Monte Carlo study of real time dynamics

Abstract

Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.

5 pages, 3 figures

References in corpus (6)

• A calculation of the bulk viscosity in SU(3) gluodynamics
• Electrical conductivity and charge diffusion in thermal QCD from the lattice
• Lattice simulations of real-time quantum fields
• Structure of Lefschetz thimbles in simple fermionic systems
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles

Cited by in corpus (68)

• Quantum Simulation for High Energy Physics
• A Primer on Resurgent Transseries and Their Asymptotics
• General Methods for Digital Quantum Simulation of Gauge Theories
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Simulation of Nonequilibrium Dynamics on a Quantum Computer
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory
• Deep Learning Beyond Lefschetz Thimbles
• Monte Carlo calculations of the finite density Thirring model
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Tempered transitions between thimbles
• Fermions at Finite Density in (2+1)d with Sign-Optimized Manifolds
• The role of boundary conditions in quantum computations of scattering observables
• Functional methods for false vacuum decay in real time
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions
• Prospects for Simulating a Qudit Based Model of (1+1)d Scalar QED
• Lattice Renormalization of Quantum Simulations
• Path integral contour deformations for observables in $SU(N)$ gauge theory
• Dynamical stabilisation of complex Langevin simulations of QCD
• Path integral contour deformations for noisy observables
• Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer
• Normalizing Flows and the Real-Time Sign Problem
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Evolution to the Quark-Gluon Plasma
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Combining the complex Langevin method and the generalized Lefschetz-thimble method
• Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
• Error-resilient Monte Carlo quantum simulation of imaginary time
• Gradient flows without blow-up for Lefschetz thimbles
• Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations
• Lattice Scalar Field Theory At Complex Coupling
• Reweighting Lefschetz Thimbles
• Towards learning optimized kernels for complex Langevin
• Phase Unwrapping and One-Dimensional Sign Problems
• Stable solvers for real-time Complex Langevin
• Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations
• A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Particle distribution in intense fields in a light-front Hamiltonian approach
• Effects of Cosine Tapering Window on Quantum Phase Estimation
• Exploring Light-Cone Distribution Amplitudes from Quantum Computing
• Scattering Amplitude from Quantum Computing with Reduction Formula
• Perturbative Removal of a Sign Problem
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Real-time correlators in 3+1D thermal lattice gauge theory
• Complex Langevin study for polarons in an attractively interacting one-dimensional two-component Fermi gas
• Getting even with CLE
• False vacuum decay of excited states in finite-time instanton calculus
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• 3+1 Dimension Schwinger Pair Production with Quantum Computers
• Regularization of Complex Langevin Method
• Towards sampling complex actions
• Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
• Lefschetz Thimbles and Quantum Phases in Zero-Dimensional Bosonic Models
• The thermodynamics of large-N QCD and the nature of metastable phases
• Performance of Complex Langevin Simulation in 0+1 dimensional massive Thirring model at finite density
• Dynamical Triplet Unravelling: A quantum Monte Carlo algorithm for reversible dynamics
• Sign optimization and complex saddle points in one-dimensional QCD
• Real-time quantum dynamics, path integrals and the method of thimbles
• On a modification method of Lefschetz thimbles
• Lattice Lindblad simulation
• Complex path simulations of geometrically frustrated ladders
• Large scale multi-node simulations of ${\mathbb{Z}}_2$ gauge theory quantum circuits using Google Cloud Platform