Coulomb Phase Research Articles

Ultrafast Mechanism of Material Removal in the Femtosecond Laser Ablation of WS2 and Its Diode Rectification Characteristics

The study investigates the two different underlying ablation mechanisms of WS2 processed by femtosecond (fs) laser with different fluences. With increasing fluence, the saturable expansion of craters and the transformation of three distinct crater morphologies are found. The material response and the transfer and deposition of laser energy are tracked by using a plasma model based on the classical single rate equation model and the Drude model. The results of the numerical simulation and time-resolved transient reflectivity reveal the two different ablation mechanisms, which are coulomb explosion and phase explosion. The mechanism of material removal is distinguished by the critical threshold of 0.85 J/cm2. In addition, the internal ablation region exhibits a high concentration of defects and WO3 according to the results of Raman spectra, X-ray photoelectron spectra, and morphology-dependent photoluminescence mapping. Due to the high concentration with high fluence, the device of WS2/Si p-n junction exhibits a 2.6 times enhancement on the current under forward bias. The findings would be of value to engineer structures to tailor the optoelectronic response of WS2 and to develop potential future optoelectronic devices.

Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor

The holographic superconductor is one of the most popular models in the context of applied holography. Despite what its name suggests, it does not describe a superconductor. On the contrary, the low temperature phase of its dual field theory is a superfluid with a spontaneously broken U(1) global symmetry. As already observed in the previous literature, a bona fide holographic superconductor can be constructed using mixed boundary conditions for the bulk gauge field. By exploiting this prescription, we study the near-equilibrium collective dynamics in the Higgs phase and reveal the characteristic features of the Anderson-Higgs mechanism. We show that second sound disappears from the spectrum and the gauge field acquires a finite energy gap of the order of the plasma frequency. We observe an overdamped to underdamped crossover for the Higgs mode which acquires a finite energy gap below ≈ Tc/2, with Tc the superconducting critical temperature. Interestingly, the energy gap of the Higgs mode at low temperature is significantly smaller than 2∆, with ∆ the superconducting energy gap. Finally, we interpret our results using Ginzburg-Landau theory and we confirm the validity of previously derived perturbative analytic expressions.

Solitonic self-sustained charge and energy transport on the superconducting cylinder

We present an exact time-dependent solution for a charged scalar field on a two-dimensional cylinder, that can be interpreted as representing a long-standing excitation on a $S$-wave superconducting state, which propagates along a nanotube constructed out of twisted bilayer graphene. The solution has a topological charge characterized by an integer number, which counts the winding of the Higgs phase winds around the cylinder. The resulting electric current generates its own electromagnetic field in a self-consistent way, without the need of any external fields to keep it alive.

Gravity as a Quantum Field Theory

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a nonlinearly realized symmetry, and like electroweak interactions, it is a gauge theory in Higgs phase, with a massive connection. I will also discuss the possibility of finding a UV complete quantum field theoretic description of all interactions.

Anomalies and phases of strongly coupled chiral gauge theories: Recent developments

After many years of investigations, our understanding of the dynamics of strongly coupled chiral gauge theories is still quite unsatisfactory today. Conventional wisdom about strongly coupled gauge theories, successfully applied to QCD, is not always as useful in chiral gauge theories. Recently, some new ideas and techniques have been developed, which involve concepts of generalized symmetries, of gauging a discrete center symmetry, and of generalizing the ’t Hooft anomaly matching constraints to include certain mixed symmetries. This new development has been applied to chiral gauge theories, leading to many interesting, sometimes quite unexpected, results. For instance, in the context of generalized Bars–Yankielowicz and generalized Georgi–Glashow models, these new types of anomalies give a rather clear indication in favor of the dynamical Higgs phase, against confining, flavor symmetric vacua. Another closely related topic is strong anomaly and the effective low-energy action representing it. It turns out that they have significant implications on the phase of chiral gauge theories, giving indications consistent with the findings based on the generalized anomalies. Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from these discussions. The aim of this work is to review these developments.

Hubbard Bands, Mott Transition and Deconfinement in Strongly Correlated Systems

The problem of deconfinement phases in strongly correlated systems is discussed. In space–time dimension d = 3 + 1, a competition of confinement and Coulomb phases occurs, but in d = 2 + 1 the confining phase dominates owing to monopole proliferation, but Dirac points can change the situation. Combining the Kotliar–Ruckenstein representation and fractionalized spin-liquid deconfinement picture, the Mott transition and Hubbard subbands are treated, general expressions in the case of an arbitrary bare band spectrum being obtained. The transition into a metallic state is determined by condensation of a gapless boson mode. The spectrum picture in the insulating state is considerably influenced by the spinon spin-liquid spectrum and hidden Fermi surface.

Fragmented Spin Ice and Multi-k Ordering in Rare-Earth Antiperovskites.

We study near-neighbor and dipolar Ising models on a lattice of corner-sharing octahedra. In an extended parameter range of both models, frustration between antiferromagnetism and a spin-ice-like three-in-three-out rule stabilizes a Coulomb phase with correlated dipolar and quadrupolar spin textures, both yielding distinctive neutron-scattering signatures. Strong further-neighbor perturbations cause the two components to order independently, resulting in unusual multi-k orders. We propose experimental realizations of our model in rare-earth antiperovskites.

Glassy correlated state induced by disorder in the frustrated antiferromagnet Tb2Zr2O7

We study the low-temperature thermomagnetic properties of the polycrystalline material Tb2Zr2O7 through ac susceptibility and specific heat measurements. This zirconate displays a defect-fluorite structure in which the magnetic Tb3+ and nonmagnetic Zr4+ cations sit randomly on the same metal sublattice. No long-range magnetic order is found down to 100 mK, although dominant antiferromagnetic interactions are observed and the spins remain dynamic down to the lowest temperatures investigated. We observed a frequency-dependent peak around 2.5 K which is well described by many models of a canonical spin-glass transition. In-field specific heat measurements and the recovered entropy of the system Rln(4) suggest a two doublets ground state separated by 7 K. Comparisons to the pyrochlores Tb2Ti2O7 and Tb2Hf2O7 reinforce the collective spin-glass-type behavior and the opening for discussions of an exotic Coulomb phase in this material.

Real-time dynamics of a critical resonating valence bond spin liquid

Implementation of the hardcore-dimer Hilbert space in cold Rydberg-atom simulators opens a new route of investigating real-time dynamics of dimer liquids under Hamiltonian quench. Here, we consider an initial Resonating Valence Bond (RVB) state on the square lattice realizing a critical Coulomb phase with algebraic and dipolar correlations. Using its representation as a special point of a broad manifold of SU($2$)-symmetric, translationnally invariant, Projected Entangled Pair States (PEPS), we compute its non-equilibrium dynamics upon turning on inter-site Heisenberg interactions. We show that projecting the time-evolution onto the PEPS manifold remains accurate at small time scales. We also find that the state evolves within a PEPS sub-manifold characterized by a U($1$) gauge symmetry, suggesting that the Coulomb phase is stable under such unitary evolution.

Coulomb effects in the high-energy part of above-threshold-ionization spectra in intense bicircular laser fields

Coulomb effects in the high-energy part of photoelectron spectra produced through the above-threshold ionization of an atom subject to intense short laser pulses are analyzed. The analysis is carried out for linearly polarized and tailored bicircular laser pulses consisting of the fundamental and the second-harmonic components. We include the Coulomb effects in the analytic semiclassical description of the photoelectron rescattering plateau using the recently developed adiabatic approach [Phys. Rev. A 104, 033109 (2021)] and the expression for the Coulomb phase derived for description of the high harmonic generation [J. Phys. B: At., Mol. Opt. Phys. 51, 144006 (2018)]. Comparisons between predictions of the analytic approach and numerical solutions of the time-dependent Schr\"odinger equation are presented. They allow the identification of the contribution of the Coulomb interaction to photoelectron spectra for different laser pulse forms. We show that the Coulomb effects appear more pronounced for bicircular fields, where they demonstrate considerable sensitivity to the photoelectron emission angle. Instead, for linear polarization, the Coulomb effect in the high-energy plateau is generally insignificant.

Pinch points and half-moons in dipolar-octupolar Nd2Hf2O7

While it is established that the pinch point scattering pattern in spin ice arises from an emergent coulomb phase associated with magnetic moment that is divergence-free, more complex Hamiltonians can introduce a divergence-full part. If these two parts remain decoupled, they give rise to the co-existence of distinct features. Here we show that the moment in ${\rm Nd_2Hf_2O_7}$ forms a static long-range ordered ground state, a flat, gapped pinch point excitation and dispersive excitations. These results confirm recent theories which predict that the dispersive modes, which arise from the divergence-full moment, host a pinch point pattern of their own, observed experimentally as `half-moons'.

Dirac pairings, one-form symmetries and Seiberg-Witten geometries

The Coulomb phase of a quantum field theory, when present, illuminates the analysis of its line operators and one-form symmetries. For 4d mathcal{N} = 2 field theories the low energy physics of this phase is encoded in the special Kähler geometry of the moduli space of Coulomb vacua. We clarify how the information on the allowed line operator charges and one-form symmetries is encoded in the special Kähler structure. We point out the important difference between the lattice of charged states and the homology lattice of the abelian variety fibered over the moduli space, which, when principally polarized, is naturally identified with a choice of the lattice of mutually local line operators. This observation illuminates how the distinct S-duality orbits of global forms of mathcal{N} = 4 theories are encoded geometrically.

Exploring bosonic and fermionic link models on (3+1)D tubes

Quantum link models (QLMs) have attracted a lot of attention in recent times as a generalization of Wilson's lattice gauge theories (LGT), and are particularly suitable for realization on quantum simulators and computers. These models are known to host new phases of matter and act as a bridge between particle and condensed matter physics. In this article, we study the Abelian $U(1)$ lattice gauge theory in $(3+1)$-d tubes using large-scale exact diagonalization (ED). We are then able to motivate the phase diagram of the model with finite size scaling techniques (FSS), and in particular propose the existence of a Coulomb phase. Furthermore, we introduce the first models involving fermionic quantum links, which generalize the gauge degrees of freedom to be of fermionic nature. We prove that while the spectra remain identical between the bosonic and the fermionic versions of the $U(1)$-symmetric quantum link models in $(2+1)$-d, they are different in $(3+1)$-d. We discuss the prospects of realizing the magnetic field interactions as correlated hopping in quantum simulator experiments.

Crystal gravity

We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space itself. Only rather recently it was realized in various context that the order parameter of the solid has a relation to Einsteins dynamical space time which is similar to the role of a Higgs field in a Yang-Mills gauge theory. Such a "crystal gravity" is therefore like the Higgs phase of gravity. The usual Higgs phases are characterized by a special phenomenology. A case in point is superconductivity exhibiting phenomena like the Type II phase, characterized by the emergence of an Abrikosov lattice of quantized magnetic fluxes absorbing the external magnetic field. What to expect in the gravitational setting? The theory of elasticity is the universal effective field theory associated with the breaking of space translations and rotations having a similar status as the phase action describing a neutral superfluid. A geometrical formulation appeared in its long history, similar in structure to general relativity, which greatly facilitates the marriage of both theories. With as main limitation that we focus entirely on stationary circumstances -- the dynamical theory is greatly complicated by the lack of Lorentz invariance -- we will present a first exploration of a remarkably rich and often simple physics of "Higgsed gravity".

Continuum solutions to the two–center Coulomb problem in prolate spheroidal coordinates

We present a computational and theoretical framework for solving the Schrödinger equation (SE) for the two–center Coulomb problem in prolate spheroidal coordinates when the energy of the SE is positive. A general and robust computer code has been produced that calculates the separation constants, spheroidal harmonic expansion coefficients, regular quasi–radial two–center Coulomb wave functions, and two–center Coulomb phase shifts. These quantities can be calculated over a range of internuclear separations, angular momentum projections, and continuum electron momenta. A representative set of results are presented and compared with previous calculations, excellent agreement is found in many cases while significant disagreements are found in others. Program summaryProgram title:spheroidal-cwCPC Library link to program files:https://doi.org/10.17632/nf5gw7vjnh.1Code Ocean capsule:https://codeocean.com/capsule/7638744Licensing provisions: MITProgramming language: Fortran 90Nature of problem: A robust and accurate computer code for calculating Coulomb wave functions in prolate spheroidal coordinate is necessary for the calculation of cross sections for photonionization, and electron and positron scattering on charged diatomic targets.Solution method: The angular solution is expanded in a series of spherical harmonics leading to the diagonalization of a pentadiagonal matrix. The eigenvectors contain the expansion coefficients and the eigenvalues are the separation constants which, unlike the SE in spherical coordinates, are also functions of the energy. The radial two–center Coulomb wave functions are started using a power series solution and then propagated using a linear multistep method. An asymptotic expansion is used to calculate the two–center Coulomb phase shift, and to normalize the radial wave function.Additional comments including restrictions and unusual features: Two–center Coulomb radial wave functions and phase shifts can be accurately calculated for internuclear separations from 0.001 to 60.0 a0, angular momentum projection |m| from 0 to 44, momentum k from 0.01 to 100.0 a.u., and a combined nuclear charge Z+ from 1 to 12.

Position-dependent excitations and UV/IR mixing in the ZN rank-2 toric code and its low-energy effective field theory

We investigate how symmetry and topological order are coupled in the ($2+1$)--dimensional ${\mathbb{Z}}_{N}$ rank-2 toric code for general $N$, which is an exactly solvable point in the Higgs phase of a symmetric rank-2 $\text{U}(1)$ gauge theory. The symmetry-enriched topological order present has a nontrivial realization of square-lattice translation (and rotation and reflection) symmetry, where anyons on different lattice sites have different types and belong to different superselection sectors. We call such particles ``position-dependent excitations.'' As a result, in the rank-2 toric code anyons can hop by one lattice site in some directions while only by $N$ lattice sites in others, reminiscent of fracton topological order in $3+1$ dimensions. We find that while there are ${N}^{2}$ flavors of $e$ charges and $2N$ flavors of $m$ fluxes, there are not ${N}^{{N}^{2}+2N}$ anyon types. Instead, there are ${N}^{6}$ anyon types, and we can use Chern-Simons theory with six $\text{U}(1)$ gauge fields to describe all of them. While the lattice translations permute anyon types, we find that such permutations cannot be expressed as transformations on the six $\text{U}(1)$ gauge fields. Thus, the realization of translation symmetry in the ${\text{U}}^{6}(1)$ Chern-Simons theory is not known. Despite this, we find a way to calculate the translation-dependent properties of the theory. In particular, we find that the ground-state degeneracy on an ${L}_{x}\ifmmode\times\else\texttimes\fi{}{L}_{y}$ torus is ${N}^{3}gcd({L}_{x},N)gcd({L}_{y},N)gcd({L}_{x},{L}_{y},N)$, where $gcd$ stands for ``greatest common divisor.'' We argue that this is a manifestation of UV/IR mixing which arises from the interplay between lattice symmetries and topological order.

Magnetic field generation from bubble collisions during first-order phase transition

We study the magnetic fields generation from the cosmological first-order electroweak phase transition. We calculate the magnetic field induced by the variation of the Higgs phase for two bubbles and three bubbles collisions. Our study shows that electromagnetic currents in the collision direction produce the ring-like magnetic field in the intersect regions of colliding bubbles, which may seed the primordial magnetic field that are constrained by intergalatic field observations.

Excitations of static isolated fermions in the Higgs phase of gauge Higgs theory

A spectrum of localized excitations of isolated static fermions has been discovered in several different gauge Higgs theories. In lattice numerical simulations, we show that the charged elementary particles can have the spectrum of excitations in the Higgs phase of SU(3) gauge Higgs theory, q=2 Abelian Higgs theory, Landau-Ginzburg theory, and in chiral U(1) gauge Higgs theory. Possibly these excited states of the isolated fermions can be observed in ARPES studies of conventional superconductors. Also, we consider that similar kinds of excitations could exist in other gauge Higgs theories, such as the electroweak sector of the Standard Model.

Coulomb phase corrections to the transverse analyzing power AN(t) in high-energy forward proton-proton scattering

Study of polarized proton-proton elastic scattering in the Coulomb-nuclear interference region allows one to measure the forward hadronic single spin-flip amplitude including its phase. However, in a precision experimental data analysis, a phase-shift correction ${\ensuremath{\delta}}_{C}$ due to the long distance Coulomb interaction should be taken into account. For unpolarized scattering, ${\ensuremath{\delta}}_{C}$ is commonly considered as well established. Here, we evaluate the Coulomb phase shifts for the forward elastic proton-proton single spin-flip electromagnetic and hadronic amplitudes. Only a small discrepancy between the spin-flip and nonflip phases was found which can be neglected in the high-energy forward elastic $pp$ studies involving transverse spin. Nonetheless, the effective alteration of the hadronic spin-flip amplitude by the long-distance electromagnetic corrections can be essential for interpretation of the experimental results.

Tensor renormalization group study of (3+1)-dimensional ℤ2 gauge-Higgs model at finite density

We investigate the critical endpoints of the (3+1)-dimensional ℤ2 gauge-Higgs model at finite density together with the (2+1)-dimensional one at zero density as a benchmark using the tensor renormalization group method. We focus on the phase transition between the Higgs phase and the confinement phase at finite chemical potential along the critical end line. In the (2+1)-dimensional model, the resulting endpoint is consistent with a recent numerical estimate by the Monte Carlo simulation. In the (3+1)-dimensional case, however, the location of the critical endpoint shows disagreement with the known estimates by the mean-field approximation and the Monte Carlo studies. This is the first application of the tensor renormalization group method to a four-dimensional lattice gauge theory and a key stepping stone toward the future investigation of the phase structure of the finite density QCD.