Quantum Monte Carlo, Or, Solving the Many-Particle Schrödinger Equation Accurately While Retaining Favorable Scaling with System Size

2011 ◽  
pp. 117-166 ◽  
Author(s):  
Michael D. Towler
Keyword(s):  
Monte Carlo ◽  
Schrödinger Equation ◽  
Quantum Monte Carlo ◽  
Schrodinger Equation ◽  
System Size ◽  
The Many

scholarly journals Ab initio solution of the many-electron Schrödinger equation with deep neural networks

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
David Pfau ◽  
James S. Spencer ◽  
Alexander G. D. G. Matthews ◽  
W. M. C. Foulkes
Keyword(s):  
Neural Networks ◽  
Schrödinger Equation ◽  
Ab Initio ◽  
Schrodinger Equation ◽  
Deep Neural Networks ◽  
The Many

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 Thermal and Quantum Fluctuation Effects in Quasiperiodic Systems in External Potentials

2019 ◽  
Vol 4 (4) ◽  
pp. 93
Author(s):  
Fabio Cinti ◽  
Tommaso Macrì
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Quantum Fluctuation ◽  
Pair Potential ◽  
Many Body ◽  
Harmonic Confinement ◽  
Intrinsic Length ◽  
Fluctuation Effects ◽  
The Many ◽  
Quantum Monte Carlo Methods

We analyze the many-body phases of an ensemble of particles interacting via a Lifshitz–Petrich–Gaussian pair potential in a harmonic confinement. We focus on specific parameter regimes where we expect decagonal quasiperiodic cluster arrangements. Performing classical Monte Carlo as well as path integral quantum Monte Carlo methods, we numerically simulate systems of a few thousand particles including thermal and quantum fluctuations. Our findings indicate that the competition between the intrinsic length scale of the harmonic oscillator and the wavelengths associated to the minima of the pair potential generically lead to a destruction of the quasicrystalline pattern. Extensions of this work are also discussed.

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