Takumi Iritani

On the definition of entanglement entropy in lattice gauge theories

A bstractWe focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the ZN gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the ZN gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.

Off-diagonal gluon mass generation and infrared Abelian dominance in maximally Abelian gauge in SU(3) lattice QCD

In SU(3) lattice QCD formalism, we propose a method to extract gauge fields from link-variables analytically. With this method, we perform the first study on effective mass generation of offdiagonal gluons and infrared Abelian dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3) lattice QCD, we investigate the propagator and the effective mass of the gluon fields in the MA gauge with U(1)3×U(1)8 Landau gauge fixing. The Monte Carlo simulation is performed on 16 at β=5.7, 5.8 and 6.0 at the quenched level. The off-diagonal gluons behave as massive vector bosons with the approximate effective mass Moff ≃ 1.1− 1.2GeV in the region of r = 0.3−0.8fm, and the propagation is limited within a short range, while the propagation of diagonal gluons remains even in a large range. In this way, infrared Abelian dominance is shown in terms of short-range propagation of off-diagonal gluons. Furthermore, we investigate the functional form of the off-diagonal gluon propagator. The functional form is well described by the four-dimensional Euclidean Yukawa-type function eoff /r with moff ≃ 1.3− 1.4GeV for r = 0.1− 0.8 fm. This also indicates that the spectral function of off-diagonal gluons has the negative-value region.

Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

A bstractSingle state saturation of the temporal correlation function is a key condition to extract physical observables such as energies and matrix elements of hadrons from lattice QCD simulations. A method commonly employed to check the saturation is to seek for a plateau of the observables for large Euclidean time. Identifying the plateau in the cases having nearby states, however, is non-trivial and one may even be misled by a fake plateau. Such a situation takes place typically for a system with two or more baryons. In this study, we demonstrate explicitly the danger from a possible fake plateau in the temporal correlation functions mainly for two baryons (ΞΞ and N N ), and three and four baryons (3He and 4He) as well, employing (2+1)-flavor lattice QCD at mπ = 0.51GeV on four lattice volumes with L = 2.9, 3.6, 4.3 and 5.8 fm. Caution is required when drawing conclusions about the bound N N , 3N and 4N systems based only on the standard plateau fitting of the temporal correlation functions.

Fate of the Tetraquark Candidate

The possible exotic meson Z_{c}(3900), found in e^{+}e^{-} reactions, is studied by the method of coupled-channel scattering in lattice QCD. The interactions among πJ/ψ, ρη_{c}, and D[over ¯]D^{*} channels are derived from (2+1)-flavor QCD simulations at m_{π}=410-700  MeV. The interactions are dominated by the off-diagonal πJ/ψ-D[over ¯]D^{*} and ρη_{c}-D[over ¯]D^{*} couplings, which indicates that the Z_{c}(3900) is not a usual resonance but a threshold cusp. Semiphenomenological analyses with the coupled-channel interaction are also presented to confirm this conclusion.

Z_c

Using the eigen-mode of the QCD Dirac operator

(3900) from Lattice QCD

\Slash D=\gamma^\mu D^\mu

Gauge-invariant formalism with a Dirac-mode expansion for confinement and chiral symmetry breaking

, we develop a manifestly gauge-covariant expansion and projection of the QCD operators such as the Wilson loop and the Polyakov loop. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculation on

Equation of state for SU(3) gauge theory via the energy-momentum tensor under gradient flow

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Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function

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Relation between confinement and chiral symmetry breaking in temporally odd-number lattice QCD

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