We study the finite density phase transition in the lattice QCD at real chemical potential. We adopt canonical approach and the canonical partition function is constructed for Nf=2 QCD. After derivation of the canonical partition function we calculate observables like the pressure, the quark number density, its second cumulant and the chiral condensate as a function of the real chemical potential. We covered a wide range of temperature region starting from the confining low to the deconfining high temperature. We observe signals for the deconfinement and the chiral restoration phase transition at real chemical potential below Tc starting from the confining phase.
We clarify regions where the canonical approach works well at the finite temperature and density in the Nambu-Jona-Lasinio (NJL) and Polyakov-NJL (PNJL) models. The canonical approach is a useful method for avoiding the sign problem in lattice QCD simulations at finite density, but it involves some parameters. We find that number densities computed from the canonical approach are consistent with exact values in most of the confinement phase within the parameters, which are applicable in lattice QCD.
We study the Lee-Yang zeros in the canonical approach to search phase transition points at finite temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The canonical approach is a promising method to avoid the sign problem in lattice QCD at finite density. We find that a set of Lee-Yang zeros computed with finite degrees of freedom can be extrapolated to those with infinite degrees of freedom, providing the correct phase transition point. We propose the present method as a useful method for actual lattice simulations for QCD.
At finite baryon density lattice QCD first-principle calculations can not be performed due to the sign problem. In order to circumvent this problem, we use the canonical approach, which provides reliable analytical continuation from the imaginary chemical potential region to the real chemical potential region. We briefly present the canonical partition function method, describe our formulation, and show the results, obtained for two temperatures: $T/T_c = 0.93$ and $T/T_c = 0.99$ in lattice QCD with two flavors of improved Wilson fermions.
We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number density for imaginary chemical potential $iμ_{qI}$. Then we restore the grand canonical partition function for imaginary chemical potential using fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using known method of the hopping parameter…
We investigate the nuclear and the quark matter at finite real chemical potential ($μ_\mathrm{R}$) and low temperature from the viewpoint of the canonical sectors constructed via the imaginary chemical potential region. Based on the large $N_\mathrm{c}$ estimation, where $N_\mathrm{c}$ is the number of color, we can discuss the confinement-deconfinement nature at finite $μ_\mathrm{R}$ from the canonical sectors. We found the expectation that the sharp change of canonical sectors at $μ_\mathrm{R} \sim M_\mathrm{B}/N_\mathrm{c}$, where $M_\mathrm{B}$ is the lowest baryon mass, is happen in the l…
The distribution of canonical determinants in QCD is determined by means of chiral perturbation theory. For a non-zero quark charge the canonical determinants take complex values. In the dilute pion gas approximation, we compute all moments of the magnitude of the canonical determinants, as well as the first nonvanishing moments of the real and imaginary parts. The non-trivial cancellation between the real and the imaginary parts of the canonical determinants is derived and the signal to noise ratio is discussed. The analytical distributions are compared to lattice data. The average density of…
We study lattice QCD at non-vanishing chemical potential using the complex Langevin equation. We compare the results with multi-parameter reweighting both from $μ=0$ and phase quenched ensembles. We find a good agreement for lattice spacings below $\approx$0.15 fm. On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on $N_t=4, 6$ and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.
We study properties of two-color QCD at imaginary chemical potential ($μ$) from the viewpoint of the Roberge-Weiss (RW) periodicity, the charge conjugation and the pseudo-reality. At $μ=\pm iπT/2$, where $T$ is temperature, the system is symmetric under the combination of the charge conjugation ${\cal C}$ and the ${\mathbb Z}_{2}$ transformation. The symmetry, called ${\cal C} {\mathbb Z}_{2}$ symmetry, is preserved at lower $T$ but broken at higher $T$. The Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model has the same properties as two-color QCD for ${\cal C} {\mathbb Z}_{2}$ symmetry …
We summarize recent results obtained in the Dyson-Schwinger formalism to study the chiral and deconfinement phase transitions of quenched and unquenched QCD at finite temperature and chemical potential. In the quenched case we compare SU(2) and SU(3) gauge theories by taking lattice data for the gluon as an input for the quark Dyson-Schwinger equation. As compared to previous investigations we find a clearer distinction between the second order transition of the two-color theory and the (weak) first order transition of the three-color gauge theory. We then extend this study to unquenched QCD a…
The canonical partition function is related to the grand canonical one through the fugacity expansion and is known to have no sign problem. In this paper we perform the fugacity expansion by a method of the hopping parameter expansion in temporal direction for the lattice QCD: winding number expansion. The canonical partition function is constructed for Nf=2 QCD starting from gauge configurations at zero chemical potential. After derivation of the canonical partition function we calculate hadronic observables like chiral condensate and quark number density and the pressure at the real chemical…
We study two flavor fermions with mismatched chemical potentials in quenched lattice QCD. We first consider a large isospin chemical potential, where a charged pion is condensed, and then introduce a small mismatch between the chemical potentials of the up quark and the anti-down quark. We find that the homogeneous pion condensate is destroyed by the mismatch of the chemical potentials. We also find that the two-point correlation function shows spatial oscillation, which indicates an inhomogeneous ground state, although it is not massless but massive in the present simulation setup.
We perform a first lattice QCD simulation including two-flavor dynamical fermion with a chiral chemical potential. Because the chiral chemical potential gives rise to no sign problem, we can exactly analyze a chirally imbalanced QCD matter by the Monte Carlo simulation. By applying an external magnetic field to this system, we obtain a finite induced current along the magnetic field, which corresponds to the chiral magnetic effect. The obtained induced current is proportional to the magnetic field and to the chiral chemical potential, which is consistent with an analytical prediction.
We draw the three-flavor phase diagram as a function of light- and strange-quark masses for both zero and imaginary quark-number chemical potential, using the Polyakov-loop extended Nambu-Jona-Lasinio model with an effective four-quark vertex depending on the Polyakov loop. The model prediction is qualitatively consistent with 2+1 flavor lattice QCD prediction at zero chemical potential and with degenerate three-flavor lattice QCD prediction at imaginary chemical potential.
We calculate the baryon chemical potential ($μ_B$) dependence of thermodynamic observables, i.e., pressure, baryon number density and susceptibility by lattice QCD using the canonical approach. We compare the results with those by the multi parameter reweighting (MPR) method; Both methods give very consistent values in the regions where errors of the MPR are under control. The canonical method gives reliable results over $μ_ B/T=3$,with $T$ being temperature. Multiple precision operations play an important roll in the evaluation of canonical partition functions.
We report our recent results on the QCD phase diagram obtained from the lattice QCD simulation. The location of the phase boundary between hadronic and QGP phases in the two-flavor QCD phase diagram is investigated. The imaginary chemical potential approach is employed, which is based on Monte Carlo simulations of the QCD with imaginary chemical potential and analytic continuation to the real chemical potential region.
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 pseudo-critical temperature. The behavior of the Roberge-Weiss endpoint at small real quark chemical potential is investigated with the perturbative expansion. The expected QCD phase diagram at complex chemical potential is presented.
We explore the phase diagram of two-flavor QCD at imaginary values of baryon and isospin chemical potentials analyzing the thermodynamic potential of QCD analytically and that of the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model numerically. QCD has no pion condensation at imaginary baryon and isospin chemical potentials, and therefore has discrete symmetries that are not present at real baryon and isospin chemical potentials. The PNJL model possesses all the discrete symmetries. The PNJL model can reproduce qualitatively lattice QCD data presented very lately.
We analyze canonical determinants, i.e., grand canonical determinants projected to a fixed net quark number. The canonical determinants are the coefficients in a fugacity expansion of the grand canonical determinant and we evaluate them as the Fourier moments of the grand canonical determinant with respect to imaginary chemical potential, using a dimensional reduction technique. The analysis is done for two mass-degenerate flavors of Wilson fermions at several temperatures below and above the confinement/deconfinement crossover. We discuss various properties of the canonical determinants and a…
The extraction of meson-baryon scattering parameters from lattice QCD is complicated by the necessity, in some channels, of including annihilation diagrams. We consider a strategy to avoid the need for these extremely costly and noisy contributions. The strategy is based on simulations with an isospin chemical potential which, contrary to a baryon chemical potential, has no sign problem. When the isospin chemical potential is larger than a critical value, a charged pion condensate forms. Baryons propagating in the pion condensate will have their masses modified by pion-baryon scattering parame…
We show the universality of phase diagrams in QCD and QCD-like theories through the large-N_c equivalence. The whole phase diagrams are identical between QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. In the chiral limit, they are also identical to that of QCD at finite chiral chemical potential. Outside the pion or diquark condensed phase in these theories, the universality of phase diagrams is applicable to QCD at finite baryon chemical potential. We further argue that the universality may work approximately even for N_c…
We investigate the QCD phase diagram for small values of baryon and strange quark chemical potentials from simulations at non-zero isospin chemical potential. Simulations at pure isospin chemical potential are not hindered by the sign problem and pion condensation can be observed for sufficiently large isospin chemical potentials. We study how the related phase boundary evolves with baryonic and strange chemical potentials via reweighting in quark chemical potentials and discuss our results. Furthermore, we propose and implement an alternative method to approach nonzero baryon (and strange qua…
A connection between the operator fermionic currents $\hatJ$ and corresponding `Grassmannian' currents $J$ in the functional integral formalism is studied. The QCD action with non--zero chemical potential $μ$ is derived. A connection between the fermionic Fock space and boundary conditions along the forth direction is discussed.
Chiral chemical potential does not cause the sign problem in the Monte Carlo simulation of lattice QCD. Using the chiral chemical potential, we study the chiral magnetic effect in two-flavor full QCD. We show that a strong external magnetic field induces an electric current in a chirally imbalanced QCD matter. The qualitative feature of the induced current is consistent with an analytical prediction.
QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although sign-free QCD-like theories have been studied intensively, relation to QCD with a finite baryon chemical potential was not clear until recently. In this talk we explain the large-Nc equivalences between QCD and various QCD-like theories, which lead us to a unified viewpoint for QCD with baryon and isospin chemical potentials, SO(2Nc) and Sp(2Nc) gauge theories. In particular two-flavor QCD with the baryon che…
We investigate the real and imaginary chemical-potential dependence of pion and $ρ$-meson screening masses in both the confinement and the deconfinement region by using two-flavor lattice QCD. The spatial meson correlators are calculated in the imaginary chemical potential region with lattice QCD simulations. We extract pion and $ρ$-meson screening masses from the correlators. The obtained meson screening masses are extrapolated to the real chemical potential region by assuming some analytic function. In the real chemical potential region, the resulting pion and $ρ$-meson screening masses mono…
We summarise recent progress in simulating QCD at nonzero baryon density using complex Langevin dynamics. After a brief outline of the main idea, we discuss gauge cooling as a means to control the evolution. Subsequently we present a status report for heavy dense QCD and its phase structure, full QCD with staggered quarks, and full QCD with Wilson quarks, both directly and using the hopping parameter expansion to all orders.
The regime of small isospin chemical potential in QCD is investigated. Using the phase quenched partition function in the $ε$-regime an expression for the chiral condensate is given, which is studied in the temperature isospin chemical potential plane. Lines of constant values of the condensate are shown and it is estimated how the critical temperature varies as a function of the isospin chemical potential. Finally, the dependency of the fermion sign problem on the chemical potential and temperature is examined.
The study of QCD phase diagram is very interesting, but we have never understood it well. This is because we face a problem at finite density in QCD. The problem is called sign problem. It causes a decrease of the calculation accuracy. This is why, we can not calculate physical quantities accurately at finite chemical potential. In this study, we try to beat the sign problem using canonical approach of finite density lattice QCD. Although it is known that the canonical approach has several numerical problems, we can reduce them and calculate thermodynamic observables accurately at finite densi…
We present unambiguous evidence from lattice simulations of QCD with three degenerate quark species for two tricritical points in the (T,m) phase diagram at fixed imaginary μ/T=iπ/3 mod 2π/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary chemical potential, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. T…
We investigate the phase diagram of QCD-like gauge theories at strong coupling at finite magnetic field $B$, temperature $T$ and baryon chemical potential $μ$ using the improved holographic QCD model including the full backreaction of the quarks in the plasma. In addition to the phase diagram we study the behavior of the quark condensate as a function of $T$, $B$ and $μ$ and discuss the fate of (inverse) magnetic catalysis at finite $μ$. In particular we observe that inverse magnetic catalysis exists only for small values of the baryon chemical potential. The speed of sound in this holographic…
Recent lattice QCD calculations strongly indicate that the chiral crossover of QCD at zero baryon chemical potential μ_B is a remnant of the second-order chiral phase transition. Universal properties of this second-order phase transition can be mapped to QCD temperature T and μ_B using non-universal parameters determined by lattice QCD recently. Motivated by these results, first, we discuss the analytic structure of the partition function in the QCD crossover regime - the so-called Yang-Lee edge singularity - solely based on universal properties. Next, utilizing the lattice QCD results for non…
We determine the (pseudo)critical lines of QCD with two degenerate staggered fermions at nonzero temperature and quark or isospin density, in the region of imaginary chemical potentials; analytic continuation is then used to prolongate to the region of real chemical potentials. We obtain an accurate determination of the curvatures at zero chemical potential, quantifying the deviation between the case of finite quark and of finite isospin chemical potential. Deviations from a quadratic dependence of the pseudocritical lines on the chemical potential are clearly seen in both cases: we try differ…
In this paper we report on lattice simulations of SU(3)-QCD with non-zero chiral chemical potential. We focus on the influence of the chiral chemical potential on the confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulation is carried out with dynamical Wilson fermions. We find that the critical temperature rises as the chiral chemical potential grows.
We propose a method to find the QCD critical point at finite density calculating the canonical partition function ${\cal Z}_{\rm C} (T,N)$ by Monte-Carlo simulations of lattice QCD, and analyze data obtained by a simulation with two-flavor p4-improved staggered quarks with pion mass $m_π \approx 770 {\rm MeV}$. It is found that the shape of an effective potential changes gradually as the temperature decreases and a first order phase transition appears in the low temperature and high density region. This result strongly suggests the existence of the critical point in the $(T, μ_q)$ phase diagra…
We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universal…
