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Register a new userPercolation of Vortices in the 3D Abelian Lattice Higgs Model
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The compact Abelian Higgs model is simulated on a cubic lattice where it possesses vortex lines and pointlike magnetic monopoles as topological defects. The focus of this high-precision Monte Carlo study is on the vortex network, which is investigated by means of percolation observables. In the region of the phase diagram where the Higgs and confinement phases are separated by a first-order transition, it is shown that the vortices percolate right at the phase boundary, and that the first-order nature of the transition is reflected by the network. In the crossover region, where the phase boundary ceases to be first order, the vortices are shown to still percolate. In contrast to other observables, the percolation observables show finite-size scaling. The exponents characterizing the critical behavior of the vortices in this region are shown to fall in the random percolation universality class.
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We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external : since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum dependent terms. We introduce a uniform external magnetic field and find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs Model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of successive approximations, which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).
We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different observables between TRG and Monte Carlo simulations finding excellent agreement between the two methods. In practice we find the TRG method to be far superior to Monte Carlo simulation for calculations of the Polyakov loop correlation function which is used to extract the static quark potential.
We present lattice Monte Carlo evidence of stable excitations of isolated static charges in the Higgs phase of the charge $q=2$ abelian Higgs model. These localized excitations are excited states of the interacting fields surrounding the static charges. Since the $q=2$ abelian Higgs model is a relativistic version of the Landau-Ginzburg effective action of a superconductor, we conjecture that excited states of this kind might be relevant in a condensed matter context. Taken together with recent related work in SU(3) gauge Higgs theory, our result suggests that a massive fermion excitation spectrum may be a general feature of gauge Higgs theories.
We derive finite-size scaling formulae for four-dimensional Higgs-Yukawa models near the Gaussian fixed point. These formulae will play an essential role in future, detailed investigation of such models. In particular, they can be used to determine the nature of the observed phase transitions, and confirm or rule out the possibility of having non-trivial fixed points in the Higgs-Yukawa models. Our scaling formula for Binders cumulant is tested against lattice simulations carried out at weak couplings, and good agreement is found. As a separate project, we also present preliminary results from our study of a chirally-invariant Higgs-Yukawa model including a dimension-six operator at finite temperature. Our work provides first indications of first-order temperature-induced phase transitions near the infinite cutoff limit in this model.
It is argued that the phase diagram of the 3D Compact U(1) Lattice Higgs Model is more refined than generally thought. The confined and Higgs phases are separated by a well-defined phase boundary, marked by proliferating vortices. It is shown that the confinement mechanism at work is precisely the dual superconductor scenario.
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