scholarly journals Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron

2018 ◽  
Author(s):  
Jonas Greitemann ◽  
Lode Pollet
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fourier Transforms ◽  
Full Detail ◽  
Many Body ◽  
Sampling Schemes ◽  
Self Energy ◽  
Extensive Documentation ◽  
Many Body Systems ◽  
The Green Function

These notes are intended as a detailed discussion on how to implement the diagrammatic Monte Carlo method for a physical system which is technically simple and where it works extremely well, namely the Fröhlich polaron problem. Sampling schemes for the Green function as well as the self-energy in the bare and skeleton (bold) expansion are disclosed in full detail. We discuss the Monte Carlo updates, possible implementations in terms of common data structures, as well as techniques on how to perform the Fourier transforms for functions with discontinuities. Control over the variety of parameters, especially in the bold scheme, is demonstrated. Sample codes are made available online along with extensive documentation. Towards the end, we discuss various extensions of the method and their applications. After working through these notes, the reader will be well equipped to explore the richness of the diagrammatic Monte Carlo method for quantum many-body systems.

scholarly journals Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications

2019 ◽  
Vol 10 (1) ◽  
pp. 337-356 ◽  
Author(s):  
Zi-Xiang Li ◽  
Hong Yao
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Hot Spot ◽  
High Temperature Superconductors ◽  
System Size ◽  
Many Body ◽  
Broken Symmetries ◽  
Sign Problem ◽  
Universal Quantum ◽  
Many Body Systems

Reliable simulations of correlated quantum systems, including high-temperature superconductors and frustrated magnets, are increasingly desired nowadays to further our understanding of essential features in such systems. Quantum Monte Carlo (QMC) is a unique numerically exact and intrinsically unbiased method to simulate interacting quantum many-body systems. More importantly, when QMC simulations are free from the notorious fermion sign problem, they can reliably simulate interacting quantum models with large system size and low temperature to reveal low-energy physics such as spontaneously broken symmetries and universal quantum critical behaviors. Here, we concisely review recent progress made in developing new sign-problem-free QMC algorithms, including those employing Majorana representation and those utilizing hot-spot physics. We also discuss applications of these novel sign-problem-free QMC algorithms in simulations of various interesting quantum many-body models. Finally, we discuss possible future directions of designing sign-problem-free QMC methods.

scholarly journals Particle entanglement in continuum many-body systems via quantum Monte Carlo

2014 ◽  
Vol 89 (14) ◽  
Author(s):  
C. M. Herdman ◽  
P.-N. Roy ◽  
R. G. Melko ◽  
A. Del Maestro
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Many Body ◽  
Many Body Systems

Monte Carlo Studies of the Dynamics of Quantum Many-Body Systems

1985 ◽  
Vol 55 (11) ◽  
pp. 1204-1207 ◽  
Author(s):  
H. -B. Schüttler ◽  
D. J. Scalapino
Keyword(s):  
Monte Carlo ◽  
Many Body ◽  
Monte Carlo Studies ◽  
Many Body Systems

Symplectic Schrödinger equation for many-body systems

2020 ◽  
Vol 35 (06) ◽  
pp. 2050033
Author(s):  
R. G. G. Amorim ◽  
M. C. B. Fernandes ◽  
F. C. Khanna ◽  
A. E. Santana ◽  
J. D. M. Vianna
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Basic Element ◽  
Space Representation ◽  
Many Body ◽  
Many Body Systems ◽  
The Green Function ◽  
Phase Space Representation

Using elements of symmetry, as gauge invariance, many aspects of a Schrödinger equation in phase space are analyzed. The number (Fock space) representation is constructed in phase space and the Green function, directly associated with the Wigner function, is introduced as a basic element of perturbative procedure. This phase space representation is applied to the Landau problem and the Liouville potential.

scholarly journals Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 853 ◽  
Author(s):  
M. Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Numerical Solutions ◽  
Fourier Transforms ◽  
Integral Transform ◽  
Finite Degree ◽  
Differential Problem ◽  
Numerical Convergence ◽  
The Monte Carlo Method ◽  
Gaussian Quadratures

This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random Gaussian quadratures and the Monte Carlo method. The recovery of the solution of the original random partial differential problem throughout the inverse integral transform allows its numerical approximation using Gaussian quadratures involving the evaluation of the solution of the random ordinary differential problem at certain concrete values, which are approximated using Monte Carlo method. Numerical experiments illustrating the numerical convergence of the method are included.

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