Continuous unitary transformations in two-level boson systems

S. Dusuel, J. Vidal, J. M. Arias, J. Dukelsky, J. E. Garcia-Ramos

Published 2005-09-28, updated 2006-01-02Version 3

Two-level boson systems displaying a quantum phase transition from a spherical (symmetric) to a deformed (broken) phase are studied. A formalism to diagonalize Hamiltonians with $O(2L+1)$ symmetry for large number of bosons is worked out. Analytical results beyond the simple mean-field treatment are deduced by using the continuous unitary transformations technique. In this scheme, a 1/N expansion for different observables is proposed and allows one to compute the finite-size scaling exponents at the critical point. Analytical and numerical results are compared and reveal the power of the present approach to compute the finite-size corrections in such a context.