Monte Carlo simulation of systems of identical bosons

Naoki Kawashima, 川島 直輝

Hans A. De Raedt

C. Lavalle, Marcos Rigol, M. Feldbacher +3 more

Dr Md Enamul Hoque

Bose-Einstein condensation has been attained using Monte Carlo simulation on non-interacting ideal bosons confined in a harmonic potential trap at near-zero temperature (~0K). A connection has been established between the cyclic paths originated by the interchange of identical bosons and condensation. At low temperatures, long cycles appear and condensation is obtained consequently. The simulated result is in perfect agreement with the corresponding theoretical findings.

V. Apaja

Using imaginary time, quantum statistical mechanics of a finite-temperature system in thermodynamical equilibrium turns into a problem of classical ring polymers made of particle paths. We need to consider all possible ring polymers at a given temperature, which again is where Monte Carlo methods are effective, especially using a so-called worm algorithm. We show how paths can be sampled using Monte Carlo, and how the physical properties, such as energy and radial distribution, are computed from the paths. Identical particles can have their paths exchanged at will, and we see how boson superfluidity comes out of this picture. Finally, the stochastic series expansion method is introduced to show finite temperature Hubbard model can be simulated.

V. Apaja, Olav F. Syljuåsen