# Schwinger-Keldysh formalism on the lattice: A faster algorithm and its application to field theory

@article{Alexandru2017SchwingerKeldyshFO, title={Schwinger-Keldysh formalism on the lattice: A faster algorithm and its application to field theory}, author={Andrei Alexandru and Gokce Basar and Paulo F. Bedaque and Gregory W. Ridgway}, journal={Physical Review D}, year={2017}, volume={95} }

A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the…

## 40 Citations

### Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations

- Computer ScienceJournal of High Energy Physics
- 2022

This paper proposes a fast Hybrid Monte Carlo algorithm for evaluating the integral, where the force of the fictitious Hamilton dynamics on the deformed contour is backpropagate to that on the original contour, thereby reducing the required computational cost by a factor of the system size.

### Worldvolume approach to the tempered Lefschetz thimble method

- Computer Science
- 2020

A novel Hybrid Monte Carlo algorithm is proposed, in which molecular dynamics is performed on a continuum set of integration surfaces foliated by the antiholomorphic gradient flow, and solves the sign and multimodal problems simultaneously as the original TLTM does.

### Real-time quantum dynamics, path integrals and the method of thimbles

- PhysicsJournal of High Energy Physics
- 2019

A bstractDirect numerical evaluation of the real-time path integral has a well-known sign problem that makes convergence exponentially slow. One promising remedy is to use Picard-Lefschetz theory to…

### Finite density QED1+1 near Lefschetz thimbles

- MathematicsPhysical Review D
- 2018

One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination…

### Lefschetz Thimbles and Wigner Functions

- MathematicsJournal of Applied Mathematics and Physics
- 2020

The major difficulty for the Feynman Path Integral Monte Carlo (PIMC) simulations of the quantum systems of particles is the so called “sign problem”, arising due to the fast oscillations of the path…

### Finite-density Monte Carlo calculations on sign-optimized manifolds

- MathematicsPhysical Review D
- 2018

We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field…

### Worldvolume tempered Lefschetz thimble method and its error estimation

- MathematicsProceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021)
- 2022

The worldvolume tempered Lefschetz thimble method (WV-TLTM) is an algorithm towards solving the sign problem, where hybrid Monte Carlo updates are performed on a continuous accumulation of flowed…

### Complex Paths Around The Sign Problem.

- Physics
- 2017

A new set of ideas recently developed to tackle the sign problem based on the complexification of field space and the Picard-Lefshetz theory accompanying it are reviewed.

### Sign Problems in Quantum Field Theory: Classical and Quantum Approaches

- Physics
- 2020

Monte Carlo calculations in the framework of lattice field theory provide non-perturbative access to the equilibrium physics of quantum fields. When applied to certain fermionic systems, or to the…

### Numerical sign problem and the tempered Lefschetz thimble method

- PhysicsProceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)
- 2022

The numerical sign problem is a major obstacle to thequantitative understanding of manyimportant physical systems with ﬁrst-principles calculations. Typical examples for such systems include…

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