=1/2. We focus on the precursor regime in cosmology, assuming a power law scale factor a∝tα. We obtain the scaling exponent as a function of the external parameter, κ(α), by explicit computation in 1+1 and 2+1 dimensions, and find a smooth transition from nonrelativistic scaling with κ≃1/2 for α≲1/2 to DW gas regime κ≃α for α≳1/2, confirming previous arguments. The precise form of the transition κ(α) is surprisingly independent of dimension, suggesting that similar results should also be valid in 3+1 dimensions. Published by the American Physical Society 2024

Nuclear Matter and Finite Nuclei: Recent Studies Based on Parity Doublet Model

In this review, we summarize recent studies on nuclear matter and finite nuclei based on parity doublet models. We first construct a parity doublet model (PDM), which includes the chiral invariant mass m0 of nucleons together with the mass generated by the spontaneous chiral symmetry breaking. We then study the density dependence of the symmetry energy in the PDM, which shows that the symmetry energy is larger for smaller chiral inavariant mass. Then, we investigate some finite nuclei by applying the Relativistic Continuum Hartree–Bogoliubov (RCHB) theory to the PDM. We present the root-mean-square deviation (RMSD) of the binding energies and charge radii, and show that m0=700 MeV is preferred by the nuclear properties. Finally, we modify the PDM by adding the isovector scalar meson a0(980), and show that the inclusion of the a0(980) enlarges the symmetry energy of the infinite nuclear matter.

Small field chaos in spin glasses: Universal predictions from the ultrametric tree and comparison with numerical simulations

Replica symmetry breaking (RSB) for spin glasses predicts that the equilibrium configuration at two different magnetic fields are maximally decorrelated. We show that this theory presents quantitative predictions for this chaotic behavior under the application of a vanishing external magnetic field, in the crossover region where the field intensity scales proportionally to [Formula: see text], being N the system size. We show that RSB theory provides universal predictions for chaotic behavior: They depend only on the zero-field overlap probability function [Formula: see text] and are independent of other system features. In the infinite volume limit, each spin-glass sample is characterized by an infinite number of states that have a tree-like structure. We generate the corresponding probability distribution through efficient sampling using a representation based on the Bolthausen-Sznitman coalescent. Using solely [Formula: see text] as input we can analytically compute the statistics of the states in the region of vanishing magnetic field. In this way, we can compute the overlap probability distribution in the presence of a small vanishing field and the increase of chaoticity when increasing the field. To test our computations, we have simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model, finding in both cases excellent agreement with the universal predictions.

Monopoles and fermions in the Standard Model

We consider all magnetic monopoles that could have settled in the Standard Model after descending from a generic microscopic theory. These monopoles have Standard Model quantum numbers, are stable, and we also require that their magnetic fluxes are consistent with the electroweak symmetry breaking. Scattering processes involving quarks, leptons and protons on these monopoles are studied using partial waves decomposition. These processes in the lowest partial wave are known to be unsuppressed by the monopole mass and are relevant for monopole catalysis of proton decay. We provide estimates for scattering cross-sections and investigate and confirm the applicability of the twisted sector approach to scattering processes on these Standard Model monopoles. We find that the SM monopole catalysis processes are universal and model-independent.

Encoding spatiotemporal asymmetry in artificial cilia with a ctenophore-inspired soft-robotic platform

A remarkable variety of organisms use metachronal coordination (i.e., numerous neighboring appendages beating sequentially with a fixed phase lag) to swim or pump fluid. This coordination strategy is used by microorganisms to break symmetry at small scales where viscous effects dominate and flow is time-reversible. Some larger organisms use this swimming strategy at intermediate scales, where viscosity and inertia both play important roles. However, the role of individual propulsor kinematics-especially across hydrodynamic scales-is not well-understood, though the details of propulsor motion can be crucial for the efficient generation of flow. To investigate this behavior, we developed a new soft robotic platform using magnetoactive silicone elastomers to mimic the metachronally coordinated propulsors found in swimming organisms. Furthermore, we present a method to passively encode spatially asymmetric beating patterns in our artificial propulsors. We investigated the kinematics and hydrodynamics of three propulsor types, with varying degrees of asymmetry, using Particle Image Velocimetry and high-speed videography. We find that asymmetric beating patterns can move considerably more fluid relative to symmetric beating at the same frequency and phase lag, and that asymmetry can be passively encoded into propulsors via the interplay between elastic and magnetic torques. Our results demonstrate that nuanced differences in propulsor kinematics can substantially impact fluid pumping performance. Our soft robotic platform also provides an avenue to explore metachronal coordination at the meso-scale, which in turn can inform the design of future bioinspired pumping devices and swimming robots.

Subsymmetry protected topology in topological insulators and superconductors

Exploration of topology protected by a certain symmetry is central in condensed matter physics. A recent idea of subsymmetry protected (SSP) topology—remains of a broken symmetry can still protect specific topological boundary states—has been developed and demonstrated in a photonic system [], but not in topological superconductors. Here, we extend this idea further by applying subsymmetry protecting perturbation (SSPP) to one-dimensional topological insulating and superconducting systems using the Su-Schrieffer-Hegger (SSH) and Kitaev models. Using the tight-binding and low-energy effective theory, we show that the SSP boundary states retain topological properties while the SSPP results in the asymmetry of boundary states. For the SSH model, an SSP zero-energy edge state localized on one edge possesses quantized polarization. In contrast, the other edge state is perturbed to have nonzero energy, and its polarization is not quantized. For topological superconductors, SSP zero-energy Majorana boundary states for spinful Kitaev models emerge on only one edge, contrary to the conventional belief that Majorana fermions emerge at opposite edges. Our findings can be used as a platform to expand our understanding of topological materials as they broaden our understanding of the symmetry in a topological system and a method to engineer Majorana fermions. Published by the American Physical Society 2024

Coexisting Charge Density Waves in Twisted Bilayer NbSe2.

Twisted bilayers of 2D materials have emerged as a tunable platform for studying broken symmetry phases. While most interest has been focused toward emergent states in systems whose constituent monolayers do not feature broken symmetry states, assembling monolayers that exhibit ordered states into twisted bilayers can also give rise to interesting phenomena. Here, we use first-principles density-functional theory calculations to study the atomic structure of twisted bilayer NbSe2 whose constituent monolayers feature a charge density wave. We find that different charge density wave states coexist in the ground state of the twisted bilayer: monolayer-like 3 × 3 triangular and hexagonal charge density waves are observed in low-energy stacking regions, while stripe charge density waves are found in the domain walls surrounding the low-energy stacking regions. These predictions, which can be tested by scanning tunneling microscopy experiments, highlight the potential to create complex charge density wave ground states in twisted bilayer systems.

Observation of Circular Dichroism Induced by Electronic Chirality.

Chiral phases of matter, characterized by a definite handedness, abound in nature, ranging from the crystal structure of quartz to spiraling spin states in helical magnets. In 1T-TiSe_{2} a source of chirality has been proposed that stands apart from these classical examples as it arises from combined electronic charge and quantum orbital fluctuations. This may allow its chirality to be accessed and manipulated without imposing either structural or magnetic handedness. However, direct bulk evidence that broken inversion symmetry and chirality are intrinsic to TiSe_{2} remains elusive. Here, employing resonant elastic x-ray scattering technique, we reveal the presence of circular dichroism, i.e., polarization dependence of the resonant diffraction intensity, up to ∼40% at forbidden Bragg peaks that emerge at the charge and orbital ordering transition. The dichroism varies dramatically with incident energy and azimuthal angle. Comparison to calculated scattering intensities traces its origin to bulk chiral electronic order in TiSe_{2} and establishes resonant elastic x-ray scattering as a sensitive probe to electronic chirality.