We study the properties of low-lying Dirac modes in quenched compact QED at $β=1.01$, employing $12^3\times N_t$ ($N_t =4,6,8,10,12$) lattices and the overlap formalism for the fermion action. We pay attention to the spatial distributions of low-lying Dirac modes below and above the ``phase transition temperature'' $T_c$. Near-zero modes are found to have universal anti-correlations with monopole currents, and are found to lose their temporal structures above $T_c$ exhibiting stronger spatial localization properties. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a Wigner-Poisson transition.
A polynomial transformation for non-Hermitian matrices is presented, which provides access to wedge-shaped spectral windows. For Wilson-Dirac type matrices this procedure not only allows the determination of the physically interesting low-lying eigenmodes but also provides a substantial acceleration of the eigenmode algorithm employed.
We outline our implementation of the adaptive thick-restart Lanczos algorithm ($a$-TRLan) for the projection of the low-lying eigenmodes of the overlap Dirac operator in lattice QCD, and compare the performances of our code and the widely used package ARPACK.
We calculate the low-lying eigenvalues and eigenvectors of the hermitian domain wall Dirac operator on various gauge backgrounds by Ritz minimization. The mass dependence of these eigenvalues is studied to extract the physical 4 dimensional $λ$, whose spectral density is related to $<\barψ ψ>$ through the Banks-Casher relation, and $δm$, which represents the effects of the residual chiral symmetry breaking in domain wall formalism on a per eigenmode basis. The topological structure of the underlying gauge field is examined by measuring the $Γ_5$ matrix elements between the low-lying eigenmodes…
As a quantitative measure of localization, the inverse participation ratio of low lying Dirac eigenmodes and topological charge density is calculated on quenched lattices over a wide range of lattice spacings and volumes. Since different topological objects (instantons, vortices, monopoles, and artifacts) have different co-dimension, scaling analysis provides information on the amount of each present and their correlation with the localization of low lying eigenmodes.
We study the properties of low-lying Dirac modes in quenched compact QED at $β$=0.99, 1.01 and 1.03, employing $12^3\times 12$ lattices and the overlap formalism for the fermion action. We pay special attention to the spatial distributions of the low-lying Dirac modes. Near-zero modes are found to have universal anti-correlations with monopole currents below/above the critical $β$. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a signal of a Wigner-Poisson transition. We make a possible speculation on the chiral phase transition in 4D compact QED.
We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with gamma-5. For a twisted Ginsparg-Wilson operator the spectrum is located on two arcs in the complex plane. Modes due to non-trivial topological charge of the underlying gauge field have their eigenvalues at the edges of these arcs and obey a remnant index theorem. For configurations in the confined phase we find that the twist mainly affects the zero modes, while…
We consider properties of zero and near-zero modes for overlap fermion operator in SU(2) lattice gluodynamics. The density of the states is of the order of Lambda(QCD) while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. The situation changes drastically when we study "vortex removed" configurations.
The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of 't Hooft "would-be" zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological "would-be" zeromodes could be associated.
The probability density of low-lying eigenvectors of the hermitian Wilson-Dirac operator is examined. Comparisons in position and size between eigenvectors, topological charge and action density are made. We do this for standard Monte-Carlo generated SU(3) background fields and for single instanton background fields. Both hot and cooled SU(3) background fields are considered. An instanton model is fitted to eigenmodes and topological charge density and the sizes and positions of these are compared.
Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool for investigating the topological structure of the vacuum. Applying this formulation to zero-temperature quenched SU(3) configurations generated by means of the Luescher-Weisz action, we define the topological charge density with and without UV filtering and study its properties by looking at the density profile and the two-point correlation function. We observe that the density possesses global sign coherent structures, which get increasingly tangled as more and more modes are included. This change …
We present preliminary results for the topological charge and susceptibility determined from the low-lying eigenmodes of the Wilson-Dirac operator. These modes have been computed on dynamical configurations with Nf=2 non-perturbatively improved Wilson fermions. We compare our results with the eigenmodes of fermions in the quenched approximation.
Using the eigenmodes of the overlap-Dirac operator, we study the topological structure of the QCD vacuum. We investigate the space-time profile of the low-lying eigenmodes and their contribution to the vacuum action density and chiral condensate under the existence of static color sources. We demonstrate that the low-lying Dirac eigenmode shows the flux-tube structure, which suggests the relevance to confinement. We also analyze the chiral condensate in the flux-tube. Chiral symmetry is partially restored inside the flux, and the reduction of the condensate is about 20% at the center of the tu…
A nonvanishing spectral density of the low-lying eigenmodes of the Dirac operator naturally is a signal for dynamical chiral symmetry breaking (D$χ$SB) via the Banks-Casher relation. The low-lying eigenmodes alone saturate the pseudoscalar channel and the corresponding propagator successfully reproduces the pion mass. In this paper we investigate the effects on the mass generation of hadrons other than pions. The evolution of these masses upon inclusion of an increasing number of the low-lying eigenmodes is confronted with the hadron mass spectrum upon removal of such eigenmodes.
Using the Dirac-mode expansion method, which keeps the gauge invariance, we analyze the Polyakov loop in terms of the Dirac modes in SU(3) quenched lattice QCD in both confined and deconfined phases. First, to investigate the direct correspondence between confinement and chiral symmetry breaking, we remove low-lying Dirac-modes from the confined vacuum generated by lattice QCD. In this system without low-lying Dirac modes, while the chiral condensate $\langle \bar{q} q\rangle$ is extremely reduced, we find that the Polyakov loop is almost zero and $Z_3$-center symmetry is unbroken, which indic…
In situations where the low lying eigenmodes of the Dirac operator are suppressed one observed degeneracies of some meson masses. Based on these results a hidden symmetry was conjectured, which is not a symmetry of the Lagrangian but emerges in the quantization process. We show here how the difference between classes of meson propagators is governed by the low modes and shrinks when they disappear.
Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.
We compare the low-lying eigenmodes of the O(a) improved Wilson-Dirac operator on quenched and dynamical configurations and investigate methods of probing the topological properties of gauge configurations
We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with gamma-5. For a twisted Ginsparg-Wilson operator the spectrum is located on two arcs in the complex plane. Modes due to non-trivial topological charge of the underlying gauge field have their eigenvalues at the edges of these arcs and obey a remnant index theorem. For configurations in the confined phase we find that the twist mainly affects the zero modes, while…
We study the influence of center vortices on the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. For center-projected configurations, one finds that the low-lying near-zero modes are present in the staggered (asqtad) formulation, but not in the overlap and "chirally-improved" formulations. We argue that this is due to the absence of a field-independent chiral symmetry in the latter formulations, when the Dirac operator is evaluated on the very rough configurations generated by center projection. We also confirm and extend the results of Kovalenko et al.…
We study correlations between center vortices and the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. In particular we address a puzzle raised some years ago by Gattnar et al. [Nucl. Phys. B 716, 105 (2005)], who noted that the low-lying Dirac eigenmodes required for chiral symmetry breaking do not appear to be present in center-projected configurations. We show that the low-lying modes are in fact present in the staggered (asqtad) formulation, but not in the overlap and ``chirally improved'' formulations, and suggest a reason for this difference. We al…
We discuss the utility of low-lying Dirac eigenmodes for studying the nature of topological charge fluctuations in QCD. The implications of previous results using the local chirality histogram method are discussed, and the new results using the overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported. While the degree of local chirality does not change appreciably closer to the continuum limit, we find that the size and density of local structures responsible for chiral peaking do change significantly. The resulting values are in d…
We present a study of the instanton size and spatial distributions in pure SU(3) gauge theory using under-relaxed cooling. We also investigate the low-lying eigenmodes of the (improved) Wilson-Dirac operator, in particular, the appearance of zero-modes and their space-time localisation with respect to instantons in the underlying gauge field.
We derive an analytical gauge-invariant formula between the Polyakov loop $L_P$ and the Dirac eigenvalues $λ_n$ in QCD, i.e., $L_P \propto \sum_n λ_n^{N_t -1} \langle n|\hat U_4|n \rangle$, in ordinary periodic square lattice QCD with odd-number temporal size $N_t$. Here, $|n\rangle$ denotes the Dirac eigenstate, and $\hat U_4$ temporal link-variable operator. This formula is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\rangle$. Because of the factor $λ_n^{N_t -1}$ in the Dirac spectral sum, this formula indicates negligibly small contribution of low-ly…
We present a quenched calculation of meson correlators with the overlap fermion at very small masses 2.6--13 MeV. In this region the pion Compton wavelength is larger than our lattice size L\simeq 1.23fm and the system is in the so-called epsilon-regime of chiral perturbation theory. We found that the scalar and pseudo-scalar correlators are precisely approximated by a few hundred low-lying fermion eigenmodes in this regime, whereas axial-vector correlator receives significant contributions from higher eigenmodes. We also measure the disconnected pseudo-scalar correlator, which is well saturat…
We calculate the low-lying eigenmodes of the Neuberger overlap-Dirac operator for $4d$ compact lattice QED in the quenched approximation. In the strong coupling phase we find exact zero-modes, quite similar as in non-Abelian lattice QCD. Subsequently we make an attempt to identify responsible topological excitations of the U(1) lattice gauge theory.
We consider $4d$ compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying eigenmodes of the Neuberger overlap-Dirac operator. In the strong coupling phase we find exact zero-modes. Subsequently we discuss possibly related topological excitations of the U(1) lattice gauge theory.
The reasons for using low-lying Dirac eigenmodes to probe the local structure of topological charge fluctuations in QCD are discussed, and it is pointed out that the qualitative double-peaked behavior of the local chiral orientation probability distribution in these modes is necessary, but not sufficient for dominance of instanton-like fluctuations. The results with overlap Dirac operator in Wilson gauge backgrounds at lattice spacings ranging from a~0.04 fm to a~0.12 fm are reported, and it is found that the size and density of local structures responsible for double-peaking of the distributi…
We investigate the effects of the violation of the Ginsparg-Wilson (GW) relation in the Möbius domain-wall fermion formulation on the lattice with finite fifth dimension. Using a decomposion in terms of the eigenmodes of its four-dimensional effective Dirac operator, we isolate the GW-violating terms for various physical quantities including the residual mass and the meson susceptibilities relevant for the effective restoration of the axial U(1) symmetry at finite temperature. Numerical result shows that the GW-violating effect is more significant, or even overwhelming, for the quantities that…
We investigate the distribution of low-lying eigenmodes of hermitian Wilson-Dirac operator, $H_W$, with the gauge action whose form is designed to avoid topology change, as well as with the standard plaquette action. On the quenched lattices, the former gauge action exhibits less density of low-lying eigenmodes of $H_W$ compared to the latter at the same lattice spacing. We also show preliminary results for the dynamical simulation with two flavors of overlap fermions.
We use low lying eigenvectors of the overlap-Dirac operator as a probe of the QCD vacuum. If instantons play a significant role one would expect the low lying eigenmodes of the overlap-Dirac operator to consist mainly of the mixed ``would be zero modes''. Then, the eigenmodes should exhibit local chirality. Studying a recently introduced local chirality parameter, we find evidence supporting this picture.
The precision of lattice QCD calculations has been steadily improving for some time and is now approaching, or has surpassed, the 1% level for multiple quantities. At this level QED effects, i.e. the fact that quarks carry electric as well as color charge, come into play. In this report we will summarise results from the first lattice QCD+QED computations of the properties of ground-state charmonium and bottomonium mesons by the HPQCD Collaboration.
We investigate several examples of Yang-Mills gauge configurations containing center vortex structures, including intersection points between vortices and nontrivial color structures residing on the vortex world-surfaces. Various topological charge contributions of the color structures and intersection points are studied in these configurations. Low-lying eigenmodes of the (overlap) Dirac operator in the presence of these vortex backgrounds are analyzed. The results indicate characteristic properties for spontaneous chiral symmetry breaking.
Starting from thermalized quenched SU(2) configurations we apply cooling or iterated smearing, respectively, to produce sequences of gauge configurations with less and less fluctuations. We compute the low lying spectrum and eigenmodes of the lattice Dirac operator and compare them for the two types of smoothing. Many characteristic properties of the eigensystem remain invariant for all configurations in our sequences. We also find that cooling and smearing produce surprisingly similar results. Both observations could be indications that the two filtering methods do not drastically alter the l…
Some meson correlation functions have a large contribution from the low lying eigenmodes of the Dirac operator. The contribution of these eigenmodes can be averaged over all positions of the source. This can improve the signal in these channels significantly. We test the method for meson two-point functions.
Truncating the low-lying modes of the lattice Dirac operator results in an emergence of the chiral-spin symmetry $SU(2)_{CS}$ and its flavor extension $SU(2N_F)$ in hadrons. These are symmetries of the quark - chromo-electric interaction and include chiral symmetries as subgroups. Hence the quark - chromo-magnetic interaction, which breaks both symmetries, is located at least predominantly in the near - zero modes. Using as a tool the expansion of propagators into eigenmodes of the Dirac operator we here analytically study effects of a gap in the eigenmode spectrum on baryon correlators. We fi…
The lowest eigenmodes of the Dirac operator are related to the dynamical breaking of the chiral symmetry in Quantum Chromodynamics (QCD). In our work we construct quark propagators which exclude a varying number of the lowest Dirac eigenmodes and study the influence thereof on meson correlators and the meson spectrum. That procedure partially restores the chiral symmetry (in the valence sector) and we observe degeneracies in the spectrum while confinement seems not to be affected.
The lowest zeros of the lattice partition function for non-compact QED are found in the complex fermion mass plane on $6^4$, $8^4$ and $10^4$ lattices at intermediate values of the coupling. The scaling of the low lying zeros with lattice size is analysed.
We demonstrate the utility of a spectral approximation to fermion loop operators using low-lying eigenmodes of the hermitian Dirac-Wilson matrix, Q. The investigation is based on a total of 400 full QCD vacuum configurations, with two degenerate flavors of dynamical Wilson fermions at beta =5.6, at two different sea quark masses. The spectral approach is highly competitive for accessing both topological charge and disconnected diagrams, on large lattices and small quark masses. We propose suitable partial summation techniques that provide sufficient saturation for estimating Tr Q^{-1}, which i…
The spectral properties of the Wilson-Dirac operator in 2-dimensional QED responsible for the appearance of exceptional configurations in quenched simulations are studied in detail. The mass singularity structure of the quenched functional integral is shown to be extremely compicated, with multiple branch points and cuts. The connection of lattice topological charge and exactly real eigenmodes is explored using cooling techniques. The lattice volume and spacing dependence of these modes is studied, as is the effect of clover improvement of the action. A recently proposed modified quenched appr…
The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks-Casher relation. At the same time the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT) with the Gaussian Unitary Ensemble (GUE). Then it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related $SU(2)_{CS}$ and $SU(2…
A quantitative study of the effects of dynamical chiral symmetry breaking on the mass generation of the low-lying hadrons in a dynamical lattice QCD simulation is presented. The evolution of light hadron masses upon increasing the number of low-lying Dirac operator eigenmodes in the quark propagators is confronted with the hadron masses obtained upon removal of such low-lying eigenmodes from standard full quark propagators. The low-lying chiral symmetry breaking modes provide roughly two third of the nucleon and $ρ$ masses, while the $a_1$ mass is affected to a much smaller degree.
In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $λ_n$ in QCD, i.e., $\langle L_P \rangle \propto \sum_n λ_n^{N_t -1} \langle n|\hat U_4|n \rangle$, by considering ${\rm Tr} (\hat{U}_4\hat{\not{D}}^{N_t-1})$ on a temporally odd-number lattice, where the temporal lattice size $N_t$ is odd. This formula is a Dirac spectral representation of the Polyakov loop in terms of Dirac eigenmodes $|n\rangle$. We here use an ordinary square lattice with the normal (nontwisted) periodic boundary condition for…
We study the spectrum of low-lying eigenmodes of the kinetic operator for scalar particles, in the color adjoint representation of Yang-Mills theory. The kinetic operator is the covariant Laplacian, plus a constant which serves to renormalize mass. In the pure gauge theory, our data indicates that the interval between the lowest eigenvalue and the mobility edge tends to infinity in the continuum limit. On these grounds, it is suggested that the perturbative expression for the scalar propagator may be misleading even at distance scales that are small compared to the confinement scale. We also m…
We study the isoscalar and isovector $J=0,1$ mesons with the overlap operator within two flavour lattice QCD. After subtraction of the lowest-lying Dirac eigenmodes from the valence quark propagator all disconnected contributions vanish and all possible point-to-point $J=0$ correlators become identical, signaling a simultaneous restoration of both $SU(2)_L \times SU(2)_R$ and $U(1)_A$ symmetries. The ground states of the $π,σ,a_0,η$ mesons do not survive this truncation. All possible $J=1$ states have a very clean exponential decay and become degenerate, demonstrating a $SU(4)$ symmetry of a d…
We investigate the effects of low-lying fermion eigenmodes on the QCD partition function in the $ε$-regime. The fermion determinant is approximated by a truncated product of low-lying eigenvalues of the overlap-Dirac operator. With two flavors of dynamical quarks, we observe that the lattice results for the lowest eigenvalue distribution, eigenvalue sum rules and partition function reproduce the analytic predictions made by Leutwyler and Smilga, which strongly depend on the topological charge of the background gauge configuration. The value of chiral condensate extracted from these measurement…
Using SU(3) lattice QCD, we investigate role of spatial gluons for hadron masses in the Coulomb gauge, considering the relation between QCD and the quark model. From the Coulomb-gauge configurations at the quenched level on a $16^3 \times 32$ lattice at $β$ = 6.0, we consider the $\vec{A} = 0$ projection, where all the spatial gluon fields are set to zero. In this projection, the inter-quark potential is unchanged. We investigate light hadron masses and find that nucleon and delta baryon masses are almost degenerate. This result suggests that the N-$Δ$ mass difference arises from the color-mag…
Finite size scaling studies of monopole condensation in noncompact quenched lattice $QED$ indicate an authentic second order phase transition lying in the universality class of four dimensional percolation. Since the upper critical dimension of percolation is six, the measured critical indices are far from mean-field values. We propose a simple set of ratios as the exact critical indices for this transition. The implication of these results for critical points in Abelian gauge theories are discussed.
Recently we reported on the infrared behavior of the Landau gauge gluon and ghost dressing functions in SU(3) Wilson lattice gluodynamics with special emphasis on the Gribov problem. Here we add an investigation of the spectral properties of the Faddeev-Popov operator at $β$=5.8 and 6.2 for lattice sizes 12^4, 16^4 and 24^4. The larger the volume the more of its eigenvalues are found accumulated close to zero. Using the eigenmodes for the spectral representation it turns out that for our smallest lattice O(200) eigenmodes are sufficient to saturate the ghost propagator at lowest momentum. We a…
We describe and test a method known in the literature as low mode averaging to improve Euclidean two-point functions in lattice QCD using the low-lying eigenmodes of the Wilson-Dirac operator D. The contribution from the low modes is averaged over all positions of the quark sources while the contribution from high modes is calculated in the traditional way using one source point per lattice. We apply this method to different baryon and meson two-point functions and we compare the improvements using the eigenmodes of the non-hermitian operator D and the eigenmodes of the hermitian operator Q=ga…
We study the embedded QCD monopoles (``quark monopoles'') using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anti-correlated with the …
We study the axial U(1)A symmetry of Nf = 2 QCD at finite temperature using the Dirac eigenvalue spectrum. The gauge configurations are generated employing the Mobius domain-wall fermion action on 16^3x8 and 32^3x8 lattices. The physical spatial size of these lattices is around 2 fm and 4 fm, respectively, and the simulated temperature is around 200 MeV, which is slightly above the critical temperature of the chiral phase transition. Although the Mobius domain-wall Dirac operator is expected to have a good chiral symmetry and our data actually show small values of the residual mass, we observe…
Results are presented for the electromagnetic mass splittings of the low lying hadrons. These are used to determine the non-degenerate light quark masses. It is found that m_u=2.24(10)(34), m_d=4.65(15)(32), and $m_s=97.6(2.9)(5.5)$ MeV (MSbar scheme, 2 GeV scale). The first error is statistical and the second systematic. We find the lowest order electromagnetic splitting (m_pi+-m_pi0)_QED=3.38(23) MeV, the splittings including next-to-leading order, (m_pi+-m_pi0)_QED=4.50(23) MeV, (m_K+-m_K0)_QED=1.87(10) MeV, and the m_u != m_d contribution to the kaon mass difference, (m_K+-m_K0)_(m_u-m_d)=…
We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal non-twisted periodic boundary condition for the link-variables. We find that the low-lying Dirac modes yield negligible contributions to the Polyakov loop fluctuations. This property is confirmed to be valid in confined and deconfined phase by numerical simulations in SU(3) quenched QCD. These results indicate that there is no direct, one-to-one correspondence between confinement and chiral sy…
We study the chiral properties of domain-wall quarks at high temperatures on an ensemble of quenched configurations. Low lying eigenmodes of the Dirac operator are calculated and used to check the extent to which the Atiyah-Singer index theorem is obeyed on lattices with finite $N_5$. We calculate the connected and disconnected screening propagators for the lowest mass scalar and pseudoscalar mesons in the sectors of different topological charge and note that they behave as expected. Separating out the would-be zero eigenmodes enables us to accurately estimate the disconnected propagators with…
We perform a systematic study of low-lying eigenmodes of $H_w$ with various gauge actions to find the optimal choice for dynamical overlap fermion simulations, with which one may achieve lower numerical cost for HMC and better locality property of the overlap kernel. For this purpose, our study is made with emphasis on the distribution of low-lying eigenvalues and the mobility edge with and without dynamical overlap fermions.
In order to investigate the direct relation between confinement and chiral symmetry breaking in QCD, we investigate the Polyakov loop in terms of the Dirac eigenmodes in both confined and deconfined phases. Using the Dirac-mode expansion method in SU(3) lattice QCD, we analyze the contribution of low-lying and higher Dirac-modes to the Polyakov loop, respectively.In the confined phase below T_c, after removing low-lying Dirac-modes, the chiral condensate $< \bar{q} q>$ is largely reduced, however, the Polyakov loop remains almost zero and Z_3-center symmetry is unbroken. These results indicate…
Ample numerical evidence from lattice calculations shows a strong connection between the confining properties of gauge theories at finite temperature and the localisation properties of the low-lying Dirac eigenmodes. In this contribution we discuss recent progress on this topic, focussing on results for QCD at imaginary chemical potential $μ_I/T = π$ at temperatures above the Roberge-Weiss transition temperature. These confirm the general picture of low modes turning from delocalised to localised at the deconfinement transition, in a previously unexplored setup with a genuine, physical transit…
To clarify the relation between chiral symmetry breaking and color confinement, we investigate the Polyakov loop in terms of the Dirac eigenmodes in SU(3) lattice QCD. We analyze the low-lying (IR) and UV Dirac-mode contribution to the Polyakov loop, respectively, using the Dirac-mode expansion method. In the confined phase, the Polyakov loop $< L_P >$ remains almost zero and $Z_3$ center symmetry is thus unbroken, even after removing low-lying Dirac-modes, which are responsible to chiral symmetry breaking. In the confined phase, the Polyakov loop $< L_P >$ also remains almost zero by UV Dirac…
We explore the properties of low lying eigenmodes of fermions in the quenched approximation of lattice QCD. The fermion action is a recently proposed overlap action and has exact chiral symmetry. We find that chiral zero-eigenvalue modes are localized in space and their positions correlate strongly with the locations (as defined through the density of pure gauge observables) of instantons of the appropriate charge. Nonchiral modes are also localized with peaks which are strongly correlated with the positions of both charges of instantons. These correlations slowly die away as the fermion eigen…
