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Vicente Azcoiti

Publications and source records attributed to Vicente Azcoiti.

At least 19 recordsLinked to original sources
arXiv2023

Spectral density of the Dirac-Ginsparg-Wilson operator, chiral $U(1)_A$ anomaly, and analyticity in the high temperature phase of $QCD$

Using general properties of the $Q=0$ topological sector we previously argued that a vector-like theory, with chiral $U(1)_A$ anomaly, and exact non-Abelian chiral symmetry, should exhibit divergent susceptibilities in the chiral limit, the two-flavor Schwinger model being a paradigmatic example of the realization of this scenario. Two flavor $QCD$ at $T>T_c$ satisfies all the above conditions, and it is also expected that the $U(1)_A$ axial symmetry remains effectively broken in its high temperature phase. Therefore we would expect a non-analyticity in the quark mass dependence of the free energy density, in contrast with the Dilute Instanton Gas Approximation (DIGA) prediction. We investigate in this work whether the aforementioned results can also be reproduced making only use of standard properties of the spectral density of the Dirac operator, without having to resort to general properties of the $Q=0$ topological sector. We show that the only way to derive a non-trivial $θ$-dependence, and an analytical free energy density in $QCD$ with two degenerate flavors is that the spectral density, $ρ\left(λ,m\right)$, of the absolute value of the non-zero modes of the Dirac-Ginsparg-Wilson operator develops a $m^2δ(λ)$ function in the thermodynamic limit. This is the expected result in the DIGA, where interactions between instantons in the dilute gas are fully neglected. However, at temperatures close to $T_c$ the interaction between instantons should become non-negligible, and the splitting from zero of the near-zero modes, which has been neglected in the DIGA, should be taken into account. Therefore we expect that the $m^2δ(λ)$ contribution to the spectral density is no longer correct at these temperatures, and that the free energy density becomes a non-analytic function of the quark mass.some clarifications added

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arXiv2021

Axial $U_A(1)$ Anomaly: a New Mechanism to Generate Massless Bosons

Prior to the establishment of $QCD$ as the correct theory describing hadronic physics, it was realized that the essential ingredients of the hadronic world at low energies are chiral symmetry and its spontaneous breaking. Spontaneous symmetry breaking is a non-perturbative phenomenon and thanks to massive $QCD$ simulations on the lattice we have at present a good understanding on the vacuum realization of the non-abelian chiral symmetry as a function of the physical temperature. As far as the $U_A(1)$ anomaly is concerned, and especially in the high temperature phase, the current situation is however far from satisfactory. The first part of this article is devoted to review the present status of lattice calculations, in the high temperature phase of $QCD$, of quantities directly related to the $U_A(1)$ axial anomaly. In the second part I will analyze some interesting physical implications of the $U_A(1)$ anomaly, recently suggested, in systems where the non-abelian axial symmetry is fulfilled in the vacuum. More precisely I will argue that, if the $U_A(1)$ symmetry remains effectively broken, the topological properties of the theory can be the basis of a mechanism, other than Goldstone's theorem, to generate a rich spectrum of massless bosons at the chiral limit.

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arXiv2019

Interplay between $SU(N_f)$ chiral symmetry, $U(1)_A$ axial anomaly and massless bosons

The standard wisdom on the origin of massless bosons in the spectrum of a Quantum Field Theory $(QFT)$ describing the interaction of gauge fields coupled to matter fields is based on two well known features: gauge symmetry, and spontaneous symmetry breaking of continuous global symmetries. However we will show in this article how the topological properties, that originate the $U(1)_A$ axial anomaly in a $QFT$ which describes the interaction of fermion matter fields and gauge bosons, are the basis of an alternative mechanism to generate massless bosons in the chiral limit, if the non-abelian $SU(N_f)_A$ chiral symmetry is fulfilled in the vacuum. We will also test our predictions with the results of a well known two-dimensional model, the two-flavour Schwinger model, which was analyzed by Coleman long ago, and will give a reliable answer to some of the questions he asked himself on the spectrum of the model in the strong-coupling (chiral) limit. We will also analyze what are the expectations for the $U(N)$ gauge-fermion model in two dimensions, and will discuss on the impact of our results in the chirally symmetric high temperature phase of $QCD$, which was present in the early universe, and is expected to be created in heavy-ion collision experiments.

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arXiv2017

Topology in the $SU(N_f)$ chiral symmetry restored phase of unquenched QCD and axion cosmology

The axion is one of the more interesting candidates to make the dark matter of the universe, and the axion potential plays a fundamental role in the determination of the dynamics of the axion field. Moreover, the way in which the $U(1)_A$ anomaly manifests itself in the chiral symmetry restored phase of $QCD$ at high temperature could be tested when probing the $QCD$ phase transition in relativistic heavy ion collisions. With these motivations, we investigate the physical consequences of the survival of the effects of the $U(1)_A$ anomaly in the chiral symmetric phase of $QCD$, and show that the free energy density is a singular function of the quark mass $m$, in the chiral limit, and that the $σ$ and $\barπ$ susceptibilities diverge in this limit at any $T\ge T_c$. We also show that the difference between the $\barπ$ and $\barδ$ susceptibilities diverges in the chiral limit at any $T\ge T_c$, a result that can be contrasted with the existing lattice calculations; and discuss on the generalization of these results to the $N_f\ge 3$ model.

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arXiv2017

Massive Schwinger model at finite $θ$

Using the approach developed in [V. Azcoiti, G. Di Carlo, A. Galante, V. Laliena, \textit{Phys. Lett.} \textbf{B563}, (2003) 117], we are able to reconstruct the behavior of the massive 1-flavor Schwinger model with a $θ$ term and a quantized topological charge. We calculate the full dependence of the order parameter with $θ$. Our results at $θ= π$ are compatible with Coleman's conjecture on the phase diagram of this model.

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arXiv2017

Antiferromagnetic Ising model in an imaginary magnetic field

We study the two-dimensional antiferromagnetic Ising model with a purely imaginary magnetic field, which can be thought of as a toy model for the usual $θ$ physics. Our motivation is to have a benchmark calculation in a system which suffers from a strong sign problem, so that our results can be used to test Monte Carlo methods developed to tackle such problems. We analyze here this model by means of analytical techniques, computing exactly the first eight cumulants of the expansion of the effective Hamiltonian in powers of the inverse temperature, and calculating physical observables for a large number of degrees of freedom with the help of standard multi-precision algorithms. We report accurate results for the free energy density, internal energy, standard and staggered magnetization, and the position and nature of the critical line, which confirm the mean-field qualitative picture, and which should be quantitatively reliable, at least in the high-temperature regime, including the entire critical line.

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arXiv2017

Topology in the SU(N_f) chiral symmetry restored phase of unquenched QCD and axion cosmology II

We investigate the physical consequences of the survival of the effects of the U(1)_A anomaly in the chiral symmetric phase of QCD, and show that the free energy density is a singular function of the quark mass m, in the chiral limit, and that the $σ$ and $\barπ$ susceptibilities diverge in this limit at any $T\ge T_c$. We also show that the difference between the $\barπ$ and $\barδ$ susceptibilities diverges in the chiral limit at any $T\ge T_c$, a result which seems to be excluded by recent results of Tomiya et al. from numerical simulations of two-flavor QCD. We also discuss on the generalization of these results to the $N_f\ge 3$ model.

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arXiv2016

Topology in the SU(Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology

We investigate the topological properties of unquenched $QCD$ on the basis of numerical results of simulations at fixed topological charge, recently reported by Borsanyi et al.. We demonstrate that their results for the mean value of the chiral condensate at fixed topological charge are inconsistent with the analytical prediction of the large volume expansion around the saddle point, and argue that the most plausible explanation for the failure of the saddle point expansion is a vacuum energy density $θ$-independent at high temperatures, but surprisingly not too high $(T\sim 2T_c)$, a result which would imply a vanishing topological susceptibility, and the absence of all physical effects of the $U(1)$ axial anomaly at these temperatures. We also show that under a general assumption concerning the high temperature phase of $QCD$, where the $SU(N_f)_A$ symmetry is restored, the analytical prediction for the chiral condensate at fixed topological charge is in very good agreement with the numerical results of Borsanyi et al., all effects of the axial anomaly should disappear, the topological susceptibility and all the $θ$-derivatives of the vacuum energy density vanish and the theory becomes $θ$-independent at any $T>T_c$ in the infinite volume limit.

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arXiv2013

Elucidating the Vacuum Structure of the Aoki Phase

In this paper, we discuss the vacuum structure of QCD with two flavors of Wilson fermions, inside the Aoki phase. We provide numerical evidence, coming from HMC simulations in $4^4$, $6^4$ and $8^4$ lattices, supporting a vacuum structure for this model at strong coupling more complex than the one assumed in the standard wisdom, with new vacua where the expectation value of $i\barψγ_5ψ$ can take non-zero values, and which can not be connected with the Aoki vacua by parity-flavour symmetry transformations.

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arXiv2012

Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations

We investigate the critical behaviour at theta=pi of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of theta, and on scaling transformations that allow a controlled analytic continuation to real values of theta. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2)_1 Wess-Zumino-Novikov-Witten model, for sufficiently small values of the coupling.

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arXiv2011

Progress in numerical simulations of systems with a $θ-$vacuum like term: The two and three-dimensional Ising model within an imaginary magnetic field

Using the approach developed in \cite{REFVIC2}, we succeeded in reconstructing the behaviour of the antiferromagnetic Ising model with imaginary magnetic field $iθ$ for two and three dimensions in the low temperature regime. A mean-field calculation, expected to work well for high dimensions, is also carried out, and the mean-field results coincide qualitatively with those of the two- and three-dimensional Ising model. The mean field analysis reveals also a phase structure more complex than the one expected for $QCD$ with a topological $θ-$therm.

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arXiv2009

Geometric Algorithm for Abelian-Gauge Models

Motivated by the sign problem in several systems, we have developed a geometric simulation algorithm based on the strong coupling expansion which can be applied to abelian pure gauge models. We have studied the algorithm in the U(1) model in 3 and 4 dimensions, and seen that it is practical and is similarly efficient to the standard heat-bath algorithm, but without the ergodicity problems which comes from the presence of vortices. We have also applied the algorithm to the Ising gauge model at the critical point, and we find hints of a better asymptotic behaviour of the autocorrelation time, which therefore suggests the possibility of a smaller dynamical critical exponent with respect to the standard heat-bath algorithm.

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arXiv2005

Phase diagram of QCD with four quark flavors at finite temperature and baryon density

We analyze the phase diagram of QCD with four staggered flavors in the (mu, T) plane using a method recently proposed by us. We explore the region T > 0.7 Tc and mu <1.4 Tc, where Tc is the transition temperature at zero baryon density, and find a first order transition line. Our results are quantitatively compatible with those obtained with the imaginary chemical potential approach and the double reweighting method, in the region where these approaches are reliable, T > 0.9 Tc and mu < Tc. But, in addition, our method allows us to extend the transition line to lower temperatures and higher chemical potentials.

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arXiv2005

Phase structure of four flavor QCD in the T μplane from a new method for simulations of lattice gauge theories at non zero baryon density

We review a method for numerical simulations of lattice gauge theories at non-zero baryonic chemical potential we recently proposed. We first report on a test of the method using a solvable model and then present results for the phase structure of four flavour QCD. For the first time the region of chemical potential up to 1.4 T_C is explored, finding a first order transition line.

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arXiv2005

Finite Density QCD: a New Approach

We introduce a new approach to analyze the phase diagram of QCD at finite chemical potential and temperature, test it in the Gross-Neveu model at finite baryon density, and apply it to the study of the chemical potential-temperature phase diagram of QCD with four degenerate flavors of Kogut-Susskind type.

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arXiv2004

Strong coupling analysis of diquark condensation

The phenomenon of diquark condensation at non-zero baryon density and zero temperature is analyzed in the strong coupling limit of lattice QCD. The results indicate that there is attraction in the quark-quark channel also at strong coupling, and that the attraction is more effective at high baryon density, but for infinite coupling it is not enough to produce diquark condensation. It is argued that the absence of diquark condensation is not a peculiarity of the strong coupling limit, but persists at sufficiently large finite couplings.

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arXiv2004

New Ideas in Finite Density QCD

We introduce a new approach to analyze the phase diagram of QCD at finite chemical potential and temperature, based on the definition of a generalized QCD action. Several details of the method will be discussed, with particular emphasis on the advantages respect to the imaginary chemical potential approach.

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