Numerical treatment of spin systems with unrestricted spin length S: A functional renormalization group study

Abstract

We develop a generalized pseudofermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case S=1/2 to the classical limit S→∞. Within this framework, spins of magnitude S are realized by implementing M=2S copies of spin-1/2 degrees of freedom on each lattice site. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudofermion constraint in previous spin-1/2 PFFRG studies. We apply this method to the antiferromagnetic J1−J2 honeycomb Heisenberg model with nearest-neighbor J1>0 and second-neighbor J2>0 interactions. Mapping out the phase diagram in the J2/J1−S plane, we find that upon increasing S, quantum fluctuations are rapidly decreasing. In particular, already at S=1 we find no indication for a magnetically disordered phase. In the limit S→∞, the known phase diagram of the classical system is exactly reproduced. More generally, we prove that for S→∞ the PFFRG approach is identical to the Luttinger-Tisza method.