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Two possible schematic QCD phase diagrams at finite complex chemical potential. The top (bottom) panel represents the correlated (uncorrelated) case between the chiral and RW transition surfaces.
Source publication
The pseudo-critical temperature of the confinement-deconfinement transition
and the phase transition surface are investigated by using the complex chemical
potential. We can interpret the imaginary chemical potential as the
Aharonov-Bohm phase, then the analogy of the topological order suggests that
the Roberge-Weiss endpoint would define the pseud...
Contexts in source publication
Context 1
... taking into account our perturbative result and the sym- metry argument, we can sketch expected QCD phase diagrams at finite complex chemical potential. Phase diagrams expected from our present discussions are summarized in Fig. 2. Because of the RW periodicity, the phase structure should be periodic along the θ ...Context 2
... the first order phase boundary on the (T, µ R ) plane forms a chiral transition surface in the (T, µ R , θ) space, and connects the (T, µ R ) plane and the (T, θ) plane. The RW transition line extends in the finite µ R region and forms an RW transition surface in the (T, µ R , θ) space. The RW endpoint may reach T = 0 as shown in the top panel of Fig. 2 or it may deviate from the chiral transition sur- face at some temperature. There is the possibility that T RW line becomes smaller than the chiral critical surface at moderate µ R and finally becomes larger than the chiral transition surface.. It is deeply related with a strength of the correlation between the chiral transition ...Context 3
... possibility is that the first order transition lines on the (T, θ) plane are topologically separated from the first order phase boundary on the (T, µ R ) plane, as shown in the bottom panel of Fig. 2. T RW first decreases at small µ R , but does not goes across the chiral transition surface. In this case, the de- confinement transition represented by the RW transition line on the (T, θ) plane has less relevance to the first order phase bound- ary, which would be the chiral transition, on the (T, µ R ) plane. Therefore, we can call ...Similar publications
I present the highlights of a recent study of the effective QCD phase diagram
on the temperature T and quark chemical potential mu plane, where the strong
interactions are modeled using the linear sigma model coupled to quarks. The
phase transition line is found from the effective potential at finite T and mu
taking into account the plasma screenin...
Citations
... Furthermore, the existence of the RW transition may be related to the deconfinement nature of QCD from the nontrivial degeneracy of free energy, see Refs. [32][33][34]; in these studies, the authors propose the analogy between the nontrivial free-energy degeneracy and the ground-state degeneracy of the confinement-deconfinement transition at finite temperature (T = 0), but this classification of the confinement-deconfinement transition is still conjecture. In this study, we try to investigate the confinement-deconfinement transition using spatial topology; the center domain structure plays a crucial role in the nontrivial free-energy degeneracy and thus it is not unnatural to think that the spacial topology has some hints to understand the confinement-deconfinement transition. ...
Recently, persistent homology analysis has been used to investigate phase structure. In this study, we apply persistent homology analysis to the QCD effective model with heavy quarks at finite imaginary chemical potential; i.e., the Potts model with the suitably tuned external field. Since we try to obtain a deeper understanding of the relationship between persistent homology and phase transition in QCD, we consider the imaginary chemical potential because the clear phase transition, which is closely related to the confinement-deconfinement transition, exists. In the actual analysis, we employ the point-cloud approach to consider persistent homology. In addition, we investigate the fluctuation of persistent diagrams to obtain additional information on the relationship between the spatial topology and the phase transition.
... Actually, we can introduce the flux insertion operation to the hole of the imaginary time direction. Then, the Aharonov-Bohm phase appears as the dimensionless imaginary chemical potential, θ; for example, see Ref. [36]. ...
... For example, the strong coupling limit of QCD which is always in the confined phase does not have the RW transition [12,23]. Therefore, we may clarify the confinement and the deconfinement nature via the existence of the RW transition [36,[40][41][42]. ...
At sufficiently low temperature, without requiring any numerical data at finite real chemical potential, we can clarify the canonical partition function with a fixed quark number via the imaginary chemical potential region with few Ansätze. The canonical partition function relates to the multiplicity distribution which can be observed in collider experiments and thus we may access important information of the properties of the QCD matter based on the canonical method. In this paper, we estimate the multiplicity entropy, the configuration entropy, and the pointwise information which can be calculable with the canonical partition function to understand the properties of the cold QCD matter at finite density. With a large-Nc limit where Nc is the number of colors, we can simply estimate the tendency of them, and then the relation to the quarkyonic phase is clarified. In addition, we discuss the nontrivial ground-state degeneracy from the viewpoint of the canonical sectors.
... These transitions correspond to a change in the center sector favored by the fermions. The RW transition lines and their end points have been thoroughly investigated by lattice simulations [1,2,6,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] and effective models [38][39][40][41][42][43][44][45][46][47][48][49][50]. Depending on the value of the quark masses, the first order lines end at a second order point at T RW , or alternatively at a triple point, which is connected via a (pseudo)critical line to the (pseudo)critical temperature at vanishing chemical potential. ...
We study the localization properties of the low-lying Dirac eigenmodes in QCD at imaginary chemical potential μ^I=π at temperatures above the Roberge-Weiss (RW) transition temperature TRW. We find that modes are localized up to a temperature-dependent “mobility edge” and delocalized above it and that the mobility edge extrapolates to zero at a temperature compatible with TRW. This supports the existence of a strong connection between localization of the low Dirac modes and deconfinement, studied here for the first time in a model with a genuine deconfinement transition in the continuum limit in the presence of dynamical fermions.
... Actually, there have been some attempts to investigate the confinement-deconfinement nature based on this expectation [4][5][6]. ...
... This transition is described by the spontaneous shift symmetry, (Z 2 ) shift , breaking; the symmetry at θ = (2k − 1)π/N c is the invariance under the transformation associated with the time reversal (T ) or the charge conjugation (C) and Z N c transformations via the semidirect product [27][28][29][30]. This difference has been used to describe the confinement-deconfinement transition as gauge-invariant criteria [4,31]. Intuitively, the difference of the RW periodicity is induced from the dominant degree of freedoms in the low and high T regions. ...
... These observations indicate that properties of the system at a finite T with µ R = 0 are characterized by the phase structure at finite imaginary chemical potential; the canonical sectors represent elementary excitation modes in the system and thus structural changes of the relevant canonical sectors are important factors to understand the thermal confinementdeconfinement transition. This result is almost consistent with the results obtained in [4][5][6] and also the crossover behavior reported in several studies. In the case with µ R = 0, Equation (6) is no longer valid, and thus we cannot proceed with our discussion straightforwardly; we keep this extension for our future work. ...
We discuss the thermal phase structure of quantum chromodynamics (QCD) at zero real chemical potential (μR=0) from the viewpoint of canonical sectors. The canonical sectors take the system to pieces of each elementary excitation mode and thus seem to be useful in the investigation of the confinement–deconfinement nature of QCD. Since the canonical sectors themselves are difficult to compute, we propose a convenient quantity which may determine the structural changes of the canonical sectors. We discuss the quantity qualitatively by adopting lattice QCD prediction for the phase structure with finite imaginary chemical potential. In addition, we numerically estimate this quantity by using the simple QCD effective model. It is shown that there should be a sharp change of the canonical sectors near the Roberge–Weiss endpoint temperature at μR=0. Then, the behavior of the quark number density at finite imaginary chemical potential plays a crucial role in clarifying the thermal QCD properties.
... The PNJL model is the extended model of the NJL model to include the Polyakov-loop dynamics by considering the mean field of the temporal component of the gluon field (A 4 ) with the homogeneous ansatz. Of course, it does not contain the exact confinement mechanism, but it can mimic not only the approximated confinement nature but also several important properties such as the RW periodicity and its transition, which are closely related with physical degrees of freedom of the system [45,46]. Therefore, we here employ the PNJL model to estimate canonical sectors and show that the estimation is matched with the result obtained in Sec. ...
We investigate the nuclear and quark matters at finite real chemical potential (μR) and low temperature from the viewpoint of the canonical sectors constructed via the imaginary chemical potential region. Based on the large Nc estimation, where Nc is the number of colors, we can discuss the confinement-deconfinement nature at finite μR from the canonical sectors. We find the expectation that the sharp changes of canonical sectors at μR∼MB/Nc, where MB is the lowest baryon mass, happens in the large Nc regime, and it is matched with the quarkyonic picture. In addition, we discuss the color superconductivity and the chiral properties from the structure of canonical sectors. Even in the present anatomy from the canonical sectors, we obtain a suitable picture for the dense QCD matter.
... However, it has been recently discussed in Ref. [1] that the confinement and deconfinement states at zero temperature can be clarified via the topological order [2], and then it is not necessary that local order-parameters exist and several observables show singular behaviors for the confinement-deconfinement transition. The analogy of the topological order has been applied to the thermal QCD by employing the imaginary chemical potential, μ ¼ ð0; μ I Þ, and then it is expected that confinement-deconfinement transition may be determined from the topological viewpoint [3][4][5]; see also Ref. [6] for the pioneering work with the imaginary chemical potential and Ref. [7] for the review of the imaginary chemical potential. In the case of the chiral symmetry breaking which is another important feature of QCD, one interesting investigation from the information theoretical view was done by using the thermodynamic geometry [8,9]. ...
... The imaginary chemical potential can be interpreted as the flux insertion to the fictitious hole of the time direction in the QCD with the imaginary time formulation. In this case, we do not encounter the sign problem, and also there is the Roberge-Weiss (RW) transition along the θ ≔ μ=ðiTÞ direction in addition to the confinement-deconfinement transition [55][56][57][58][59]. Also, there may be the possibility that we can pick up some information of the confinementdeconfinement transition from this region [3][4][5]. It should be noted that the following results are the first results which explicitly show the detailed behavior of the Roberge-Weiss periodicity and the transition in the Potts model with the external field. ...
To understand the phase transition phenomena, information theoretical approaches can pick up some important properties of the phenomena based on the probability distribution. In this paper, we show information theoretical aspects of the three-dimensional three-state Potts model with the external field which is corresponded to the QCD effective model with heavy quarks. The transfer mutual information which represents the information flow of two spin variables is numerically estimated based on the Markov-chain Monte Carlo method. The transfer mutual information has the peak near the confinement-deconfinement transition, and it may be used to detect the precursors of the transition. Since the transfer mutual information still has the peak even if the Polyakov-loop changes continuously and smoothly, we may pick up some aspects of the confinement-deconfinement nature from the information flow properties. Particularly, the transfer mutual information shows the significantly different behavior below and above the Roberge-Weiss endpoint existed in the pure imaginary chemical potential region, which may indicate the system change by the confinement-deconfinement transition.
... If we can directly perform the Monte-Carlo calculation with finite complexified parameters, there is the possibility that we can better understand properties of the phase structure via the Lee-Yang zero analysis. In addition, such complexification of chemical potential may be related to the investigation of the confinement-deconfinement transition at finite density [13,14]. ...
In this article, we apply the path optimization method to handle the complexified parameters in the 1+1 dimensional pure U(1) gauge theory on the lattice. Complexified parameters make it possible to explore the Lee-Yang zeros which helps us to understand the phase structure and thus we consider the complex coupling constant with the path optimization method in the theory. We clarify the gauge fixing issue in the path optimization method; the gauge fixing helps to optimize the integration path effectively. With the gauge fixing, the path optimization method can treat the complex parameter and control the sign problem. It is the first step to directly tackle the Lee-Yang zero analysis of the gauge theory by using the path optimization method.
... Thus, this region is very useful. In addition, it has been recently proposed that the structure of QCD at finite μ I may be related with the confinement-deconfinement transition [8] based on the analogy of the topological order at T ¼ 0 [9,10]. Because of these reasons, it is interesting and important to know detailed properties of QCD at finite μ I . ...
... However, some lattice QCD simulations indicate the second-order RW endpoint even below the physical quark mass in the 2 þ 1 flavor system [16][17][18]. Based on these properties, several studies for the confinement-deconfinement transition have been done; the first attempt is Ref. [19], and some related discussions are show in Ref. [8] and this paper. Also, some of them have been used to investigate the correlation between the confinement-deconfinement transition and the chiral phase transition via the state-of-art anomaly matching [20][21][22]. ...
... Recently, it was proposed that the structure of QCD at finite μ I may be related with the confinement-deconfinement transition [8] based on the analogy of the topological order at T ¼ 0 [9,10] and thus it is interesting to know detailed properties of QCD at finite μ I . We hope that this analysis shed some light on the mysterious property of the confinement-deconfinement transition. ...
To obtain deeper understanding of QCD properties at finite temperature, we consider the Fourier decomposition of the grand-canonical partition function based on the canonical ensemble method via the imaginary chemical potential. Expectation values are, then, represented by summation over each canonical sector. We point out that the modified Polyakov loop can play an important role in the canonical ensemble; for example, the Polyakov-loop paradox which is known in the canonical ensemble method can be evaded by considering the quantity. In addition, based on the periodicity issue of the modified Polyakov loop at finite imaginary chemical potential, we can construct the systematic way to compute the dual quark condensate which has strong unclearness in its foundation in the presence of dynamical quarks so far.
... However, it has been recently discussed in Ref. [26] that the confinement and deconfinement states at zero temperature can be clarified via the topological order [27] and then it is not necessary that the local order-parameter exists and several observable show singular behaviors. The analogy of the topological order has been applied to the thermal QCD by employing the imaginary chemical potential and then it is expected that confinement-deconfinement transition may be determined from the topological viewpoint [28][29][30]. This suggests that the imaginary chemical potential can give us important information of the confinement-deconfinement transition. ...
In this review, we present of an overview of several interesting properties of QCD at finite imaginary chemical potential and those applications to exploring the QCD phase diagram. The most important properties of QCD at a finite imaginary chemical potential are the Roberge–Weiss periodicity and the transition. We summarize how these properties play a crucial role in understanding QCD properties at finite temperature and density. This review covers several topics in the investigation of the QCD phase diagram based on the imaginary chemical potential.
... The PNJL model can describe the chiral symmetry breaking/restoration and the approximate confinement-deconfinement transition. Also, it can well reproduce QCD properties at finite imaginary chemical potential which is a big advantage from the viewpoint of the topologically determined confinement-deconfinement transition [38][39][40]. The following formulation and the computation of the Monte-Carlo PNJL model is based on Ref. [41]. ...
We apply the path optimization method to a QCD effective model with the Polyakov loop at finite density to circumvent the model sign problem. The Polyakov-loop extended Nambu–Jona-Lasinio model is employed as the typical QCD effective model and then the hybrid Monte Carlo method is used to perform the path integration. To control the sign problem, the path optimization method is used with complexification of temporal gluon fields to modify the integral path in the complex space. We show that the average phase factor is well improved on the modified integral-path compared with that on the original one. This indicates that the complexification of temporal gluon fields may be enough to control the sign problem of QCD in the path optimization method.
