Compact Electrodynamics Research Articles

Detecting phase transitions in lattice gauge theories: Production and dissolution of topological defects in 4D compact electrodynamics

We present the application of microcanonical inflection point analysis (MIPA)—a novel and powerful method for the systematic identification and classification of phase transitions (PTs)—to the microcanonical formulation of lattice gauge theories. Specifically, we explore how this approach sheds light on collective phenomena such as the emergence of topological order in quantum field theories. As a case study, we show how to systematically characterize PTs in 4D U(1) lattice electrodynamics. Beyond identifying the well-established deconfinement PT (DPT) associated with pair dissolution, classified as a first-order PT, we uncover two higher-order PTs not observed before. Thanks to the application of the MIPA, we identify an independent third-order PT in the confined phase and indications of a dependent third-order PT in the deconfined (Coulomb) phase. To gain physical insights into these PTs, we numerically compute the average number density of monopolar and pair defects as a function of energy. Notably, our findings reveal that the pair dissolution mechanism extends beyond a singular transitional phenomenon coinciding with the DPT. Instead, it encompasses a spectrum of transitional phenomena, as indicated by the rates of acceleration and deceleration in the dissolution of pairs as a function of energy. Finally, we briefly discuss how such a method can be extended to more complex quantum field theories on a lattice. Published by the American Physical Society 2024

Space clusters of magnetic currents in modified U(1) gauge model: Geometrical approach

The aim of this work is to study the spatial arrangement of magnetic currents in lattice compact electrodynamics with additional magnetic number chemical potential introduced. The behavior of the magnetic currents’ correlator on the plane of model parameters indicates the presence of several phases. By considering the mutual arrangement of microscopic currents in 4D space, two methods of geometric description of the magnetic currents’ properties are formulated. An analysis of the trends in the behavior of their characteristics shows a systematic change under the magnetic number chemical potential’s increase.

Inhomogeneous confining-deconfining phases in rotating plasmas

We discuss the effects of rotation on confining properties of gauge theories focusing on compact electrodynamics in two spatial dimensions as an analytically tractable model. We show that at finite temperature, the rotation leads to a deconfining transition starting from a certain distance from the rotation axis. A uniformly rotating confining system possesses, in addition to the usual confinement and deconfinement phases, a mixed inhomogeneous phase which hosts spatially separated confinement and deconfinement regions. The phase diagram thus has two different deconfining temperatures. The first deconfining temperature can be made arbitrarily low by sufficiently rapid rotation while the second deconfining temperature is largely unaffected by the rotation. Implications of our results for the phase diagram of QCD are presented. We point out that uniformly rotating quark-gluon plasma should therefore experience an inverse hadronization effect when the hadronization starts from the core of the rotating plasma rather than from its boundary.

Crystals of Topological Vortices in Compact Electrodynamics

This study concerns the changes in the topological properties of four-dimensional compact lattice electrodynamics. The requirement of model compactness leads to the appearance of topological defects (monopoles) creating magnetic currents. Available calculations demonstrate the occurrence of a phase transition for the birth of monopoles. In this work, a phase transition between various states has been revealed inside this phase along with some indications to the possibility of a single “monopole” phase to separate into smaller ones, which differ in the order of the arrangement of magnetic currents and their intensity. The regularity of this consideration and the consequences confirming the presence of a second phase transition in the model are substantiated. The dependence of the correlation properties of magnetic currents on the direction is demonstrated. A new method that comprehensively illustrates the changes in currents in different states with the use of geometric construction is proposed for the analysis of phase transitions.

Topological defects and confinement with machine learning: The case of monopoles in compact electrodynamics

We investigate the advantages of machine learning techniques to recognize the dynamics of topological objects in quantum field theories. We consider the compact U(1) gauge theory in three spacetime dimensions as the simplest example of a theory that exhibits confinement and mass gap phenomena generated by monopoles. We train a neural network with a generated set of monopole configurations to distinguish between confinement and deconfinement phases, from which it is possible to determine the deconfinement transition point and to predict several observables. The model uses a supervised learning approach and treats the monopole configurations as three-dimensional images (holograms). We show that the model can determine the transition temperature with accuracy, which depends on the criteria implemented in the algorithm. More importantly, we train the neural network with configurations from a single lattice size before making predictions for configurations from other lattice sizes, from which a reliable estimation of the critical temperatures are obtained.

Gauge-invariant rotor Hamiltonian from dual variables of 3D U(1) gauge theory

We present a tensor formulation for free compact electrodynamics in three Euclidean dimensions and use this formulation to construct a quantum Hamiltonian in the continuous-time limit. Gauge-invariance is maintained at every step and the resulting Hamiltonian can be written as a rotor model. The energy eigenvalues for this Hamiltonian are computed using the tensor formulation, and compared with perturbation theory. We find good agreement between the calculations demonstrating a smooth passage from the statistical lattice Lagrangian description to the quantum Hamiltonian description.

Impact of axions on confinement in three and two dimensions

In this paper we discuss well-known three- and two-dimensional models with confinement, namely, the Polyakov compact electrodynamics in 3D and two-dimensional CP(N-1) sigma model, and reveal changes in the confining regimes of these model upon adding the axion field. In both cases the addition of axion has a drastic impact. In the CP(N-1) model the axion-induced deconfinement was known previously, but we discuss a new feature not considered in the previous publication.

Model of fractionalization of Faraday lines in compact electrodynamics

Motivated by ideas of fractionalization and intrinsic topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models. Specifically, we show that a compact quantum electrodynamics (CQED) can have, besides the familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength. We construct a model that has $N$-tupled monopole condensation and realizes $1/N$ fractionalization of the quantum Faraday lines. This phase has another excitation which is a ${Z}_{N}$ quantum surface in spatial dimensions five and higher, but can be viewed as a quantum line or a quantum particle in four or three spatial dimensions, respectively. These excitations have statistical interactions with the fractionalized Faraday lines; for example, in three spatial dimensions, the particle excitation picks up a Berry phase of ${e}^{i2\ensuremath{\pi}/N}$ when going around the fractionalized Faraday line excitation. We demonstrate the existence of this phase by Monte Carlo simulations in (3+1) space-time dimensions.

Monopoles, confinement and deconfinement in lattice compact QED in (2+1)D with external fields

Finite temperature compact electrodynamics in (2+1) dimensions is studied in the presence of external electromagnetic fields. The deconfinement temperature is found to be insensitive to the external fields. This result corroborates our observation that external fields create additional small—size magnetic dipoles from the vacuum which do not spoil the confining properties of the model at low temperature. However, the Polyakov loop is not an order parameter of confinement. It can vanish in deconfinement in the presence of external field. This does not mean the restoration of confinement for certain external field fluxes. As a next step in the study of (2+1)D QED, the influence of monopoles on the photon propagator is studied. First results are presented showing this connection in the confining phase (without external field).

Critical behaviour of compact electrodynamics in 4− ϵ dimensions

Using truncated generalized Sierpinski carpets constructed from embedding hypercubic lattices we investigate the phase structure of the U(1) gauge theory for 4− ϵ dimensions. Slightly below d = 4 the first order phase transition disappears, d = 4 is conjectured to be the upper critical dimension.

Glueballs in 3-dimensional PQED with and wothout dynamical fermions

Measurements are presented of the glueball spectrum in 3D compact electrodynamics with and without dynamical fermions. The expected weak coupling behaviour of the pure gauge theory is observed on a 12 3 lattice for β > 1.5. In the coupling range studied the predominant effect of dynamical fermions is accounted for by a shift of order 0.15 relative to the pure gauge theory or, equivalently, by a mass reduction of order 25% at fixed coupling. The dependence on fermion mass is apparently weak for bare masses below 0.2.

Glueballs in 3D QED with and without dynamical fermions

Abstract Measurements are presented of the glueball spectrum in 3D compact electrodynamics with and without dynamical fermions. The expected weak coupling behaviour of the pure gauge theory is observed for β > 1.5. In the coupling range studied, the predominant effect of dynamical fermions is accounted for by a shift in β of order 0.15 relative to the pure gauge theory. There is no evidence of dramatic mixing effects when light fermions are included in the glueball-mass calculations. Evidence is also presented for spontaneous breaking of a chiral symmetry in the quenched theory. In the full dynamical theory less convincing evidence is found. The relative efficiency of Langevin, microcanonical and Metropolis algorithms for generating independent configurations are discussed and two methods for extracting glueball masses are compared.

The Monte Carlo method in lattice gauge theories

Applications of the Monte Carlo method in lattice gauge theories, including applications in quantum chromodynamics, are reviewed. The lattice formulation of gauge theories, the corresponding concepts, and the corresponding methods are introduced. The Monte Carlo method as it is applied to lattice gauge theories is described. Some specific calculations by the Monte Carlo method and their results are examined. The phase structure of lattice gauge theories with Abelian groups ZN and U(1) (a lattice formulation of a compact electrodynamics) is discussed. The non-Abelian groups SU(2), SU(3) (a lattice formulation of quantum chromodynamics), and others are also discussed. The procedure for calculating quantities referring to the continuum limit by the Monte Carlo method is discussed for quantum chromodynamics. A detailed analysis is made of results calculated for the continuum theory: string tensions and interaction potentials, which show that quarks are confined; glueball mass spectra; and the temperature of the transition from the phase of hadronic matter to the phase of a quark-gluon plasma. Masses calculated for hadrons consisting of quarks are briefly discussed.

Compact U(1) in 2+1 dimensions: The finite-lattice Hamiltonian approach

We have studied the mass spectrum and phase structure of compact electrodynamics in D = 2+1 dimensions using the finite-lattice Hamiltonian approach. The numerical results are generally comparable to, but not significantly better than, available strong-coupling series results. Evidence for roughening of the ''on-axis'' string is found at g/sup 2/ = e/sup 2/aapprox. =1.5 while the vacuum and glueball sectors of the theory are smooth for all attainable g/sup 2/ (> or approx. =0.08). Comparisons with results from applying weak-coupling approximations to the theory are also presented.

Microcanonical Ensemble Formulation of Lattice Gauge Theory

A new formulation of lattice gauge theory without explicit path integrals or sums is obtained by using the microcanonical ensemble of statistical mechanics. Expectation values in the new formalism are calculated by solving a large set of coupled, nonlinear, ordinary differential equations. The average plaquette for compact electrodynamics calculated in this fashion agrees with standard Monte Carlo results. Possible advantages of the microcanonical method in applications to fermionic systems are discussed.

A renormalisation group technique for spin and gauge systems with topological excitations

The authors' present a real space renormalisation group technique able to deal explicitly with gases of topological excitations. As examples they consider the two-dimensional XY model and the three-dimensional compact electrodynamics.

Renormalization-group calculations for U(1)-symmetric spin systems and gauge theories

We present a real-space renormalization-group analysis for the U(1) spin model in two and three dimensions and for compact electrodynamics in three and four dimensions. The Hamiltonian formulation of the theory defined on a hypercubic spatial lattice is used. The nonperturbative renormalization-group transformations we derive give continuous phase transitions for the spin models, in two and three dimensions. In three dimensions the gap exponent agrees remarkably well with series-expansion results. For the gauge theory we find, in agreement with Polyakov, that compact electrodynamics in three dimensions confines for all values of the coupling constant. A calculation for the string tension shows that it vanishes with an essential singularity at zero coupling. In four dimensions for weak enough coupling confinement is lost and the theory shows a phase transition between a charge-confining and a free-photon phase.

On the problem of θ-vacua in compact gauge theories

θ-vacua are constructed in two Abelian gauge lattice theories with a compact gauge group. One of them is the Higgs model in 1 + 1 dimensions, the other is 2 + 1 dimensional compact electrodynamics. The dependence of physics on the θ-parameter in these two models is studied. In 2 + 1 dimensional compact electrodynamics in the confinement phase, all the θ-vacua are equivalent, but in the quark emission phase there are processes which violate CP symmetry, and have amplitudes proportional to sin θ. In the Higgs model in the confinement phase CP violation is observed, provided θ ≠ 0.