4,042 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
Topological aspects of quantum spin Hall effect in graphene: Z topological order and spin Chern number
For generic time-reversal invariant systems with spin-orbit couplings, we
clarify a close relationship between the Z topological order and the spin
Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively,
in the quantum spin Hall effect. It turns out that a global gauge
transformation connects different spin Chern numbers (even integers) modulo 4,
which implies that the spin Chern number and the Z topological order yield
the same classification. We present a method of computing spin Chern numbers
and demonstrate it in single and double plane of graphene.Comment: 5 pages, 3 figure
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