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Classification of sign-problem-free relativistic fermions on the basis of the Majorana positivity
https://repo.scoap3.org/record/19823
We classify the sign-problem-free relativistic fermion actions on the basis of the Majorana representation. In the Majorana representation, the sign-problem-free condition is given by the semi-positivity of a Pfaffian. We show that the known sign-problem-free actions of the Dirac fermions, which are usually understood from the semi-positivity of a determinant, e.g., the action of quantum chromodynamics with nonzero chiral chemical potential or nonzero isospin chemical potential, can also be understood from the semi-positivity of a Pfaffian. We also derive new classes of the sign-problem-free relativistic fermion actions with Majorana-type source terms.Hayata, TomoyaFri, 21 Apr 2017 15:20:23 GMThttps://repo.scoap3.org/record/19823urn:ISSN:1347-4081Oxford University Press/Physical Society of Japan2017-04-21Complex saddle points and the sign problem in complex Langevin simulation
https://repo.scoap3.org/record/16668
We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.Hayata, TomoyaWed, 03 Aug 2016 13:16:36 GMThttps://repo.scoap3.org/record/16668urn:ISSN:0550-3213Elsevier2017-03-18Lefschetz-thimble analysis of the sign problem in one-site fermion model
https://repo.scoap3.org/record/14547
The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for an idea or a technique to attack the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.Tanizaki, YuyaTue, 01 Mar 2016 17:16:15 GMThttps://repo.scoap3.org/record/14547urn:ISSN:1367-2630Institute of Physics Publishing/Deutsche Physikalische Gesellschaft2016-03-01Inhomogeneous Polyakov loop induced by inhomogeneous chiral condensates
https://repo.scoap3.org/record/9944
We study the spatial inhomogeneity of the Polyakov loop induced by inhomogeneous chiral condensates. We formulate an effective model of gluons on the background fields of chiral condensates, and perform its lattice simulation. On the background of inhomogeneous chiral condensates, the Polyakov loop exhibits an in-phase spatial oscillation with the chiral condensates. We also analyze the heavy quark potential and show that the inhomogeneous Polyakov loop indicates the inhomogeneous confinement of heavy quarks.Hayata, TomoyaMon, 20 Apr 2015 14:51:05 GMThttps://repo.scoap3.org/record/9944urn:ISSN:0370-2693Elsevier2015-05-11Broken spacetime symmetries and elastic variables
https://repo.scoap3.org/record/2992
We discuss spontaneous breaking of continuum symmetries, whose generators do explicitly depend on the spacetime coordinates. We clarify the relation between broken symmetries and elastic variables at both zero and finite temperatures, and/or finite densities, and show the general counting rule that is model-independently determined by the symmetry breaking pattern. We apply it to three intriguing examples: rotational, conformal, and gauge symmetries.Hayata, TomoyaFri, 27 Jun 2014 13:59:54 GMThttps://repo.scoap3.org/record/2992urn:ISSN:0370-2693Elsevier2014-07-30Schwinger mechanism with stochastic quantization
https://repo.scoap3.org/record/2942
We prescribe a formulation of the particle production with real-time Stochastic Quantization. To construct the retarded and the time-ordered propagators we decompose the stochastic variables into positive- and negative-energy parts. In this way we demonstrate how to derive a standard formula for the Schwinger mechanism under time-dependent electric fields. We discuss a mapping to the Schwingerâ€“Keldysh formalism and a relation to the classical statistical simulation.Fukushima, KenjiFri, 27 Jun 2014 13:58:30 GMThttps://repo.scoap3.org/record/2942urn:ISSN:0370-2693Elsevier2014-07-30