We study the deconfinement transition line in QCD for quark chemical potentials up to $μ_q \sim 5 T$ ($μ_B \sim 15 T$). To circumvent the sign problem we use the complex Langevin equation with gauge cooling. The plaquette gauge action is used with two flavors of naive Wilson fermions at a relatively heavy pion mass of roughly 1.3 GeV. A quadratic dependence describes the transition line well on the whole chemical potential range.
We investigate the effects of dissipation in the deconfinement transition for pure SU(2) and SU(3) gauge theories. Using an effective theory for the order parameter, we study its Langevin evolution numerically. Noise effects are included for the case of SU(2). We find that both dissipation and noise have dramatic effects on the spinodal decomposition of the order parameter and delay considerably its thermalization. For SU(3) the effects of dissipation are even larger than for SU(2).
Exploring the phase diagram of QCD at finite density is a challenging problem since first-principle calculations based on standard Monte Carlo methods suffer from the sign problem. As a promising approach to this issue, the complex Langevin method (CLM) has been pursued intensively.In this work, we investigate the applicability of the CLM in the vicinity of the deconfinement phase transition using the four-flavor staggered fermions. In particular, we look for a signal of the expected first order phase transition within the validity region of the CLM.
Monte Carlo methods cannot probe far into the QCD phase diagram with a real chemical potential, due to the famous sign problem. Complex Langevin simulations, using adaptive step-size scaling and gauge cooling, are suited for sampling path integrals with complex weights. We report here on tests of the deconfinement transition in pure Yang-Mills SU(3) simulations and present an update on the QCD phase diagram in the limit of heavy and dense quarks.
We employ the Complex Langevin method for simulation of complex-valued actions. First, we show how to test for convergence of the method by explicitely computing boundary terms and demonstrate this in a model. Then we investigate the deconfinement phase transition of QCD with $N_f=2$ Wilson-fermions using the Complex Langevin Method and. We give preliminary results for the transition temperatures up to $μ/T_c(μ=0)\approx 5$ and compute the curvature coefficient $κ_2$.
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in…
The complex Langevin method (CLM) provides a promising way to perform the path integral with a complex action using a stochastic equation for complexified dynamical variables. It is known, however, that the method gives wrong results in some cases, while it works, for instance, in finite density QCD in the deconfinement phase or in the heavy dense limit. Here we revisit the argument for justification of the CLM and point out a subtlety in using the time-evolved observables, which play a crucial role in the argument. This subtlety requires that the probability distribution of the drift term sho…
Contribution of the quark back reaction to the deconfinement phase transition is studied in the thermodynamical potential of the gluonic sector which consists of the gluon and ghost propagators calculated in the lattice QCD simulations. Starting from QCD thermodynamic potential, we define the gluonic potential in the leading-order of the 2PI formalism, which can describe the deconfinement phase transition. Then the gluonic potential can be written by using the microscopic characters; the gluon and ghost propagators in Landau gauge fixing. To include effects of the quark back reaction, we calcu…
We show that recent available lattice data for the renormalized Polyakov loop above the deconfinement phase transition exhibit unequivocal inverse power temperature corrections driven by a dimension 2 gluon condensate. This simple ansatz provides a good overall description of the data throughout the deconfinement phase until near the critical temperature with just two parameters. One of the parameters is consistent with perturbation theory while a second, non perturbative, parameter provides a numerical value of the condensate which is close to existing zero and finite temperature determinatio…
We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. We performed calculations using asqtad and HISQ/tree actions using lattices with temporal extent N_tau=6, 8 and 12 allowing to control the approach to the continuum limit. We analyze the chiral transition in terms of universal O(N) scaling functions. From peaks in the scaling functions we perform a simultaneous continuum extrapolation for HISQ/tree and asqtad to derive the critical temperature, T_c= 157 +/- 6 MeV.
The dual superconductivity is a promising mechanism of quark confinement. In the preceding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we focus on the the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. By using our new formulation of lattice Yang-Mills theory and numerical simulations on the lattice, we extract the dominant mode for confinement by decomposing the Yang-Mills field, and we investigate the Polyakov loop av…
We provide evidence for partial deconfinement -- the deconfinement of a SU($M$) subgroup of the SU($N$) gauge group -- by using lattice Monte Carlo simulations. We take matrix models as concrete examples. By appropriately fixing the gauge, we observe that the $M\times M$ submatrices deconfine. This gives direct evidence for partial deconfinement at strong coupling. We discuss the applications to QCD and holography.
The deconfinement transition in SU($N_c$) Yang--Mills is investigated by Monte Carlo simulations of the gauge theory discretized on a spacetime lattice. We present new results for $ 4 \le N_c \le 8$ (in particular, for $N_c = 5$ and $N_c = 7$), which are analysed together with previously published results. The increased amount of data, the improved statistics and simulations closer to the continuum limit provide us with better control over systematic errors. After performing the thermodynamic limit, numerical results for the ratio of the critical temperature $T_c$ over the square root of the s…
The maximum entropy method is used to compute the quark spectral function at nonzero temperature. We solve the gap equation of quantum chromodynamics (QCD) self-consistently, employing a rainbow kernel which phenomenologically models results from Dyson-Schwinger equations (DSE) and lattice QCD. We use the criterion of positivity restoration of the spectral function as a signal for deconfinement. Our calculation indicates that the critical temperature of deconfinement $T_d$ is slightly smaller than the one of chiral symmetry restoration $T_c$: $T_d\sim 94% T_c$ in the chiral limit, and $T_d\sim…
We determine the theta dependence of the deconfinement temperature of SU(3) pure gauge theory, finding that it decreases in presence of a topological theta term. We do that by performing lattice simulations at imaginary theta, then exploiting analytic continuation. We also give an estimate of such dependence in the limit of a large number of colors N, and compare it with our numerical results.
In this paper we consider the influence of relativistic rotation on the confinement/deconfinement transition in gluodynamics within lattice simulation. We perform the simulation in the reference frame which rotates with the system under investigation, where rotation is reduced to external gravitational field. To study the confinement/deconfinement transition the Polyakov loop and its susceptibility are calculated for various lattice parameters and the values of angular velocities which are characteristic for heavy-ion collision experiments. Different types of boundary conditions (open, periodi…
We conjecture that the confinement- deconfinement phase transition in QCD at large number of colors N and N_f\ll N at T\neq 0 and μ\neq 0 is triggered by the drastic change in θbehavior. The conjecture is motivated by the holographic model of QCD where confinement -deconfinement phase transition indeed happens precisely at the value of temperature T=T_c where θdependence experiences a sudden change in behavior[1]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the θdependence) are under complete theoretical control for T>T_c, s…
We propose a picture that the chiral phase transition at zero quark mass and the deconfinement transition at infinite quark mass are continuously connected. This gives a simple interpretation on the coincidence of the pseudo-critical temperatures observed in lattice QCD. We discuss a possible dynamical mechanism behind the simultaneous crossovers and show the results in a model study.
We study the confinement-deconfinement transition in $SU(2)$ gauge theory in the presence of massless bosons using lattice Monte Carlo simulations. The nature of this transition depends on the temporal extent ($N_τ$) of the Euclidean lattice. We find that the transition is a cross-over for $N_τ=2,4$ and second order with $3D$ Ising universality class for $N_τ=8$. Our results show that the second order transition is accompanied by realization of the $Z_2$ symmetry.
We examine the finite-temperature deconfinement phase transition of (2+1)-dimensional SU(5) Yang-Mills theory via non-perturbative lattice simulations. Unsurprisingly, we find that the transition is of first order, however it appears to be weak. This fits naturally into the general picture of "large" gauge groups having a first order deconfinement transition, even when the center symmetry associated with the transition might suggest otherwise.
The Z(N) center symmetry plays an important role in the deconfinement phase transition of SU(N) Yang-Mills theory at finite temperature. The exceptional group G(2) is the smallest simply connected gauge group with a trivial center. Hence, there is no symmetry reason why the low- and high-temperature regimes in G(2) Yang-Mills theory should be separated by a phase transition. Still, we present numerical evidence for the presence of a first order deconfinement phase transition at finite temperature. Via the Higgs mechanism, G(2) breaks to its SU(3) subgroup when a scalar field in the fundamental…
In the weak coupling limit of ${\rm SU}(N)$ Yang-Mills theory and the ${\rm O}(N)$ vector model, explicit state counting allows us to demonstrate the existence of a partially deconfined phase: $M$ of $N$ colors deconfine, and $\frac{M}{N}$ gradually grows from zero (confinement) to one (complete deconfinement). We point out that the mechanism admits a simple interpretation in the form of spontaneous breaking of gauge symmetry. In terms of the dual gravity theory, such breaking occurs during the formation of a black hole. We speculate whether the breaking and restoration of gauge symmetry can s…
We propose a method to determine the total magnetic susceptibility of strongly interacting matter by lattice QCD simulations, and present first numerical results for the theory with two light flavors, which suggest a weak magnetic activity in the confined phase and the emergence of strong paramagnetism in the deconfined, Quark-Gluon Plasma phase.
Using non-perturbative lattice method we studied hadronic screening correlators above and immediately below the deconfinement transition temperature, Tc, in the quenched approximation with lattice spacing of 1/(8T) using clover improved Wilson fermions. Simulations were performed at temperatures T /Tc = 0, 0.95 and 1.5. Mesonic screening correlators show no statistically significant thermal effects below Tc, and clear evidence for weakly interacting quarks above Tc . Baryon screening correlators yield similar physics above Tc, but show precursor effects for chiral symmetry restoration below Tc…
We perform SU(3) Lattice Gauge Theory simulations of the deconfinement transition attempting to mimic conditions encountered in heavy ion collisions. Specifically, we perform a sudden temperature quench across the deconfinement temperature, and follow the response of the system in successive simulation sweeps under spatial lattice expansion and temperature fall-off. In measurements of the Polyakov loop and structure functions a robust strong signal of global instability response is observed through the exponential growth of low momentum modes. Development of these long range modes isotropizes …
We present results on the chiral transition temperature Tc in 2+1 flavor QCD extrapolated to the continuum limit and the physical light quark mass. The extrapolations are based on the data from simulations on lattices with temporal extent Ntau=6, 8 and 12 with the HISQ/tree and Ntau=8 and 12 with the asqtad action. The chiral transition is analyzed in terms of universal O(N) scaling functions. After performing simultaneous asqtad and HISQ/tree continuum extrapolation the chiral transition temperature is Tc=154 +/- 9 MeV. We also discuss the deconfinement aspects of the transition in terms of t…
In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. We investigate chromomagnetic monopole currents induced by chromoelectric flux in both confinement and deconfinement phase by the numerical simulations on a lattice at finite temperature, and discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.
We study the temperature dependence of bottomonium for temperatures in the range $0.4 T_c < T < 2.1 T_c$, using nonrelativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for $N_f=2$ light flavors on a highly anisotropic lattice. We find that the $Υ$ is insensitive to the temperature in this range, while the $χ_b$ propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behaviour consistent with nearly-free dynamics at $T \simeq 2 T_c$.
The deconfinement transition at vanishing chemical potential can be reliably studied by lattice simulations and its general features are by now well known. On the contrary, what happens at finite density is still largely unknown and we will review the results obtained in the last year regarding the dependence, for small density, of the (pseudo)critical temperature on the baryonic chemical potential.
Some time ago, Svetitsky and Yaffe have argued that -- if the deconfinement phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order -- it should be in the universality class of a d-dimensional spin model symmetric under the center of G. For d=3 these arguments have been confirmed numerically only in the SU(2) case with center Z(2), simply because all SU(N) Yang-Mills theories with N>=3 seem to have non-universal first order phase transitions. The symplectic groups Sp(N) also have the center Z(2) and provide another extension of SU(2) = Sp(1) to general N. U…
The SO(3) lattice gauge theory with a Villain form of action was investigated by Monte Carlo techniques on asymmetric lattices with Nt = 2 and 4, where Nt is the number of sites in the temporal extent. Unlike the results for higher Nt, only one transition of second order was found for Nt = 2 . An extended action with an irrelevant term to suppress Z_2 monopoles enabled us to get a better view of the deconfinement transition as the effects of bulk transition could be suppressed as well. Although the action has no global Z_2 symmetry for the SO(3) theory, unlike the SU(2) theory at finite temper…
We study the influence of an external magnetic field on the deconfinement transition in two-flavour lattice QCD with physical quark charges. We use dynamical overlap fermions without any approximation such as fixed topology and perform simulations on a $16^3 \times 6$ lattice and at a pion mass around $500MeV$. The pion mass (as well as the lattice spacing) was determined in independent runs on $12^3 \times 24$ lattices. We consider two temperatures, one of which is close to the deconfinement transition and one which is above. Within our limited statistics the dependence of the Polyakov loop a…
The ghost propagator in Landau gauge is studied at finite temperature below and above $T_c$ using lattice QCD simulations. For high temperatures, we find that the ghost propagator is enhanced, compared to the confined phase. The results suggest that the ghost propagator can be used to identify the phase transition, similarly to the gluon propagator case.
We present arguments suggesting that large size overlapping instantons are the driving mechanism of the confinement-deconfinement phase transition at nonzero chemical potential mu. The arguments are based on the picture that instantons at very large chemical potential in the weak coupling regime are localized configurations with finite size rho~1/mu. At the same time, the same instantons at smaller chemical potential in the strong coupling regime are well represented by the so-called instanton-quarks with fractional topological charge 1/Nc. We estimate the critical chemical potential mu_c(T) w…
We consider a simple massive extension of the Landau-DeWitt gauge for SU($N$) Yang-Mills theory. We compute the corresponding one-loop effective potential for a temporal background gluon field at finite temperature. At this order the background field is simply related to the Polyakov loop, the order parameter of the deconfinement transition. Our perturbative calculation correctly describes a quark confining phase at low temperature and a phase transition of second order for $N=2$ and weakly first order for $N=3$. Our estimates for the transition temperatures are in qualitative agreement with v…
Using combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to N_τ\sim 6 at finite temperature. For nonzero quark chemical potentials, the effective theor…
A new method is proposed for determining the critical indices of the deconfinement transition in gauge theories, based on the finite-size scaling analysis of simple lattice operators, such as the plaquette. A precise determination of the critical index $ν$, in agreement with the prediction of the Svetitsky-Yaffe conjecture, is obtained for SU(3) gauge theory in (2+1)-dimension. Preliminary results for SU(2) in (3+1)-dimension are also given.
We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU(3) pure gauge theory in (2+1) dimensions and obtain a precise determination of the critical index $ν$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.
A lot of effort in lattice simulations over the last years has been devoted to studies of the QCD deconfinement transition. Most state-of-the-art simulations use rooted staggered fermions, while Wilson fermions are affected by large systematic uncertainties, such as coarse lattices or heavy sea quarks. Here we report on an ongoing study of the transition, using two degenerate flavours of nonperturbatively $\Ord(a)$ improved Wilson fermions. We start with $N_{t}=12$ and 16 lattices and pion masses of 600 to 450 MeV, aiming at chiral and continuum limits with light quarks.
A recently introduced method for determining the critical indices of the deconfinement transition in gauge theories, already tested for the case of 3D SU(3) pure gauge theory, is applied here to 4D SU(2) pure gauge theory. The method is inspired by universality and based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We obtain an accurate determination of the critical index $ν$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.
We study the deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions. Our simulations have been carried out on a $16^3 \times 6$ lattice at a pion mass around 500 MeV with a special HMC algorithm without any approximation such as fixed topology. We consider several temperatures from 220 MeV which is close to the deconfinement to 280 MeV which is above it. The dependence of the Polyakov loop, the chiral condensate, the Dirac spectra and the connected part of chiral susceptibility on the inverse gauge coupling has been studied. Our data indicates that the transition p…
Analyzing correlation functions of charmonia at finite temperature ($T$) on $32^3\times(32-96)$ anisotropic lattices by the maximum entropy method (MEM), we find that $J/ψ$ and $η_c$ survive as distinct resonances in the plasma even up to $T \simeq 1.6 T_c$ and that they eventually dissociate between $1.6 T_c$ and $1.9 T_c$ ($T_c$ is the critical temperature of deconfinement). This suggests that the deconfined plasma is non-perturbative enough to hold heavy-quark bound states. The importance of having sufficient number of temporal data points in the MEM analysis is also emphasized.
We analyze the finite temperature phase diagram of$QC$ with fermions in the adjoint representation. The simulations performed with four dynamical Majorana fermions show that the deconfinement and chiral phase transitions occur at two distinct temperatures. While the deconfinement transition is first order at T_d we find evidence for a continuous chiral transition at a higher temperature $T_c ~ 8 T_d. We observe a rapid change of bulk thermodynamic observables at T_d which reflects the increase in the number of degrees of freedom. However, these show little variation at T_c, where the fermion c…
It is expected that nucleons and their parity partners become degenerate when chiral symmetry is restored. We investigate this question in the context of the thermal transition from the hadronic phase to the quark-gluon plasma, using lattice QCD simulations with N_f=2+1 flavours. We observe a clear sign of parity doubling in the quark-gluon plasma. Besides, we find that the nucleon ground state is, within the uncertainty, largely independent of the temperature, whereas temperature effects are substantial in the negative-parity (N^*) channel, already in the confined phase.
We study constraints on thermal phase transitions of ${\rm SU}(N_c)$ gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless fermions: (i) adjoint fermions, and (ii) $N_f$ flavors of fundamental fermions with a nontrivial greatest common divisor ${\rm gcd}(N_c,N_f) \neq 1$. For the first case (i), we show that the chiral symmetry restoration in terms of the standard Landau-Ginzburg effective action is impossible at a temperature lower than that of deconfinement. For the second case (ii), we introduce a modified version o…
The ab-initio simulation of quantum vortices in a Bose-Einstein condensate is performed by adopting the complex Langevin techniques. We simulate the nonrelativistic boson field theory at finite chemical potential under rotation. In the superfluid phase, vortices are generated above a critical angular velocity and the circulation is clearly quantized even in the presence of quantum fluctuations.
Using the twisted partition function on R^3 x S^1, we argue that the deconfinement phase transition in pure Yang-Mills theory for all simple gauge groups is continuously connected to a quantum phase transition that can be studied in a controlled way. We explicitly consider two classes of theories, gauge theories with a center symmetry, such as SU(N_c) gauge theory for arbitrary N_c, and theories without a center symmetry, such as G_2 gauge theory. The mechanism governing the phase transition is universal and valid for all simple groups. The perturbative one-loop potential as well as monopole-i…
A phenomenological expression for the thermodynamic potential of gluons and quarks is constructed which incorporates the features of deconfinement and chiral symmetry restoration known from lattice simulations. The thermodynamic potential is a function of the Polyakov loop and chiral condensate expectation values. The gluonic sector uses a successful model for pure (SU(N_c)) gauge theories in which the Polyakov loop eigenvalues are the fundamental order parameters for deconfinement. The quark sector is given by a Nambu-Jona-Lasinio model in which a constant background (A_0) field couples the c…
Spatial confinement-deconfinement transition in accelerated gluodynamics within lattice simulation
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（波戈留博夫理论物理实验室，俄罗斯核联合研究所）；Pacific Quantum Center, Far Eastern Federal University（太平洋量子中心，远东联邦大学）；Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Science（自动化与控制过程研究所，俄罗斯科学院远东分院）
We study finite-temperature N=1 SU(2) super Yang-Mills theory, compactified on a spatial circle of size L with supersymmetric boundary conditions. In the semiclassical small-L regime, a deconfinement transition occurs at T_c <<1/L. The transition is due to a competition between non-perturbative topological "molecules"---magnetic and neutral bion-instantons---and electrically charged W-bosons and superpartners. Compared to deconfinement in non-supersymmetric QCD(adj) arXiv:1112.6389, the novelty is the relevance of the light modulus scalar field. It mediates interactions between neutral bions (…
We study the behaviour of the flux tube thickness in the vicinity of the deconfinement transition. We show, using effective string methods, that in this regime the square width increases linearly and not logarithmically with the interquark distance. The amplitude of this linear growth is an increasing function of the temperature and diverges as the deconfinement transition is approached from below. These predictions are in good agreement with a set of simulations performed in the 3d gauge Ising model.
Fermion boundary conditions play a relevant role in revealing the confinement mechanism of N=1 supersymmetric Yang-Mills theory with one compactified space-time dimension. A deconfinement phase transition occurs for a sufficiently small compactification radius, equivalent to a high temperature in the thermal theory where antiperiodic fermion boundary conditions are applied. Periodic fermion boundary conditions, on the other hand, are related to the Witten index and confinement is expected to persist independently of the length of the compactified dimension. We study this aspect with lattice Mo…
In order to deepen our understanding of the nature of the deconfinement phase transition for various gauge groups, we investigate SU(4) Yang-Mills theory in 2+1 dimensions. We find that the transition is weakly first order. We perform extensive Monte Carlo simulations on lattices with temporal extent N_t = 3, 4 and 5, and spatial sizes up to N_s = 20 N_t. We observe coexistence of confined and deconfined phases at the critical temperature, and finite-size scaling shows consistency with first order exponents. The continuum extrapolation of the latent heat yields L_h/T_c^3=0.188(17).
