We study the Chiral Separation Effect (CSE) in finite-density SU(2) lattice gauge theory with dynamical quarks. We find that the CSE is well described by the free quark result in the high-temperature quark-gluon plasma phase. As one enters the confinement regime with broken chiral symmetry at chemical potential smaller than half of the pion mass, the CSE response is gradually suppressed towards low temperatures in comparison to the free quark result. This suppression can be approximately described by assuming that the CSE current is proportional to the charge density, rather than the chemical potential, as suggested in the literature (ArXiv:1712.01256, Phys.Rev.D97(2018)085020). We also provide an upper bound on the contribution of disconnected fermionic diagrams to the CSE, which is consistent with zero within our statistical errors and small compared to that of the connected diagrams. Our results are obtained mainly in the QCD-like regime of SU(2) gauge theory at low densities, and hence should be at least qualitatively applicable to QCD as well.
We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coefficient for the CSE in the confining and de-confining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coefficient within small statistical errors. O…
We demonstrate the non-renormalization of the Chiral Separation Effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian…
Above a pseudocritical temperature of chiral symmetry restoration T_c the energy and the pressure are very far from the quark-gluon-plasma limit (i.e. ideal gas of free quarks and gluons). At the same time very soon above T_c fluctuations of conserved charges behave as if quarks were free particles. Within the T_c - 3T_c interval a chiral spin symmetry emerges in QCD which is not consistent with free quarks and suggests that degrees of freedom are chirally symmetric quarks bound into the color-singlet objects by the chromoelectric field. Here we analyse temporal and spatial correlators in this…
We identify a non-Hermitian chiral random matrix theory that corresponds to two-color QCD at high density. We show that the partition function of the random matrix theory coincides with the partition function of the finite-volume effective theory at high density, and that the Leutwyler-Smilga-type spectral sum rules of the random matrix theory are identical to those derived from the effective theory. The microscopic Dirac spectrum of the theory is governed by the BCS gap, rather than the conventional chiral condensate. We also show that with a different choice of a parameter the random matrix …
We analytically study two-color QCD with an even number of flavors at high baryon density. This theory is free from the fermion sign problem. Chiral symmetry is broken spontaneously by the diquark condensate. Based on the symmetry breaking pattern we construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons. We identify a new epsilon-regime at high baryon density in which the quark mass dependence of the partition function can be determined exactly. We also derive Leutwyler-Smilga-type spectral sum rules for the complex eigenvalues of the Dirac operator in terms of the fermi…
Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of 1) a static monopole-antimonopole pair and 2) a magnetic flux without monopoles, on a four-dimensional Euclidean lattice. In these systems, we calculate the local chiral condensate on quasi-massless fermions coupled to the Abelian gauge field, and find that the chiral condensate is localized in the vicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlo ca…
We propose a new non-Hermitian chiral random matrix model that describes single-flavor spin-one Cooper pairing of quarks. For three colors the model shows spontaneous breaking of color $\mathrm{SU}(3)_C$ and spin $\mathrm{SO}(3)_J$ symmetries down to the diagonal $\mathrm{SO}(3)_{C+J}$ subgroup, in striking analogy to the color-spin locked phase of one-flavor QCD at high density. For two colors, color-singlet spin-one diquarks condense and trigger symmetry breaking $\mathrm{U}(1) \times \mathrm{SO}(3)_J \to \mathrm{SO}(2)_J$. In both cases the microscopic large-$N$ limit is rigorously taken an…
Using the quark eigenmodes computed on the lattice with the overlap-Dirac operator, we investigate the spatial distribution of the chiral condensate around static color sources corresponding to quark-antiquark and three-quark systems. A flux structure of chromo fields appears in the presence of such color charges. The magnitude of the chiral condensate is reduced inside the color flux, which implies partial restoration of chiral symmetry inside hadrons. Taking a static baryon source in a periodic box as a toy model of nuclear matter, we estimate the magnitude of the chiral symmetry restoration…
We study the chiral separation effect (CSE) in two-color and two-flavor QCD (QC$_2$D) to delineate quasiparticle pictures in dense matter from low to high temperatures. Both massless and massive quarks are discussed. We particularly focus on the high density domain where diquarks form a color singlet condensate with the electric charge $1/3$. The condensate breaks baryon number and $U(1)_A$ axial symmetry, and induces the electromagnetic Meissner effects. Within a quark quasiparticle picture, we compute the chiral separation conductivity at one-loop. We have checked that Nambu-Goldstone modes,…
The phase diagram of two-color QCD with non-zero chiral chemical potential is studied by means of lattice simulation. We focus on the influence of a chiral chemical potential on the confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulation is carried out with dynamical staggered fermions without rooting. The dependences of the Polyakov loop, the chiral condensate and the corresponding susceptibilities on the chiral chemical potential and the temperature are presented. The critical temperature is observed to increase with increasing chiral chemic…
The phase diagram of two-color QCD with a chiral chemical potential is studied on the lattice. The focus is on the confinement/deconfinement phase transition and the breaking/restoration of chiral symmetry. The simulations are carried out with dynamical staggered fermions without rooting. The dependence of the Polyakov loop, the chiral condensate and the corresponding susceptibilities on the chiral chemical potential and the temperature are presented.
In QCD at high density, the color-octet quark-antiquark condensate $\langle\overlineψγ_0(λ^A)_C (λ^A)_Fψ\rangle$ is generally nonzero and dynamically breaks the $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times\mathrm{SU}(3)_R$ symmetry down to the diagonal $\mathrm{SU}(3)_V$. We evaluate this condensate in the mean-field approximation and find that it is of order $μΔ^2\log(μ/Δ)$ where $Δ$ is the BCS gap of quarks. Next we propose a novel non-Hermitian chiral random matrix theory that describes the formation of colorful quark-antiquark condensates. We take the microscopic large-$N$ limit and find…
We introduce topological non-trivial colorful regions around intersection points of two perpendicular vortex pairs and investigate their influence on topological charge density and eigenmodes of the Dirac operator. With increasing distance between the vortices the eigenvalues of the lowest modes decrease. We show that the maxima and minima of the chiral densities of the low modes follow mainly the distributions of the topological charge densities. The topological non-trivial color structures lead in some low modes to distinct peaks in the chiral densities. The other low modes reflect the topol…
In preparation of lattice studies of the two-color QCD phase diagram we study chiral restoration and deconfinement at finite temperature with two flavors of staggered quarks using an RHMC algorithm on GPUs. We first study unquenching effects in local Polyakov loop distributions, and the Polyakov loop potential obtained via Legendre transformation, in a fixed-scale approach for heavier quarks. We also present the chiral condensate and the corresponding susceptibility over the lattice coupling across the chiral transition for lighter quarks. Using Ferrenberg-Swendsen reweighting we extract the m…
We investigate plane vortices with color structure. The topological charge and gauge action of such colorful plane vortices are studied in the continuum and on the lattice. These configurations are vacuum to vacuum transitions changing the winding number between the two vacua, leading to a topological charge $Q=-1$ in the continuum. After growing temporal extent of these vortices, the lattice topological charge approaches $-1$ and the index theorem is fulfilled. We analyze the low lying modes of the overlap Dirac operator in the background of these colorful plane vortices and compare them with…
We investigate the chiral properties of SU(2) gauge theory with six flavors, i.e. six light Dirac fermions in the fundamental representations by lattice simulation, and point out that the spontaneous breakdown of chiral symmetry does not occur in this system. The quark mass dependence of the mesonic spectrum provides an evidence for such a possibility. The decay constant tends to be increased by the finite size effect, which is opposite to the behavior predicted by chiral perturbation theory and indicates that the long distance dynamics in the six-flavor theory could be different from the theo…
We consider Chiral Separation Effect (CSE) in the lattice regularized quantum field theory. We discuss two types of regularization - with and without exact chiral symmetry. In the latter case this effect is described by its conventional expression for the massless fermions. This is illustrated by the two particular cases - of Wilson fermions and of the conventional overlap fermions. At the same time in the presence of the exact chiral symmetry the CSE disappears. This is illustrated by the naive lattice fermions, when the contributions of the fermion doublers cancel each other. Another example…
The electroweak symmetry breaking and origin of masses may be attributed to the breakdown of chiral symmetry due to a strong gauge dynamics. Among several candidates of such gauge systems, we focus on two-color QCD with $N_f=6$ massless Dirac fermions in the fundamental representation, and study on whether the dynamics of this gauge system trigger chiral symmetry breaking or not by simulating with Wilson fermions on lattices up to $L/a=32$. We show the result for the quark mass dependence and the volume dependence of some quantities such as the mass of the lightest pseudoscalar meson, decay co…
We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nyström-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of the Janossy densities (conditional gap probabilities). A compact formula for individual eigenvalue distributions suited for precise numerical evaluation by the Nyström-type method is obtained in an explicit form, and the $k^{\rm{\small th}}$ smallest eigenvalue distributions are numerically evaluated for chiral unitary and symplectic ensembles in the microscop…
We report on our analytical study of two-color QCD with an even number of flavors at high baryon density. Based on the pattern of chiral symmetry breaking induced by BCS-type diquark pairing we construct the low-energy effective Lagrangian for the Nambu-Goldstone bosons. We also identify a new epsilon-regime at high baryon density and derive Leutwyler-Smilga-type spectral sum rules for the complex eigenvalues of the Dirac operator in terms of the fermion gap. Our results can in principle be tested in lattice QCD simulations.
We evaluate level spacing and smallest eigenvalue distributions of chiral random matrix ensembles transiting from symplectic or orthogonal to unitary symmetry classes with a crossover parameter rho. As expected from the effective sigma model description, these results can be fitted perfectly to the fundamental or adjoint staggered Dirac spectrum of SU(2) quenched lattice gauge theory under the imaginary chemical potential (twisting) mu. The linear dependence of the parameter rho on mu determines the pion decay constant F as its proportionality constant.
We study two-color QCD with two flavors of Wilson fermion as a function of quark chemical potential mu and temperature T, for two different lattice spacings and two different quark masses. We find that the quarkyonic region, where the behaviour of the quark number density and the diquark condensate are described by a Fermi sphere of almost free quarks distorted by a BCS gap, extends to larger chemical potentials with decreasing lattice spacing or quark mass. In both cases, the quark number density also approaches its non-interacting value. The pressure at low temperature is found to approach t…
$SU(N_c)$ lattice gauge theories with $N_f$ flavors of massless staggered fermions are considered at high quark chemical potential $μ$ and any temperature $T$. In the strong coupling regime (sufficiently small $β$) they have been shown to possess a chiral phase of intact global $U(N_f)\times U(N_f)$ symmetry. The proof is by cluster expansions which converge in the infinite volume limit. Extension to weaker coupling does not appear feasible in the presence of complex fermion determinant. For theories with real determinant, however, such as 2-color QCD with fundamental fermions, or any $N_c$ wi…
By using the overlap-Dirac operator eigenmodes, we investigate spatial distribution of the chiral condensate around static color sources for both quark-antiquark and three quark systems. In the presence of color sources, a characteristic flux-tube structure appears among them, suggesting a linear confining potential. We show that the magnitude of the condensate is reduced inside the color flux, which indicates the partial restoration of chiral symmetry inside the "hadrons." Considering a periodic box containing a static baryon source, which mimics the "nuclear matter," we estimate the chiral s…
In this paper we investigate the influence of a constant external magnetic field on the finite-temperature phase structure and the chiral properties of a simplified lattice model for QCD. We assume an SU(2) gauge symmetry and employ dynamical staggered fermions of identical mass without rooting, corresponding to Nf=4 flavors of identical electric charge. For fixed mass (given in lattice units) the critical temperature is seen to rise with the magnetic field strength. For three fixed beta-values, selected such that we stay (i) within the chirally broken phase, (ii) within the transition region …
We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following spectral observables: the level density of the Hermitian Wilson Dirac operator, the distribution of chirality over the real eigenvalues, and the chiral condensate for the quenched as well as for the unquenched theory. We provide analytical expressions for all these quantities. Moreover we derive constraints for the level density of the real eigenvalues of the …
Using the overlap-Dirac eigenmodes, we study the spatial distribution of the chiral condensate around static color sources in lattice QCD. Between the color sources, there appears a color-flux tube, which leads a linear confining potential. By measuring a local value of the chiral condensate, we show that the magnitude of the condensate is reduced inside the flux-tube for both quark-antiquark and three-quark systems. These results suggest that chiral symmetry is partially restored in the flux-tube. The reduction of the condensate is estimated to be about 20 $\sim$ 30% at the center of the flux…
In this thesis, we perform the lattice QCD analysis via the energy-momentum component of gluons. By introducing the momentum cutoff to the link variable, we investigate which energy-momentum components of gluons induce each QCD phenomenon. We use the Landau gauge for the most part of the lattice QCD analysis. In lattice QCD, we analyze color confinement, spontaneous chiral symmetry breaking, topological charge, and the related topics. We also discuss several comparisons with effective theories. As for color confinement, we calculate the quark-antiquark potential, the color flux tube, and meson…
I present a numerical study of the crossover between the low temperature chirally broken phase and the high temperature chirally restored phase in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate fermion flavors. Fermion masses span a range of intermediate values (represented by the squared ratio of pseudoscalar to vector meson masses $(m_{PS}/m_V)^2\sim 0.25$ to 0.63). Observables include the temperature dependent chiral condensate and screening masses. At each fermion mass these quantities show nearly identical temperature dependence across $N_c$.
