arXiv subjects

Claudio Bonati

Publications and source records attributed to Claudio Bonati.

At least 37 records · Page 2Linked to original sources

arXiv2024

The $θ$-dependence of the Yang-Mills spectrum from analytic continuation

We study the $θ$-dependence of the string tension and of the lightest glueball mass in four-dimensional $\mathrm{SU}(N)$ Yang-Mills theories. More precisely, we focus on the coefficients parametrizing the $\mathcal{O}(θ^2)$ dependence of these quantities, which we investigate by means of numerical simulations of the lattice-discretized theory, carried out using imaginary values of the $θ$ parameter. Topological freezing at large $N$ is avoided using the Parallel Tempering on Boundary Conditions algorithm. We provide controlled continuum extrapolations of such coefficients in the $N=3$ case, and we report the results obtained on two fairly fine lattice spacings for $N=6$.

hep-lat↗

arXiv2024

Three-dimensional ${\mathbb Z}_2$-gauge $N$-vector models

We study the phase diagram and critical behaviors of three-dimensional lattice ${\mathbb Z}_2$-gauge $N$-vector models, in which an $N$-component real field is minimally coupled with a ${\mathbb Z}_2$-gauge link variables. These models are invariant under global O($N$) and local ${\mathbb Z}_2$ transformations. They present three phases characterized by the spontaneous breaking of the global O($N$) symmetry and by the different topological properties of the ${\mathbb Z}_2$-gauge correlations. We address the nature of the three transition lines separating the three phases. The theoretical predictions are supported by numerical finite-size scaling analyses of Monte Carlo data for the $N=2$ model. In this case, continuous transitions can be observed along both transition lines where the spins order, in the regime of small and large inverse gauge coupling $K$. Even though these continuous transitions belong to the same $XY$ universality class, their critical modes turn out to be different. When the gauge variables are disordered (small $K$), the relevant order-parameter field is a gauge-invariant bilinear combination of the vector field. On the other hand, when the gauge variables are ordered (large $K$), the order-parameter field is the gauge-dependent $N$-vector field, whose critical behavior can only be probed by using a stochastic gauge fixing that reduces the gauge freedom.

cond-mat.stat-mech↗

arXiv2024

Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields

We investigate the nature of the deconfinement transitions in three-dimensional lattice Abelian Higgs models, in which a complex scalar field of integer charge $Q\ge 2$ is minimally coupled with a compact $U(1)$ gauge field. Their phase diagram presents two phases separated by a transition line where static charges $q$, with $q<Q$, deconfine. We argue that these deconfinement transitions belong to the same universality class as transitions in generic three-dimensional ${\mathbb Z}_Q$ gauge models. In particular, they are Ising-like for $Q=2$, of first order for $Q=3$, and belong to the three-dimensional gauge $XY$ universality class for $Q\ge 4$. This general scenario is supported by numerical finite-size scaling analyses of the energy cumulants for $Q=2$, $Q=4$, and $Q=6$.

hep-lat↗

arXiv2024

Diverse universality classes of the topological deconfinement transitions of three-dimensional noncompact lattice Abelian-Higgs models

We study the topological phase transitions occurring in three-dimensional (3D) multicomponent lattice Abelian-Higgs (LAH) models, in which an $N$-component scalar field is minimally coupled with a noncompact Abelian gauge field, with a global SU($N$) symmetry. Their phase diagram presents a high-temperature Coulomb (C) phase, and two low-temperature molecular (M) and Higgs (H) phases, both characterized by the spontaneous breaking of the SU($N$) symmetry. The molecular-Higgs (MH) and Coulomb-Higgs (CH) transitions are topological transitions, separating a phase with gapless gauge modes and confined charges from a phase with gapped gauge modes and deconfined charged excitations. These transitions are not described by effective Landau-Ginzburg-Wilson theories, due to the active role of the gauge modes. We show that the MH and CH transitions belong to different charged universality classes. The CH transitions are associated with the $N$-dependent charged fixed point of the renormalization-group (RG) flow of the 3D Abelian-Higgs field theory (AHFT). On the other hand, the universality class of the MH transitions is independent of $N$ and coincides with that controlling the continuous transitions of the one-component ($N=1$) LAH model. In particular, we verify that the gauge critical behavior always corresponds to that observed in the 3D inverted XY model, and that the correlations of an extended charged gauge-invariant operator (in the Lorenz gauge, this operator corresponds to the scalar field, thus it is local, justifing the use of the RG framework) have an $N$-independent critical universal behavior. This scenario is supported by numerical results for $N=1,\,2,\,25$. The MH critical behavior does not apparently have an interpretation in terms of the RG flow of the AHFT, as determined perturbatively close to four dimensions or with standard large-$N$ methods.

cond-mat.stat-mech↗

arXiv2024

Comment on "Machine Learning the Operator Content of the Critical Self-Dual Ising-Higgs Gauge Model'', arXiv:2311.17994v1

We critically discuss the results reported in arXiv:2311.17994v1 by L. Oppenheim, M. Koch-Janusz, S. Gazit, and Z. Ringel, on the multicritical behavior of the three-dimensional Ising-Gauge model at the multicritical point. We argue that their results do not contradict the theoretical scenario put forward in ``Multicritical point of the three-dimensional ${\mathbb Z}_2$ gauge Higgs model'', Phys. Rev. B 105, 165138 (2022), arXiv:2112.01824, that predicted a multicritical behavior controlled by the stable $XY$ fixed point of an effective three-dimensional ${\mathbb Z}_2\oplus {\mathbb Z}_2$ Landau-Ginzburg-Wilson $Φ^4$ field theory. Actually, their results, as well as all numerical results reported so far in the literature, are consistent with a multicritical $XY$ scenario.

cond-mat.stat-mech↗

arXiv2023

Abelian Higgs gauge theories with multicomponent scalar fields and multiparameter scalar potentials

We consider multicomponent Abelian Higgs (AH) gauge theories with multiparameter scalar quartic potentials that are extensions, with a smaller global symmetry group, of $SU(N)$-invariant AH theories. In particular, we consider an AH model with a two-parameter scalar potential and $SO(N)$ global symmetry. We discuss the renormalization-group flow of the $SO(N)$-invariant AH field theory and the phase diagram and critical behavior of a corresponding three-dimensional (3D) noncompact lattice AH model. We argue that the phase diagram of 3D noncompact $SO(N)$- and $SU(N)$-symmetric lattice AH models are qualitatively similar. In both cases there are three phases: the high-temperature Coulomb phase, and the low-temperature molecular and Higgs phases that differ for the topological properties of the gauge correlations. However, the main features of the low-temperature ordered phases, and in particular of the Higgs phase, differ significantly in $SO(N)$ and $SU(N)$ models. In particular, in $SO(N)$ models they depend on the sign of the self-interaction parameter $v$ that controls the symmetry breaking from $SU(N)$ to $SO(N)$. As a consequence, also the universal features of the transitions related with the spontaneous breaking of the global symmetry (those between the high-temperature Coulomb phase and the low-temperature molecular and Higgs phases) depend on the sign of $v$.

cond-mat.stat-mech↗

arXiv2023

Quantum Algorithms for the computation of quantum thermal averages at work

Recently, a variety of quantum algorithms have been devised to estimate thermal averages on a genuine quantum processor. In this paper, we consider the practical implementation of the so-called Quantum-Quantum Metropolis algorithm. As a testbed for this purpose, we simulate a basic system of three frustrated quantum spins and discuss its systematics, also in comparison with the Quantum Metropolis Sampling algorithm.

quant-ph↗

arXiv2023

The Coulomb-Higgs phase transition of three-dimensional lattice Abelian-Higgs gauge models with noncompact gauge variables and gauge fixing

We study the critical behavior of three-dimensional (3D) lattice Abelian-Higgs (AH) gauge models with noncompact gauge variables and multicomponent complex scalar fields, along the transition line between the Coulomb and Higgs phases. Previous works that focused on gauge-invariant correlations provided evidence that, for a sufficiently large number of scalar components, these transitions are continuous and associated with the stable charged fixed point of the renormalization-group flow of the 3D AH field theory (scalar electrodynamics), in which charged scalar matter is minimally coupled with an electromagnetic field. Here we extend these studies by considering gauge-dependent correlations of the gauge and matter fields, in the presence of two different gauge fixings, the Lorenz and the axial gauge fixing. Our results for N=25 are definitely consistent with the predictions of the AH field theory and therefore provide additional evidence for the characterization of the 3D AH transitions along the Coulomb-Higgs line as charged transitions in the AH field-theory universality class. Moreover, our results give additional insights on the role of the gauge fixing at charged transitions. In particular, we show that scalar correlations are critical only if a hard Lorenz gauge fixing is imposed.

cond-mat.stat-mech↗

arXiv2023

Gauge fixing and gauge correlations in noncompact Abelian gauge models

We investigate some general properties of linear gauge fixings and gauge-field correlators in lattice models with noncompact U(1) gauge symmetry. In particular, we show that, even in the presence of a gauge fixing, some gauge-field observables (like the photon-mass operator) are not well-defined, depending on the specific gauge fixing adopted and on its implementation. Numerical tests carried out in the three-dimensional noncompact lattice Abelian Higgs model fully support the analytical results and provide further insights.

hep-lat↗

arXiv2022

Chiral critical behavior of 3D lattice fermionic models with quartic interactions

We study the critical behavior of the three-dimensional (3D) Gross-Neveu (GN) model with $N_f$ Dirac fermionic flavors and quartic interactions, at the chiral ${\mathbb Z}_2$ transition in the massless ${\mathbb Z}_2$-symmetric limit. For this purpose, we consider a lattice GN model with staggered Kogut-Susskind fermions and a scalar field coupled to the scalar bilinear fermionic operator, which effectively realizes the attractive four-fermion interaction. We perform Monte Carlo (MC) simulations for $N_f=4,8,12,16$. By means of finite-size scaling analyses of the numerical data, we obtain estimates of the critical exponents that are compared with the large-$N_f$ predictions obtained using the continuum GN field theory. We observe a substantial agreement. This confirms that lattice GN models with staggered fermions provide a nonpertubative realization of the GN quantum field theory, even though the lattice interactions explicitly break the flavor ${\rm U}(N_f)\otimes {\rm U}(N_f)$ symmetry of the GN field theory, which is only recovered in the critical limit.

hep-lat↗

arXiv2022

Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement

We study the phase diagram and phase transitions of the three dimensional multicomponent lattice Higgs model with non-compact Abelian discrete groups. The model with non-compact U(1) gauge group is known to undergo, for a sufficiently large number of scalar fields $N$, a continuous transition associated to the charged fixed point of the continuous Abelian Higgs field theory. We show that in the model with gauge group $\mathbb{Z}_q^{(nc)}\equiv 2π\mathbb{Z}/q$ only critical transitions in the orthogonal universality classes are present for small values of $N$, while a symmetry enlargement to the continuous Abelian Higgs universality class happens when $q\ge 5$ and $N$ is large enough.

hep-lat↗

arXiv2022

The QCD topological susceptibility at high temperatures via staggered fermions spectral projectors

The QCD topological observables are essential inputs to obtain theoretical predictions about axion phenomenology, which are of utmost importance for current and future experimental searches for this particle. Among them, we focus on the topological susceptibility, related to the axion mass. We present lattice results for the topological susceptibility in QCD at high temperatures obtained by discretizing this observable via spectral projectors on eigenmodes of the staggered Dirac operator, and we compare them with those obtained with the standard gluonic definition. The adoption of the spectral discretization is motivated by the large lattice artifacts affecting the standard gluonic susceptibility, related to the choice of non-chiral fermions in the lattice action.

hep-lat↗

arXiv2022

Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures

We compute the topological susceptibility of $N_f=2+1$ QCD with physical quark masses in the high-temperature phase, using numerical simulations of the theory discretized on a space-time lattice. More precisely we estimate the topological susceptibility for five temperatures in the range from $\sim200$ MeV up to $\sim600$ MeV, adopting the spectral projectors definition of the topological charge based on the staggered Dirac operator. This strategy turns out to be effective in reducing the large lattice artifacts which affect the standard gluonic definition, making it possible to perform a reliable continuum extrapolation. Our results for the susceptibility in the explored temperature range are found to be partially in tension with previous determinations in the literature.

hep-lat↗

arXiv2022

Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields

We address the interplay between local and global symmetries in determining the continuum limit of two-dimensional lattice scalar theories characterized by $SO(N_c)$ gauge symmetry and non-Abelian $O(N_f)$ global invariance. We argue that, when a quartic interaction is present, the continuum limit of these model corresponds in some cases to the gauged non-linear $σ$ model field theory associated with the real Grassmannian manifold $SO(N_f)/(SO(N_c)\times SO(N_f-N_c)$), which is characterized by the invariance under the color-flavor reflection $N_c\leftrightarrow N_f-N_c$. Monte Carlo simulations and Finite-Size Scaling analyses, performed for $N_f=7$ and several values of $N_c$, confirm the emergence of the color-flavor reflection symmetry in the scaling limit, and support the identification of the continuum limit.

hep-lat↗

arXiv2022

Scalar gauge-Higgs models with discrete Abelian symmetry groups

We investigate the phase diagram and the nature of the phase transitions of three-dimensional lattice gauge-Higgs models obtained by gauging the Z_N subgroup of the global Z_q invariance group of the Z_q clock model (N is a submultiple of q). The phase diagram is generally characterized by the presence of three different phases, separated by three distinct transition lines. We investigate the critical behavior along the two transition lines characterized by the ordering of the scalar field. Along the transition line separating the disordered-confined phase from the ordered-deconfined phase, standard arguments within the Landau-Ginzburg-Wilson framework predict that the behavior is the same as in a generic ferromagnetic model with Z_p global symmetry, p being the ratio q/N. Thus, continuous transitions belong to the Ising and to the O(2) universality class for p=2 and p>3, respectively, while for p=3 only first-order transitions are possible. The results of Monte Carlo simulations confirm these predictions. There is also a second transition line, which separates two phases in which gauge fields are essentially ordered. Along this line we observe the same critical behavior as in the Z_q clock model, as it occurs in the absence of gauge fields.

cond-mat.stat-mech↗

arXiv2022

Three-dimensional monopole-free CP$^{N-1}$ models: Behavior in the presence of a quartic potential

We investigate the phase diagram and the nature of the phase transitions in a three-dimensional model characterized by a global SU($N$) symmetry, a local U(1) symmetry, and the absence of monopoles. It represents a natural generalization of the gauge monopole-free (MF) CP$^{N-1}$ model, in which the fixed-length constraint (London limit) is relaxed. We have performed Monte Carlo simulations for $N=2$ and 25, observing a finite-temperature transition in both cases, related to the condensation of a local gauge-invariant order parameter. For $N=2$ results for the MF model are consistent with a weak first-order transition. A continuous transition would be possible only if scaling corrections were anomalously large. For $N=25$ the results in the general MF model are also consistent with a first-order transition, that becomes weaker as the size of the field-length fluctuations decreases.

cond-mat.stat-mech↗

arXiv2022

Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials

We consider three-dimensional lattice SU(Nc) gauge theories with degenerate multicomponent (Nf>1) complex scalar fields that transform under the fundamental representation of the gauge SU(Nc) group and of the global U(Nf) invariance group, interacting with the most general quartic potential compatible with the global (flavor) and gauge (color) symmetries. We investigate the phase diagrams, identifying the low-temperature Higgs phases and their global and gauge symmetries, and the critical behaviors along the different transition lines. In particular, we address the role of the quartic scalar potential, which determines the Higgs phases and the corresponding symmetry-breaking patterns. Our study is based on the analysis of the minimum-energy configurations and on numerical Monte Carlo simulations. Moreover, we investigate whether some of the transitions observed in the lattice model can be related to the behavior of the renormalization-group flow of the continuum field theory with the same symmetries and field content around its stable charged fixed points. For Nc=2, numerical results are consistent with the existence of charged critical behaviors for Nf > Nf*, with 20 < Nf* < 40.

cond-mat.stat-mech↗

arXiv2022

Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory

We investigate under which conditions the three-dimensional (3D) multicomponent Abelian-Higgs (AH) field theory (scalar electrodynamics) is the continuum limit of statistical lattice gauge models, i.e., when it characterizes the universal behavior at critical transitions occurring in these models. We perform Monte Carlo simulations of the lattice AH model with compact gauge fields and $N$-component scalar fields with charge $q\ge 2$ for $N=15$ and 25. Finite-size scaling analyses of the Monte Carlo data show that the transitions along the line separating the confined and deconfined phases are continuous and that they belong to the same universality class for any $q\ge 2$. Moreover, they are in the same universality class as the transitions in the lattice AH model with noncompact gauge fields along the Coulomb-to-Higgs transition line. We finally argue that these critical behaviors are described by the stable charged fixed point of the renormalization-group flow of the 3D AH field theory.

cond-mat.stat-mech↗