scholarly journals High-precision finite-size scaling analysis of the quantum-critical point ofS=1∕2Heisenberg antiferromagnetic bilayers

2006 ◽  
Vol 73 (1) ◽  
Author(s):  
Ling Wang ◽  
K. S. D. Beach ◽  
Anders W. Sandvik
Keyword(s):  
Critical Point ◽  
High Precision ◽  
Quantum Critical Point ◽  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Quantum Critical

SCALING LAW OF SUPERFLUID–INSULATOR TRANSITION IN THE 1D BOSE–HUBBARD MODEL

2012 ◽  
Vol 26 (04) ◽  
pp. 1250014 ◽  
Author(s):  
SHI-JIAN GU ◽  
JUNPENG CAO ◽  
SHU CHEN ◽  
HAI-QING LIN
Keyword(s):  
Hubbard Model ◽  
Critical Point ◽  
Scaling Laws ◽  
Scaling Law ◽  
Finite Size ◽  
Superfluid Density ◽  
Insulator Transition ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Size Scaling

The finite size scaling behavior of superfluid–insulator transition in the one-dimensional Bose–Hubbard model is studied. It is shown that the superfluid density of the system with finite size has a maximum at a certain interaction Um and the derivative of superfluid density has a minimum at a certain interaction Ud. The critical point Uc can be quantified by the scaling analysis of either Um or Ud. The transition point Um tends to the critical point Uc from the region of U < Uc, while the Ud tends to the Uc from the region of U > Uc. The transition points Um and Ud satisfy different finite size scaling laws and have the different critical exponents. The divergence speed of the superfluid density is much smaller than that of its derivative at the critical point.

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