Quantum Monte Carlo study of 2D spin Peierls state with multimode distortions

2D spin-Peierls states are investigated by using stochastic series expansion quantum Monte Carlo method. The obtained numerical data support the previous result derived through the exact diagonalization (ED) calculations for a small cluster, indicating that the lowest energy state of the square-lattice 2D spin-Peierls system is the so-called multimode spin-Peierls (MMSP) state with lattice distortions involving Fourier components having not only the nesting wave vector but also other wave vectors parallel to it, as long as the spin–lattice coupling constant exceeds a certain critical value, and that the transition between the antiferromagnetic SDW state and the MMSP state, due to the change of the spin–lattice coupling strength, is of the first order. Since the Monte Carlo method allows us to treat larger system sizes compared to the ED method, it is possible to discuss the size effect of the transition and the degeneracy among different distortion patterns.