Numerical Study on Spontaneous Symmetry Breaking in a XY Quantum Antiferromagnet on a Finite Triangular Lattice

Motivated by recent experiments that require more complicated macroscopic wave functions in the condensed matters, we make numerical study on a XY quantum antiferromagnet on a finite triangular lattice using the variational Monte Carlo method and the stochastic state selection method. One of our purpose is a numerical confirmation on dominance of a Nambu-Goldstone boson in low energy excitation. For another purpose, we calculate energy, an expectation value of a symmetry breaking operator and structure functions of spin by fixing a quantum number of the symmetry. These calculations are made for states that become degenerate in an infinitely large lattice. By numerical calculations we confirm existence of a Nambu-Goldstone boson, and find dependence of a square of the quantum number for the above quantities. Using these results we can discuss on complicated macroscopic wave functions in quantum spin systems.