Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model

Abstract

We develop numerical tools for Diagrammatic Monte-Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First we note that the path integral measure of such theories contributes a bare mass term in the effective action which is proportional to the bare coupling constant. This mass term renders the perturbative expansion infrared-finite and allows to study it directly in the large-N and infinite-volume limits using the Diagrammatic Monte-Carlo approach. On the exactly solvable example of a large-N O(N) sigma model in D=2 dimensions we show that this infrared-finite weak-coupling expansion contains, in addition to powers of bare coupling, also powers of its logarithm, reminiscent of re-summed perturbation theory in thermal field theory and resurgent trans-series without exponential terms. We numerically demonstrate the convergence of these double series to the manifestly non-perturbative dynamical mass gap. We then develop a Diagrammatic Monte-Carlo algorithm for sampling planar diagrams in the large-N matrix field theory, and apply it to study this infrared-finite weak-coupling expansion for large-N U(N)xU(N) nonlinear sigma model (principal chiral model) in D=2. We sample up to 12 leading orders of the weak-coupling expansion, which is the practical limit set by the increasingly strong sign problem at high orders. Comparing Diagrammatic Monte-Carlo with conventional Monte-Carlo simulations extrapolated to infinite N, we find a good agreement for the energy density as well as for the critical temperature of the "deconfinement" transition. Finally, we comment on the applicability of our approach to planar QCD at zero and finite density.

arXiv comment33 pages RevTeX, 17 figures; v2: significantly revised and clarified, accepted for Phys.Rev.D

References in corpus (63)

• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Renormalons
• Wilson Loops and Minimal Surfaces
• Worm algorithms for classical statistical models
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• A Portable High-Quality Random Number Generator for Lattice Field Theory Simulations
• The Three-Loop Free Energy for Pure Gauge QCD
• Screened Perturbation Theory
• Feynman diagrams versus Fermi-gas Feynman emulator
• String Theory and Quark Confinement
• Diagrammatic Monte Carlo
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• n-Particle irreducible effective action techniques for gauge theories
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
• Generating Non-perturbative Physics from Perturbation Theory
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
• On the nature of the electroweak phase transition
• The lattice QCD phase diagram in and away from the strong coupling limit
• A holographic model for QCD in the Veneziano limit at finite temperature and density
• Nonabelian Debye Screening in One-Loop Resummed Perturbation Theory
• Loop Equations and bootstrap methods in the lattice
• Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
• Flux representation of an effective Polyakov loop model for QCD thermodynamics
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• Principal Chiral Field at Large N
• Perturbative expansion of the plaquette to $\mathcal{O}({\alpha }^{35})$ in four-dimensional SU(3) gauge theory
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• The QCD phase diagram according to the center group
• Precision check on triviality of phi^4 theory by a new simulation method
• Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
• Polynomial complexity despite the fermionic sign
• Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
• The Operator Product Expansion, Non-perturbative Couplings and the Landau Pole: Lessons from the O(N) $\sigma$-Model
• Stability of Dirac Liquids with Strong Coulomb Interaction
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Simulating the All-Order Strong Coupling Expansion IV: CP(N-1) as a loop model
• Continuous Time Monte Carlo for Lattice QCD in the Strong Coupling Limit
• Infrared exponents and the strong-coupling limit in lattice Landau gauge
• Strong coupling expansion for finite temperature Yang-Mills theory in the confined phase
• Lattice gauge theory without link variables
• Heat Bath Efficiency with Metropolis-Type Updating
• Generating a non-perturbative mass gap using Feynman diagrams in an asymptotically free theory
• On Unitary/Hermitian Duality in Matrix Models
• Abelian color cycles: a new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory
• Two dimensional SU(N) x SU(N) chiral models on the lattice
• Performance of a worm algorithm in ${\varphi }^4$ theory at finite quartic coupling
• Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function
• Large-N phase transition in lattice 2-d principal chiral models
• Incorporating Dynamic Mean-Field Theory into Diagrammatic Monte Carlo
• A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations
• Worm Algorithm for CP(N-1) Model
• Improved Holographic QCD and the Quark-gluon Plasma
• Phenomenology of renormalons and the OPE from lattice regularization: the gluon condensate and the heavy quark pole mass
• A stochastic root finding approach: The Homotopy Analysis Method applied to Dyson-Schwinger Equations
• Nontrivial Thermodynamics in 't Hooft's Large-$N$ Limit
• Strong-coupling lattice study for QCD phase diagram including both chiral and deconfinement dynamics
• Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
• Bold Diagrammatic Monte Carlo Study of ${\varphi }^4$ Theory

Cited by in corpus (2)

• Diagrammatic Monte Carlo algorithm for the resonant Fermi gas
• Full and unbiased solution of the Dyson-Schwinger equation in the functional integro-differential representation