Path integral hybrid Monte Carlo for the bosonic many-body systems

1999 ◽  
Vol 308 (1-2) ◽  
pp. 115-122 ◽  
Author(s):  
Shinichi Miura ◽  
Susumu Okazaki
Keyword(s):  
Monte Carlo ◽  
Path Integral ◽  
Many Body ◽  
Hybrid Monte Carlo ◽  
Many Body Systems

QUASICLASSICAL FOURIER PATH INTEGRAL QUANTUM CORRECTION TERMS TO THE KINETIC ENERGY OF INTERACTING QUANTUM MANY-BODY SYSTEMS

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3979-3991
Author(s):  
K. A. GERNOTH
Keyword(s):  
Monte Carlo ◽  
Kinetic Energy ◽  
Path Integral ◽  
Quantum Correction ◽  
Many Body ◽  
Quantum Distribution ◽  
Many Body Systems ◽  
The Many ◽  
Correction Terms ◽  
Integral Quantum

A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.

scholarly journals Path integral Monte Carlo for dissipative many-body systems

2003 ◽  
Vol 237 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Luca Capriotti ◽  
Alessandro Cuccoli ◽  
Andrea Fubini ◽  
Valerio Tognetti ◽  
Ruggero Vaia
Keyword(s):  
Monte Carlo ◽  
Path Integral ◽  
Many Body ◽  
Path Integral Monte Carlo ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document