Quantum phase transition in multilayer fractional quantum Hall systems

Energetically stable states are studied for the infinite multilayer quantum Hall system. Two-dimensional incompressible quantum Hall states are stable for appropriate fillings in the limit of infinite interlayer separation, while three-dimensional compressible states are stabilized by interlayer couplings such as tunneling and Coulomb interaction in the case of small separation. Trial states are introduced for typical cases and their Coulomb energies are calculated with use of the variational Monte Carlo method and the Hartree-Fock approximation. On energetical grounds, possible quantum phase transitions are discussed in this system.