scholarly journals Many-body quantum states with exact conservation of non-Abelian and lattice symmetries through variational Monte Carlo

2021 ◽  
Vol 104 (4) ◽  
Author(s):  
Tom Vieijra ◽  
Jannes Nys
Keyword(s):  
Monte Carlo ◽  
Quantum States ◽  
Many Body ◽  
Variational Monte Carlo

scholarly journals VARIATIONAL MONTE CARLO FOR MICROSCOPIC CLUSTER MODELS

2004 ◽  
Vol 15 (10) ◽  
pp. 1329-1351
Author(s):  
THEODOROS LEONTIOU ◽  
NIELS R. WALET
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Cluster Model ◽  
Body Problem ◽  
Variance Reduction ◽  
Halo Nuclei ◽  
Direct Solution ◽  
Many Body ◽  
Variational Monte Carlo ◽  
The Many

We examine the application of the Variational Monte Carlo (VMC) method to a cluster model for halo nuclei. Particular attention is paid to the error estimate in the presence of correlations in the underlying random walk. We analyze the required steps for a reliable application of the VMC in the case of a complicated many-body problem, such as the direct solution of the nuclear Hamiltonian with realistic interactions. We also examine the possibility of variance reduction through the "zero variance principle", paying particular attention to the complexity of the many-body problem.

scholarly journals Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information

Science ◽  
2013 ◽  
Vol 340 (6137) ◽  
pp. 1205-1208 ◽  
Author(s):  
Michael Walter ◽  
Brent Doran ◽  
David Gross ◽  
Matthias Christandl
Keyword(s):  
Quantum Computing ◽  
Single Particle ◽  
Local Information ◽  
Geometric Object ◽  
Quantum States ◽  
Many Body ◽  
Arbitrary Size ◽  
Global Entanglement ◽  
Low Levels ◽  
Essential Resource

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure, multiparticle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating any given class of entanglement with an entanglement polytope—a geometric object that characterizes the single-particle states compatible with that class. Our results, applicable to systems of arbitrary size and statistics, give rise to local witnesses for global pure-state entanglement and can be generalized to states affected by low levels of noise.

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