  In the present paper, we study spin-${1 \over 2}$ antiferromagnetic (AF)
Heisenberg model on layered anisotropic triangular lattice and obtain its phase
structure. We use the Schwinger bosons for representing spin operators and also
coherent-state path integral for calculating physical quantities.
Finite-temperature properties of the system are investigated by means of the
numerical Monte-Carlo simulations. Detailed phase diagram of the system is
obtained by calculating internal energy, specific heat, spin correlation
functions, etc. There are AF N\'eel, paramagnetic and spiral states. Turning on
plaquette term (i.e., the Maxwell term on a lattice) of an emergent U(1) gauge
field that flips a pair of parallel spin-singlet bonds, we found that there
appears a phase that is regarded as a deconfined spin-liquid state, though
"transition" to this phase from the paramagnetic phase is not of second order
but a crossover. In that phase, the emergent gauge boson is a physical gapless
excitation coupled with spinons. These results support our previous study on AF
Heisenberg model on a triangular lattice at vanishing temperature.
