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

Abstract

We 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 multi thimbles must contribute to the path integration. Finally, reducing the model to a uniform field space, we study the relative importance of multiple 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.

32 pages, 14 figures (typo etc. corrected)

References in corpus (18)

• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Stochastic quantization at finite chemical potential
• Structure of Lefschetz thimbles in simple fermionic systems
• Real-time Feynman path integral with Picard--Lefschetz theory and its applications to quantum tunneling
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Complex Langevin dynamics and other approaches at finite chemical potential
• Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• A New Look At The Path Integral Of Quantum Mechanics
• Progress in complex Langevin simulations of full QCD at nonzero density
• Lefschetz thimble Monte Carlo for many body theories: application to the repulsive Hubbard model away from half filling
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Exploring the phase diagram of QCD with complex Langevin simulations
• QCD at nonzero chemical potential: recent progress on the lattice
• Complex Langevin dynamics for SU(3) gauge theory in the presence of a theta term
• Systematic approximation for QCD at non-zero density

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