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

Abstract

We develop a generalized pseudo-fermion 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 pseudo fermion 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.

Quantum Spin Liquids in Frustrated Spin-1 Diamond Antiferromagnets

“…[24]. To ensure projection into the correct subspace of the resulting spin algebra, all spin flavors κ must align ferromagnetically.…”

“…This motivates us to consider the quantum version of the minimal exchange model (1) for spins of arbitrary length S in this manuscript and ask whether qualitatively new physics arises in the crossover from the classical to the quantum regime (upon decreasing the spin length). We work with a pseudofermion functional renormalization group (pf-FRG) approach [20] that has proved capable of handling competing interactions and emergent spin liquid physics in three-dimensional, frustrated quantum magnets [21][22][23] and which has recently been generalized to spin-S systems [24]. Our numerical results indicate that a distinct classical to quantum crossover occurs for spin S = 3/2.…”

“…Pseudofermion FRG.-To explore the exchange model (1) we employ the pf-FRG approach [20], which recasts the original spin degrees of freedom in terms of auxiliary Abrikosov fermions and then applies the well-developed FRG approach of fermionic systems [25,26]. In the language of the original spin model, the pf-FRG approach amounts to a concurrent 1/S and 1/N expansion that allows to faithfully capture conventionally ordered magnetic states (typically favored already in the large-S limit of the expansion) and spin liquid states (favored in the alternate large-N limit) and is known to become exact in the separate limits of large S [24] and large N [27,28]. With the computational effort scaling quadratically with system size O(N 2 L ) and quartically with the number of frequencies O(N 4 ω ), there is a trade-off in choosing larger system sizes versus finer energy/temperature resolution.…”

Classical spiral spin liquids as a possible route to quantum spin liquids

“…4, both quantum effects, i.e., contraction of spiral contours and selection of dominant wave vectors, are suppressed for increasing S and the exact Luttinger-Tisza result is reproduced correctly as expected. 40…”

“…Our second objective is to demonstrate that these spiral spin liquids are good candidate systems for realizing a quantum spin liquid in the S = 1/2 case. Therefore, we employ the pseudofermion functional renormalization group (PFFRG) method 39,40 which is capable of treating strongly frustrated spin systems even in the case of complex two-dimensional 21,30,35,[39][40][41][42] or threedimensional 15,16,[43][44][45] lattice geometries and in the presence of long-range couplings. 15,16,21,30,35,42,44,45 Our numerical results indicate that for both models the coupling regimes of classical spiral degeneracies indeed host extended non-magnetic phases in the S = 1/2 case.…”