Syo Kamata

Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density

A bstractWe investigate Lefschetz thimble structure of the complexified path-integration in the one-dimensional lattice massive Thirring model with finite chemical potential. The lattice model is formulated with staggered fermions and a compact auxiliary vector boson (a link field), and the whole set of the critical points (the complex saddle points) are sorted out, where each critical point turns out to be in a one-to-one correspondence with a singular point of the effective action (or a zero point of the fermion determinant). For a subset of critical point solutions in the uniform-field subspace, we examine the upward and downward cycles and the Stokes phenomenon with varying the chemical potential, and we identify the intersection numbers to determine the thimbles contributing to the path-integration of the partition function. We show that the original integration path becomes equivalent to a single Lefschetz thimble at small and large chemical potentials, while in the crossover region multiple thimbles must contribute to the path integration. Finally, reducing the model to a uniform field space, we study the relative importance of multi-thimble contributions and their behavior toward continuum and low-temperature limits quantitatively, and see how the rapid crossover behavior is recovered by adding the multi-thimble contributions at low temperatures. Those findings will be useful for performing Monte-Carlo simulations on the Lefschetz thimbles.

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling β and/or large lattice size L, while they are in good agreement in the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit to keep the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model and implies that the contributions of subdominant thimbles should be summed up in order to reproduce the first order transition in the low-temperature limit.

One dimensional supersymmetric Yang-Mills theory with 16 supercharges

We report on numerical simulations of one dimensional maximally supersymmetric SU(N) Yang-Mills theory, by using the lattice action with two exact supercharges. Based on the gauge/gravity duality, the gauge theory corresponds to N D0-branes system in type IIA superstring theory at finite temperature. We aim to verify the gauge/gravity duality numerically by comparing our results of the gauge side with analytic solutions of the gravity side. First of all, by examining the supersymmetric Ward-Takahashi relation, we show that supersymmetry breaking effects from the cut-off vanish in the continuum limit and our lattice theory has the desired continuum limit. Then, we find that, at low temperature, the black hole internal energy obtained from our data is close to the analytic solution of the gravity side. It suggests the validity of the duality.

Minimal doubling fermions and hermiticity

We analyze the lattice fermion kinetic term using PT symmetry, R-hermiticity, and

Numerical simulation of the N=(2,2) Landau-Ginzburg model

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Application of the Lefschetz thimble formulation to the (0+1) dim. Thirring model at finite density

-hermiticity. R-hermiticity is a condition for Hermite action and it is related to

Lattice simulation of lower dimensional SYM with sixteen supercharges

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Non-γ5 hermiticity fermions in two dimensions

-hermiticity and PT symmetry. Assuming that a translation-invariant kinetic term with continuum and periodic function does not have PT symmetry, it can have R-hermiticity or

Non-

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-hermiticity. We prove that a kinetic term with continuum and periodic function that is PT symmetric does not reduce doublers. As a simple example, we analyze the two-dimensional two-flavor Gross-Neveu model with minimal doubling fermions. The minimal doubling fermions break PT symmetry and R-hermiticity, hence complex or non-Hermite coupling constants are caused by quantum correction.