Determinantal and worldline quantum Monte Carlo methods for many-body systems

1993 ◽  
Vol 47 (24) ◽  
pp. 16131-16140 ◽  
Author(s):  
M. Vekić ◽  
S. R. White
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Quantum Monte Carlo ◽  
Many Body ◽  
Many Body Systems ◽  
Quantum Monte Carlo Methods

scholarly journals QUANTUM MONTE CARLO METHODS FOR NUCLEI AT FINITE TEMPERATURE

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1447-1462 ◽  
Author(s):  
Y. ALHASSID
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Finite Temperature ◽  
Quantum Monte Carlo ◽  
Configuration Spaces ◽  
Many Body ◽  
Level Densities ◽  
Sign Problem ◽  
Quantum Monte Carlo Methods ◽  
Nuclear Shell

We discuss finite temperature quantum Monte Carlo methods in the framework of the interacting nuclear shell model. The methods are based on a representation of the imaginary-time many-body propagator as a superposition of one-body propagators describing non-interacting fermions moving in fluctuating auxiliary fields. Fermionic Monte Carlo calculations have been limited by a "sign" problem. A practical solution in the nuclear case enables realistic calculations in much larger configuration spaces than can be solved by conventional methods. Good-sign interactions can be constructed for realistic estimates of certain nuclear properties. We present various applications of the methods for calculating collective properties and level densities.

Quantum monte carlo methods for constrained systems

2014 ◽  
Vol 114 (10) ◽  
pp. 611-625 ◽  
Author(s):  
Sarah Wolf ◽  
Emanuele Curotto ◽  
Massimo Mella
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Quantum Monte Carlo ◽  
Constrained Systems ◽  
Quantum Monte Carlo Methods

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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