Chiral Transition Research Articles

Baryon number fluctuations and the phase structure in the PNJL model

We investigate the kurtosis and skewness of net-baryon number fluctuations in the Polyakov loop extended Nambu–Jona-Lasinio (PNJL) model, and discuss the relations between fluctuation distributions and the phase structure of quark-gluon matter. The calculation shows that the traces of chiral and deconfinement transitions can be effectively reflected by the kurtosis and skewness of net-baryon number fluctuations not only in the critical region but also in the crossover region. The contour plot of baryon number kurtosis derived in the PNJL model can qualitatively explain the behavior of net-proton number kurtosis in the STAR beam energy scan experiments. Moreover, the three-dimensional presentations of the kurtosis and skewness in this study are helpful to understand the relations between baryon number fluctuations and QCD phase structure.

Multiple critical endpoints in magnetized three flavor quark matter

The magnetized phase diagram for three-flavor quark matter is studied within the Polyakov extended Nambu--Jona-Lasinio model. The order parameters are analyzed with special emphasis on the strange quark condensate. We show that the presence of an external magnetic field induces several critical endpoints (CEPs) in the strange sector, which arise due to the multiple phase transitions that the strange quark undergoes. The spinodal and binodal regions of the phase transitions are shown to increase with external magnetic field strength. The influence of strong magnetic fields on the isentropic trajectories around the several CEPs is analyzed. A focusing effect is observed on the region towards the CEPs that are related with the strange quark phase transitions. Compared to the chiral transitions, the deconfinement transition turns out to be less sensitive to the external magnetic field and the crossover nature is preserved over the whole phase diagram.

Axial anomaly and nesting in the inhomogeneous chiral phase

Axial anomaly and nesting is elucidated in the context of the inhomogeneous chiral phase. Using the Gross-Neveu models in 1+1 dimensions, we shall discuss axial anomaly and nesting from two different points of view: one is homogeneous chiral transition and the other is the Ferrel-Fulde-Larkin-Ovchinnikov (FFLO) state in superconductivity, which are closely related to each other by way of duality. It is shown that axial anomaly leads to a particular kind of the FFLO state within the two dimensional Nambu-Jona Lasinio model, where axial anomaly is manifested in a different mode. Nesting is a driving mechanism for both phenomena, but its realization has different features. We reconsider the effect of nesting in the context of duality.

Chiral crossover transition in a finite volume**Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment & Technology in Huazhong University of Science & Technology (DMETKF2015015)

Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature of the crossover, showing a significant decrease in as L decreases below 3 fm.

Dual Formulation and Phase Diagram of Lattice QCD in the Strong Coupling Regime

We present the computation of invariants that arise in the strong coupling expansion of lattice QCD. These invariants are needed for Monte Carlo simulations of Lattice QCD with staggered fermions in a dual, color singlet representation. This formulation is in particular useful to tame the finite density sign problem. The gauge integrals in this limiting case β → 0 are well known, but the gauge integrals needed to study the gauge corrections are more involved. We discuss a method to evaluate such integrals. The phase boundary of lattice QCD for staggered fermions in the μB – T plane has been established in the strong coupling limit. We present numerical simulations away from the strong coupling limit, taking into account the higher order gauge corrections via plaquette occupation numbers. This allows to study the nuclear and chiral transition as a function of β.

Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

We report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge-fixing method and which show an improved agreement with the continuum results. By relating the Gribov confinement scenario to the center vortex picture of confinement, it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector, a vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. The effective potential of the Polyakov loop is evaluated from the zero-temperature variational solution. For pure Yang–Mills theory, the deconfinement phase transition is found to be second order for SU(2) and first order for SU(3), in agreement with the lattice results. The corresponding critical temperatures are found to be 275 MeV and 280 MeV, respectively. When quarks are included, the deconfinement transition turns into a crossover. From the dual and chiral quark condensate, one finds pseudocritical temperatures of 198 MeV and 170 MeV, respectively, for the deconfinement and chiral transition.

Probing the tricritical endpoint of QCD phase diagram at NICAFAIR energies

In this contributions we discuss the novel version of hadron resonance gas model which is based on the induced surface tension concept. Also we present new arguments in favor of a hypothesis that the chiral symmetry restoration transition in central nuclear collisions may occur at the center of mass energies 4.3-4.9 GeV and that the deconfinement phase transition may occur at the center of mass energies 8.8-9.2 GeV. These arguments are based on the unique thermostatic properties of the mixed phase and the ones of an exponential mass spectrum of hadrons.

Instanton-dyon ensembles reproduce deconfinement and chiral restoration phase transitions

Paradigm shift in gauge topology at finite temperatures, from the instantons to their constituents – instanton-dyons – has recently lead to studies of their ensembles and very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at suffciently high density explains the chiral symmetry breaking transition. Unlike instantons, these objects have electric and magnetic charges. Simulations of the instanton-dyon ensembles have demonstrated that their back reaction on the Polyakov line modifies its potential and generates the deconfinement phase transition. For the Nc = 2 gauge theory the transition is second order, for QCD-like theory with Nc = 2 and two light quark flavors Nf = 2 both transitions are weak crossovers at happening at about the same condition. Introduction of quark-flavor-dependent periodicity phases (imaginary chemical potentials) leads to drastic changes in both transitions. In particulaly, in the so called Z(Nc) – QCD model the deconfinement transforms to strong first order transition, while the chiral condensate does not disappear at all. The talk will also cover more detailed studies of correlations between the dyons, effective eta’ mass and other screening masses.

Recent Advances in Cooperative Catalysis of Chiral Lewis Base and Transition Metal Catalyst

Recent Advances in Cooperative Catalysis of Chiral Lewis Base and Transition Metal Catalyst

Chiral Transition of SU(4) Gauge Theory with Fermions in Multiple Representations

We report preliminary results on the finite temperature behavior of SU(4) gauge theory with dynamical quarks in both the fundamental and two-index antisymmetric representations. This system is a candidate to present scale separation behavior, where fermions in different representations condense at different temperature or coupling scales. Our simulations, however, reveal a single finite-temperature phase transition at which both representations deconfine and exhibit chiral restoration. It appears to be strongly first order. We compare our results to previous single-representation simulations. We also describe a Pisarski-Wilczek stability analysis, which suggests that the transition should be first order.

Particle states of lattice QCD

We determine the degeneracy factor and the average particle mass of particles that produce the lattice QCD pressure and specific entropy at zero baryon chemical potential. The number of states of the gluons and the quarks are found to converge above T=230 MeV to almost constant values, close to the number of states of an ideal quark–gluon phase, while their assigned masses retain high values. The number of states and the average mass of a system containing quarks in interaction with gluons are found to decrease steeply with increase of temperature between T sim 150 and 160 MeV, a region contained within the region of the chiral transition. The minimum value of the number of states within this temperature interval indicates that the states are of hadronic nature.

Effect of chiral selective tunneling on quantum transport in magnetic topological-insulator thin films

The electronic transport properties in magnetically doped ultra-thin films of topological-insulators is investigated by using Landauer-buttiker formalism. The chiral selective tunneling is addressed in such systems which leads to transport gap and as a consequence current blocking. This quantum blocking of transport occurs when the magnetic states with opposite chirality are aligned energetically. This can be obsereved when an electron tunnels through a barrier or well of magnetic potential induced by the exchange field. It is proved and demonstrated that this chiral transition rule fails when structural inversion asymmetric potential or an in-plane magnetization is turning on. This new finding is useful to interpret quantum transport through topological-insulator thin films especially to shed light on longitudinal conductance behavior of quantum anomalous Hall effect. Besides, one can design electronic devices by means of magnetic topological-insulator thin films based on the chiral selective tunneling leading to negative differential resistance.

Concentration-dependent multiple chirality transition in halogen-bond-driven 2D self-assembly process

The concentration-dependent self-assembly of iodine substituted thienophenanthrene derivative (5,10-DITD) is investigated at the 1-octanic acid/graphite interface using scanning tunneling microscopy. Three kinds of chiral arrangement and transition of 2D molecular assembly mainly driven by halogen bonding is clearly revealed. At high concentration the molecules self-assembled into a honeycomb-like chiral network. Except for the interchain van der Waals forces, this pattern is stabilized by intermolecular continuous CO⋯I⋯S halogen bonds in each zigzag line. At moderate concentration, a chiral kite-like nanoarchitecture are observed, in which the CO⋯I⋯S and I⋯OC halogen bonds, along with the molecule–solvent CO⋯I⋯H halogen bonds are the dominated forces to determine the structural formation. At low concentration, the molecules form a chiral cyclic network resulting from the solvent coadsorption mainly by molecule–molecule CO⋯I⋯S halogen bonds and molecule–solvent CO⋯I⋯H halogen bonds. The density of molecular packing becomes lower with the decreasing of the solution concentration. The solution-concentration dependent self-assembly of thienophenanthrene derivative with iodine and ester chain moieties reveals that the type of intermolecular halogen bond and the number of the co-adsorbing 1-octanic acids by molecule–solvent CO⋯I⋯H halogen bonds determine the formation and transformation of chirality. This research emphasizes the role of different types of halogen (I) bonds in the controllable supramolecular structures and provides an approach for the fabrication of chirality.

Phase structure and propagators at nonvanishing temperature for QCD and QCD-like theories

We investigate the universality of truncation schemes for Dyson-Schwinger equations developed for quantum chromodynamics in theories which differ from quantum chromodynamics only in the gauge group. Our specific choices are the gauge groups $SU(2)$ and $G_2$, for which lattice calculations at nonvanishing chemical potential are possible. Thus, corresponding calculations can provide benchmarks for testing calculations with functional equations. We calculate the quark and gluon propagators and determine the chiral and dual chiral condensates at vanishing density to determine the confinement/deconfinement and chiral transitions, respectively. We can reproduce the expected type of transitions in the quenched and unquenched cases. In general, all three theories react very similarly to modifications of the employed model for the quark-gluon vertex.

A universal order parameter for Inverse Magnetic Catalysis

We revisit the chiral transition in the finite density Sakai-Sugimoto model and find that, at fixed temperature T, the magnetisation near the critical line μc(B) acts as an order parameter to distinguish Inverse Magnetic Catalysis from Magnetic Catalysis. Moreover, we propose a universal relation between μc(B) and the magnetisation that allows us to predict the behaviour of the former from the behaviour of the latter. We find that a similar relation holds, at fixed chemical potential μ, for the critical line Tc(B). Our results are obtained by investigating a fully numerical solution to the relevant equations. At low temperatures our results reduce to those obtained by Preis, Rebhan and Schmitt [1], based on a semi-analytic approximation.

How tetraquarks can affect the chiral phase transition

We discuss the possible role which scalar mesons composed of tetraquarks can play in the chiral phase transition for three colors and two or three light flavors. For two flavors the tetraquark is an isoscalar, and isn't expected to significantly affect the chiral transition. For three flavors, however, one can naturally form a tetraquark field which in the same representation as the usual chiral field. Having two fields can alter the chiral transition significantly: for light fields, they may produce two chiral phase transitions. For QCD, in the plane of temperature and chemical potential we argue that a crossover line for the tetraquark condensate naturally connects to a line of phase transitions for color superconductivity.

Higher-order baryon number susceptibilities: Interplay between the chiral and the nuclear liquid-gas transitions

We use an improved version of the SU(3) flavour parity-doublet quark-hadron model to investigate the higher order baryon number susceptibilities near the chiral and the nuclear liquid-gas transitions. The parity-doublet model has been improved by adding higher-order interaction terms of the scalar fields in the effective mean field Lagrangian, resulting in a much-improved description of nuclear ground-state properties, in particular the nuclear compressibility. The resulting phase diagram of the model agrees qualitatively with expectations from lattice QCD, i.e., it shows a crossover at zero net baryo-chemical potential and a critical point at finite density. Using this model, we investigate the dependence of the higher-order baryon number susceptibilities as function of temperature and chemical potential. We observe a strong interplay between the chiral and liquid-gas transition at intermediate baryo chemical potentials. Due to this interplay between the chiral and the nuclear liquid-gas transitions, the experimentally measured cumulants of the net baryon number may show very different beam energy dependence, subject to the actual freeze-out temperature.

Landau-Ginzburg-Wilson approach to critical phenomena in the presence of gauge symmetries

We critically reconsider the Landau-Ginzburg-Wilson (LGW) approach to critical phenomena in the presence of gauge symmetries. In the LGW framework, to obtain the universal features of a continuous transition, one identifies the order parameter $\mathrm{\ensuremath{\Phi}}$ and considers the corresponding most general ${\mathrm{\ensuremath{\Phi}}}^{4}$ field theory that has the same symmetries as the original model. In the presence of gauge symmetries, one usually considers a gauge-invariant order parameter and a LGW field theory that is invariant under the global symmetries of the original model. We show that this approach, in which the gauge dynamics is effectively integrated out, may sometimes lead to erroneous conclusions on the nature of the critical behavior. As an explicit example, we show that the above-described LGW approach generally fails for the three-dimensional ferromagnetic and antiferromagnetic ${\mathrm{CP}}^{N\ensuremath{-}1}$ models, which are invariant under global $\mathrm{U}(N)$ and local U(1) transformations. We point out possible implications for the finite-temperature chiral transition of nuclear matter.

Baryon number fluctuations in chiral effective models and their phenomenological implications

We study the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics (QCD) is modeled by the Polykov-loop extended Quark-Meson Lagrangian, that includes the coupling of quarks to vector meson and temporal gauge fields. The Functional Renormalization Group is employed to properly account for the $O(4)$ criticality at the phase boundary. We focus on the properties and systematics of ratios of the net-baryon-number cumulants $\chi_B^n$, for ${1\leq n\leq 6}$, near the phase boundary. The results are presented in the context of the recent experimental data of the STAR Collaboration on fluctuations of the net proton number in heavy ion collisions at RHIC. We show that the model results for the energy dependence of the cumulant ratios are in good overall agreement with the data, with one exception. At center-of-mass energies below ${19.6\;\mathrm{GeV}}$, we find that the measured fourth-order cumulant deviates considerably from the model results, which incorporate the expected $O(4)$ and $Z(2)$ criticality. We assess the influence of model assumptions and in particular of repulsive vector-interactions, which are used to modify the location of the critical endpoint in the model, on the cumulants ratios. Finally, we discuss a possibility to test to what extent the fluctuations are affected by nonequilibrium dynamics by comparing certain ratios of cumulants.

Auxiliary-Field MonteCarlo Method to Tackle Strong Interactions and Frustration in Lattice Bosons.

We introduce a new numerical technique, the bosonic auxiliary-field MonteCarlo method, which allows us to calculate the thermal properties of large lattice-boson systems within a systematically improvable semiclassical approach, and which is virtually applicable to any bosonic model. Our method amounts to a decomposition of the lattice into clusters, and to an ansatz for the density matrix of the system in the form of a cluster-separable state-with nonentangled, yet classically correlated clusters. This approximation eliminates any sign problem, and can be systematically improved upon by using clusters of growing size. Extrapolation in the cluster size allows us to reproduce numerically exact results for the superfluid transition of hard-core bosons on the square lattice, and to provide a solid quantitative prediction for the superfluid and chiral transition of hardcore bosons on the frustrated triangular lattice.