96 research outputs found
On a modification method of Lefschetz thimbles
The QCD at finite density is not well understood yet, where standard Monte
Carlo simulation suffers from the sign problem. In order to overcome the sign
problem, the method of Lefschetz thimble has been explored. Basically, the
original sign problem can be less severe in a complexified theory due to the
constancy of the imaginary part of an action on each thimble. However, global
phase factors assigned on each thimble still remain. Their interference is not
negligible in a situation where a large number of thimbles contribute to the
partition function, and this could also lead to a sign problem.In this study,
we propose a method to resolve this problem by modifying the structure of
Lefschetz thimbles such that only a single thimble is relevant to the partition
function. It can be shown that observables measured in the original and
modified theories are connected by a simple identity. We exemplify that our
method works well in a toy model.Comment: 7 pages, 4 figures, talk presented at the 35th International
Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spai
Low-Dimensional Fluctuations and Pseudogap in Gaudin-Yang Fermi Gases
Pseudogap is a ubiquitous phenomenon in strongly correlated systems such as
high- superconductors, ultracold atoms and nuclear physics. While
pairing fluctuations inducing the pseudogap are known to be enhanced in
low-dimensional systems, such effects have not been explored well in one of the
most fundamental 1D models, that is, Gaudin-Yang model. In this work, we show
that the pseudogap effect can be visible in the single-particle excitation in
this system using a diagrammatic approach. Fermionic single-particle spectra
exhibit a unique crossover from the double-particle dispersion to pseudogap
state with increasing the attractive interaction and the number density at
finite temperature. Surprisingly, our results of thermodynamic quantities in
unpolarized and polarized gases show an excellent agreement with the recent
quantum Monte Carlo and complex Langevin results, even in the region where the
pseudogap appears.Comment: 6 pages, 5 figure
Relation between Confinement and Chiral Symmetry Breaking in Temporally Odd-number Lattice QCD
In the lattice QCD formalism, we investigate the relation between confinement
and chiral symmetry breaking. A gauge-invariant analytical relation connecting
the Polyakov loop and the Dirac modes is derived on a temporally odd-number
lattice, where the temporal lattice size is odd, with the normal (nontwisted)
periodic boundary condition for link-variables. This analytical relation
indicates that low-lying Dirac modes have little contribution to the Polyakov
loop, and it is numerically confirmed at the quenched level in both confinement
and deconfinement phases. This fact indicates no direct one-to-one
correspondence between confinement and chiral symmetry breaking in QCD. Using
the relation, we also investigate the contribution from each Dirac mode to the
Polyakov loop. In the confinement phase, we find a new "positive/negative
symmetry" of the Dirac-mode matrix element of the link-variable operator, and
this symmetry leads to the zero value of the Polyakov loop. In the
deconfinement phase, there is no such symmetry and the Polyakov loop is
nonzero. Also, we develop a new method for spin-diagonalizing the Dirac
operator on the temporally odd-number lattice modifying the Kogut-Susskind
formalism.Comment: 15pages, 9 figure
Quark tensor charge and electric dipole moment within the Schwinger-Dyson formalism
We calculate the tensor charge of the quark in the QCD-like theory in the
Landau gauge using the Schwinger-Dyson formalism. It is found that the dressed
tensor charge of the quark is significantly suppressed against the bare quark
contribution, and the result agrees qualitatively with the analyses in the
collinear factorization approach and lattice QCD. We also analyze the quark
confinement effect with the phenomenological strong coupling given by
Richardson, and find that this contribution is small. We show that the
suppression of the quark tensor charge is due to the superposition of the spin
flip of the quark arising from the successive emission of gluons which dress
the tensor vertex. We also consider the relation between the quark and the
nucleon electric dipole moments by combining with the simple constituent quark
model.Comment: 16 pages, 11 figures. arXiv admin note: text overlap with
arXiv:1401.285
Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD
We analytically study the relation between quark confinement and spontaneous
chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive
some formulae for the Polyakov loop, its fluctuations, and the string tension
from the Wilson loop. We also investigate the Polyakov loop in terms of the
eigenmodes of the Wilson, the clover and the domain wall fermion kernels,
respectively. For the confinement quantities, the low-lying Dirac/fermion
eigenmodes are found to give negligible contribution, while they are essential
for chiral symmetry breaking. These relations indicate no direct one-to-one
correspondence between confinement and chiral symmetry breaking in QCD, which
seems to be natural because confinement is realized independently of the quark
mass
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