Related papers: Structure of Lefschetz thimbles in simple fermioni…
The topological Lifshitz phase transition is studied systematically within an effective model of QCD, in which the chiral symmetry, broken at zero temperature, is not restored at high temperature and/or baryon chemical potential. It is…
We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign problem that afflicts Monte Carlo…
We present a study of the finite density lattice Thirring model in 1+1 dimensions using the world-line/fermion-bag algorithm. The model has features similar to QCD and provides a test case for exploring the accuracy of various methods of…
Recently, we have proposed a novel approach (arxiv:1205.3996) to deal with the sign problem that hinders Monte Carlo simulations of many quantum field theories (QFTs). The approach consists in formulating the QFT on a Lefschetz thimble. In…
A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen…
The sign problem is a major obstacle to our understanding of the phase diagram of QCD at finite baryon density. Several numerical methods have been proposed to tackle this problem, but a full solution to the sign problem is still elusive.…
We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the…
The numerical sign problem has long been a major obstacle to first-principles calculations in various important fields of physics. We report that the recently proposed algorithm, tempered Lefschetz thimble method (TLTM), and its worldvolume…
Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow…
This is an introductory level review of recent applications of resurgent trans-series and Picard-Lefschetz theory to quantum mechanics and quantum field theory. Resurgence connects local perturbative data with global topological structure.…
We discuss the chiral phase diagram in the parameter space of lattice QCD with minimal-doubling fermions, which can be seen as lattice fermions with flavored chemical potential terms. We study strong-coupling lattice QCD with the…
We analyze the phase diagram of compact QED on the torus with a chirally symmetric four fermion interaction added to the usual Wilson action. Inside a mean field approximation for the four fermion term, a line of first order phase…
In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the…
Non-compact three-dimensional QED is studied by computer simulations to understand its chiral symmetry breaking features for different values of the number of fermion flavors N_f. We consider the four-component formulation for the fermion…
We revisit the path-integral approach to the wave function of the Universe by utilizing Lefschetz thimble analyses and resurgence theory. The traditional Euclidean path-integral of gravity has the notorious ambiguity of the direction of…
The sign problem obstructs the determination of the QCD phase diagram in the temperature-baryon chemical potential plane using lattice QCD. We review the sign problem in QCD and related field theories, including applications to real-time…
We present a novel reweighting technique to calculate the relative weights in the Lefschetz thimble decomposition of a path integral. Our method is put to work using a $U(1)$ one-link model providing for a suitable testing ground and…
We present a method to compute real-time path integrals numerically, by Monte-Carlo sampling on near-Lefschetz thimbles. We present a collection of tools based on the Lefschetz thimble methods, which together provide an alternative to…
The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing…
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach…