Dipole Symmetry Research Articles

Analysis of fracton-gravity stability

We study the stability of fracton gravity, a variant of linearized gravity where the gauge symmetry is restricted to longitudinal diffeomorphisms. These transformations can be connected to a spacetime generalization of dipole symmetry, hence the tag fracton. We find that fracton gravity features an instability in the spin-1 sector corresponding to solutions with growing amplitude. This dynamical instability can be removed by tuning the couplings of the theory. Nonetheless, the Hamiltonian for the spin-1 modes remains always unbounded from below when evaluated on the classical solutions. We find no other sources of instability in the spin-2 or spin-0 sectors. We analyze in detail the canonical formulation and the constraints arguing that neither auxiliary fields nor gauge-fixing conditions can be employed to remove the problematic vector modes or stabilize them. Published by the American Physical Society 2024

Anomaly inflow for dipole symmetry and higher form foliated field theories

In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied — multipole symmetry, associated with conservation of multipoles. Based on algebraic relation between dipole and global charges, we introduce a series of (d + 1)-dimensional BF theories with p-form gauge fields, which admit dipole of spatially extended excitations, and study their physical properties. We elucidate that gauge invariant loops have unusual form, containing linear function of the spatial coordinate, which leads to the position dependent braiding statistics and unusual ground state degeneracy dependence on the system size. We also show that the theories exhibit a mixed ’t Hooft anomaly between p-form and (d − p)-form dipole symmetries, which is canceled by an invertible theory defined in one dimensional higher via anomaly inflow mechanism.

Dissipative fracton superfluids

We present a comprehensive study of hydrodynamic theories for superfluids with dipole symmetry. Taking diffusion as an example, we systematically construct a hydrodynamic framework that incorporates an intrinsic dipole degree of freedom in analogy to spin density in micropolar (spinful) fluids. Subsequently, we study a dipole condensed phase and propose a model that captures the spontaneous breaking of the U(1) charge. The theory explains the role of the inverse Higgs constraint for this class of theories, and naturally generates the gapless field. Next, we introduce finite temperature theory using the Hamiltonian formalism and study the hydrodynamics of ideal fracton superfluids. Finally, we postulate a derivative counting scheme and incorporate dissipative effects using the method of irreversible thermodynamics. We verify the consistency of the dispersion relations and argue that our counting is systematic.

Non-invertible duality interfaces in field theories with exotic symmetries

In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse according to a group law. Only recently has the interplay between these two been examined. In this paper, we provide further examples of the interplay in the XY plaquette model, XY cube model, 1+1 d theory with global dipole symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of the momentum symmetry on half of spacetime and then performing a duality transformation. We analyze the fusion rules of the symmetries and find that they are condensation defects from an analog of higher gauging exotic symmetries. We also address their dependence on the UV cutoff when relevant.

Reciprocity relations in a biologically inspired nanomagnonic system with dipolar coupling

Magnetosome chains in magnetotactic bacteria present ideal nanomagnonic model systems for studying collective resonance modes of dipolar-coupled single domain particles in relation to their spatial arrangement. Using microresonator-based ferromagnetic resonance (FMR) spectroscopy, electron microscopy, and micromagnetic modeling, we here provide insights into the complex magnonic activity within a single magnetosome chain. While the angular dependence of its FMR spectrum is dominated by twofold symmetry features due to the uniaxial anisotropy of linear chain segments, we also observed an unexpected behavior such as interrupted lines and flat bands due to the intricate geometrical details of this particular chain, such as a cross-like structural anomaly where a pair of particles is oriented perpendicular to the main axis of the chain and thus breaks the prevailing axial dipolar coupling symmetry. Such a cross junction formed by four particles exhibits interesting magnonic network properties. Notably, we observe reciprocity in the sense that the spectral response of one particle to an excitation of another one is identical to the response of the latter given an excitation of the former. Furthermore, we have identified that magnonic coupling between A and B can be facilitated via a dark state, as in magnonic stimulated Raman adiabatic passage, and that this dark-state coupling can be made non-reciprocal between A and B by breaking the symmetry of the spatial arrangement of the four particles.

Fracton gravity from spacetime dipole symmetry

Dipole charge conservation forces isolated charges to be immobile fractons. These couple naturally to spatial two-index symmetric tensor gauge fields that resemble a spatial metric. We propose a spacetime Lorentz-covariant version of dipole symmetry and study the theory of the associated gauge fields. In the presence of a suitable background field, these contain a massive antisymmetric and a massless symmetric two-index tensors. The latter transforms only under longitudinal diffeomorphisms, making the massless sector similar to linearized gravity, but with additional modes of lower spin. We show that the theory can be consistently coupled to a curved background metric and study its possible interaction terms with itself and with matter. In addition, we construct a map between solutions of linearized gravity in Kerr-Schild form and solutions of fracton gravity coupled to matter. Published by the American Physical Society 2024

Noncommutative field theory of the Tkachenko mode: Symmetries and decay rate

We construct an effective field theory describing the collective Tkachenko oscillation mode of a vortex lattice in a two-dimensional rotating Bose-Einstein condensate in the long-wavelength regime. The theory has the form of a noncommutative field theory of a Nambu-Goldstone boson, which exhibits a noncommutative version of dipole symmetry. From the effective field theory, we show that, at zero temperature, the decay width Γ of the Tkachenko mode scales with its energy E as Γ∼E3 in the low-energy limit. We also discuss the width of the Tkachenko mode at a small temperature. Published by the American Physical Society 2024

Large N Fractons.

We consider theories of N-component fields with exotic spacetime symmetries, including a conserved dipole moment. Microscopic charges are immobile by symmetry, and so resemble fractons. Using collective fields we solve these models to leading order in large N. The large N solution reveals that these models are strongly correlated, and that interactions dress the microscopic charges so that they become mobile, long-lived quasiparticles. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description.

Unidirectional Subsystem Symmetry in a Hole-Doped Honeycomb-Lattice Ising Magnet.

We study a model of a hole-doped collinear Ising antiferromagnet on the honeycomb lattice as a route toward realization of subsystem symmetry. We find nearly exact conservation of dipole symmetry verified both numerically with exact diagonalization on finite clusters and analytically with perturbation theory. The emergent symmetry forbids the motion of single holes-or fractons-but allows hole pairs-or dipoles-to move freely along a one-dimensional line, the antiferromagnetic direction, of the system; in the transverse direction both fractons and dipoles are completely localized. This presents a realization of a "unidirectional" subsystem symmetry. By studying interactions between dipoles, we argue that the subsystem symmetry is likely to continue to persist up to finite (but probably small) hole concentrations.

Breaking Radial Dipole Symmetry in Planar Macrocycles Modulates Edge-to-Edge Packing and Disrupts Cofacial Stacking.

Dipolar interactions are ever-present in supramolecular architectures, though their impact is typically revealed by making dipoles stronger. While it is also possible to assess the role of dipoles by altering their orientations by using synthetic design, doing so without altering the molecular shape is not straightforward. We have now done this by flipping one triazole unit in a rigid macrocycle, tricarb. The macrocycle is composed of three carbazoles (2 Debye) and three triazoles (5 Debye) defining an array of dipoles aligned radially but organized alternately in and out. These dipoles are believed to dictate edge-to-edge tiling and face-to-face stacking. We modified our synthesis to prepare isosteric macrocycles with the orientation of one triazole dipole rotated 40°. The new dipole orientation guides edge-to-edge contacts to reorder the stability of two surface-bound 2D polymorphs. The impact on dipole-enhanced π stacking, however, was unexpected. Our stacking model identified an unchanged set of short-range (3.4 Å) anti-parallel dipole contacts. Despite this situation, the reduction in self-association was attributed to long-range (~6.4 Å) dipolar repulsions between π-stacked macrocycles. This work highlights our ability to control the build-up and symmetry of macrocyclic skeletons by synthetic design, and the work needed to further our understanding of how dipoles control self-assembly.

Dynamical Asymmetries, the Bayes’ Theorem, Entanglement, and Intentionality in the Brain Functional Activity

We discuss the asymmetries of dynamical origin that are relevant to functional brain activity. The brain is permanently open to its environment, and its dissipative dynamics is characterized indeed by the asymmetries under time translation transformations and time-reversal transformations, which manifest themselves in the irreversible “arrow of time”. Another asymmetry of dynamical origin arises from the breakdown of the rotational symmetry of molecular electric dipoles, triggered by incoming stimuli, which manifests in long-range dipole-dipole correlations favoring neuronal correlations. In the dissipative model, neurons, glial cells, and other biological components are classical structures. The dipole vibrational fields are quantum variables. We review the quantum field theory model of the brain proposed by Ricciardi and Umezawa and its subsequent extension to dissipative dynamics. We then show that Bayes’ theorem in probability theory is intrinsic to the structure of the brain states and discuss its strict relation with entanglement phenomena and free energy minimization. The brain estimates the action with a higher Bayes probability to be taken to produce the aimed effect. Bayes’ rule provides the formal basis of the intentionality in brain activity, which we also discuss in relation to mind and consciousness.

Dipole symmetry breaking and fractonic Nambu-Goldstone mode

We introduce a family of quantum field theories for fields carrying monopole and dipole charges. In contrast to previous realizations, fields have quadratic two-derivative kinetic terms. The dipole symmetry algebra is realized in a discretized internal space and connected to the physical space through a background gauge field. We study spontaneous symmetry breaking of dipole symmetry in 1+1 dimensions in a large-NN limit. The trivial classical vacuum is lifted by quantum corrections into a vacuum which breaks dipole symmetry while preserving monopole charge. By means of a Hubbard-Stratonovich transformation, heat-kernel and large-NN techniques, we compute the effective action for the low-energy modes. We encounter a fractonic immobile Nambu-Goldstone mode whose dispersion characteristics avoid Coleman-Hohenberg-Mermin-Wagner theorem independently of the large-NN limit.

A Chern-Simons theory for dipole symmetry

We present effective field theories for dipole symmetric topological matters that can be described by the Chern-Simons theory. Unlike most studies using higher-rank gauge theory, we develop a framework with both U(1)U(1) and dipole gauge fields. As a result, only the highest multipole symmetry can support the ’t Hooft anomaly. We show that with appropriate point group symmetries, the dipolar Chern-Simons theory can exist in any dimension and, moreover, the bulk-edge correspondence can depend on the boundary. As two applications, we draw an analogy between the dipole anomaly and the torsional anomaly and generalize particle-vortex duality to dipole phase transitions. All of the above are in the flat spacetime limit, but our framework is able to systematically couple dipole symmetry to curved spacetime. Based on that, we give a proposal about anomalous dipole hydrodynamics. Moreover, we show that the fracton-elasticity duality arises naturally from a non-abelian Chern-Simons theory in 3D.

Non-Fermi liquids from dipolar symmetry breaking

Non-Fermi liquids from dipolar symmetry breaking

Dipole superfluid hydrodynamics

We construct a theory of hydrodynamic transport for systems with conserved dipole moment, U(1) charge, energy, and momentum. These models have been considered in the context of fractons, since their elementary and isolated charges are immobile by symmetry, and have two known translation-invariant gapless phases: a “p-wave dipole superfluid” phase where the dipole symmetry is spontaneously broken and a “s-wave dipole superfluid” phase where both the U(1) and dipole symmetries are spontaneously broken. We argue on grounds of symmetry and thermodynamics that there is no transitionally-invariant gapless fluid with unbroken dipole symmetry. In this work, we primarily focus on the hydrodynamic description of p-wave dipole superfluids, including leading dissipative corrections. That theory has, in a sense, a dynamical scaling exponent z = 2, and its spectrum of fluctuations includes novel subdiffusive modes ω ∼ −ik4 in the shear sector and magnon-like sound mode ω ∼ ±k2 − ik2. By coupling the fluid to background fields, we find response functions of the various symmetry currents. We also present a preliminary generalization of our work to s-wave dipole superfluids, which resemble z = 1 fluids and feature sound waves and diffusive shear modes, as in an ordinary fluid. However, the spectrum also contains a magnon-like second-sound mode ω ∼ ±k2 ± k4 − ik4 with subdiffusive attenuation.

Halogenation effects on the bridgehead position of the adamantane molecule

Halogen substitution effects on the bridgehead positioned carbon of adamantane molecule portraits many significant characteristics for the adamantane halides. As a result of the induction and electrostatic interaction caused by the substitution, large electron densities are formed around the halogens and a small positive electrostatic potential (σ-hole) is developed along the z-direction parallel to C-X bond axis. Computational study performed through EOM-CCSD method, B3LYP and WB97XD functionals of the density functional theory effectively supports this investigation in terms of molecular structure, vibrational properties, bonding behavior and electrostatic potential surfaces. Accordingly, substitution give rise to the change in the dipole moment and symmetry of the molecules. In addition, polarizabilities of the molecules along the C-X bond axis increases with respect to electron densities. HOMO-LUMO energy gap and positive σ-holes are found to decrease with the increase in the negative electron affinity. An anisotropic charge distribution developed upon substitution allows the adamantane halides to exhibit two different binding motifs like halogen and hydrogen bonding along the parallel and perpendicular directions of C-X bond. These characteristics feature of the halo adamantane finds applications in self-assembled monolayers, crystal engineering and biomedical applications.

Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation

We develop a Schwinger-Keldysh effective field theory describing the hydrodynamics of a fluid with conserved charge and dipole moments, together with conserved momentum. The resulting hydrodynamic modes are highly unusual, including sound waves with quadratic (magnon-like) dispersion relation and subdiffusive decay rate. Hydrodynamics itself is unstable below four spatial dimensions. We show that the momentum density is, at leading order, the Goldstone boson for a dipole symmetry which appears spontaneously broken at finite charge density. Unlike an ordinary fluid, the presence or absence of energy conservation qualitatively changes the decay rates of the hydrodynamic modes. This effective field theory naturally couples to curved spacetime and background gauge fields; in the flat spacetime limit, we reproduce the “mixed rank tensor fields” previously coupled to fracton matter.

Liquid Crystals as Multifunctional Interfaces for Trapping and Characterizing Colloidal Microplastics.

Identifying and removing microplastics (MPs) from the environment is a global challenge. This study explores how the colloidal fraction of MPs assemble into distinct 2D patterns at aqueous interfaces of liquid crystal (LC) films with the goal of developing surface-sensitive methods for identifying MPs. Polyethylene (PE) and polystyrene (PS) microparticles are measured to exhibit distinct aggregation patterns, with addition of anionic surfactant amplifying differences in PS/PE aggregation patterns: PS changes from a linear chain-like morphology to a singly dispersed state with increasing surfactant concentration whereas PE forms dense clusters at all surfactant concentrations. Statistical analysis of assembly patterns using deep learning image recognition models yields accurate classification, with feature importance analysis confirming that dense, multibranched assemblies are unique features of PE relative to PS. Microscopic characterization of LC ordering at the microparticle surfaces leads to predict LC-mediated interactions (due to elastic strain) with a dipolar symmetry, a prediction consistent with the interfacial organization of PS but not PE. Further analysis leads to conclude that PE microparticles, due to their polycrystalline nature, possess rough surfaces that lead to weak LC elastic interactions and enhanced capillary forces. Overall, the results highlight the potential utility of LC interfaces for rapid identification of colloidal MPs based on their surface properties.

Renormalization in Quantum Brain Dynamics

We show renormalization in Quantum Brain Dynamics (QBD) in 3+1 dimensions, namely Quantum Electrodynamics with water rotational dipole fields. First, we introduce the Lagrangian density for QBD involving terms of water rotational dipole fields, photon fields and their interactions. Next, we show Feynman diagrams with 1-loop self-energy and vertex function in dipole coupling expansion in QBD. The counter-terms are derived from the coupling expansion of the water dipole moment. Our approach will be applied to numerical simulations of Kadanoff–Baym equations for water dipoles and photons to describe the breakdown of the rotational symmetry of dipoles, namely memory formation processes. It will also be extended to the renormalization group method for QBD with running parameters in multi-scales.

Hohenberg-Mermin-Wagner-type theorems and dipole symmetry

We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For $d$-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}4$, while dipole symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$. For $T=0$, we show that charge symmetry cannot be spontaneously broken for $d\ensuremath{\le}2$ if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.