Linear flavor-wave theory for fully antisymmetric SU( N ) irreducible representations

Abstract

The extension of the linear flavor-wave theory (LFWT) to fully antisymmetric irreducible representations (irreps) of SU(N ) is presented in order to investigate the color order of SU(N ) antiferromagnetic Heisenberg models in several two-dimensional geometries. The square, triangular and honeycomb lattices are considered with m fermionic particles per site. We present two different methods: the first method is the generalization of the multiboson spin-wave approach to SU(N ) which consists of associating a Schwinger boson to each state on a site. The second method adopts the Read and Sachdev bosons which are an extension of the Schwinger bosons that introduces one boson for each color and each line of the Young tableau. The two methods yield the same dispersing modes, a good indication that they properly capture the semi-classical fluctuations, but the first one leads to spurious flat modes of finite frequency not present in the second one. Both methods lead to the same physical conclusions otherwise: long-range Néel-type order is likely for the square lattice for SU(4) with two particles per site, but quantum fluctuations probably destroy order for more than two particles per site, with N = 2m. By contrast, quantum fluctuations always lead to corrections larger than the classical order parameter for the tripartite triangular lattice (with N = 3m) or the bipartite honeycomb lattice (with N = 2m) for more than one particle per site, m > 1, making the presence of color very unlikely except maybe for m = 2 on the honeycomb lattice, for which the correction is only marginally larger than the classical order parameter.

SU(4)-symmetric spin-orbital liquids on the hyperhoneycomb lattice

“…10(a). The energy of the stripy state at the SU(4) symmetric point is E stripy ≈ −0.3079N J, close to the value of E ≈ −0.314N J found for the two-color ordered states on the honeycomb lattice [47]. Although this energy is not variational, it is significantly higher than the ones of the previously stud-ied QSOLs and indicates that the stripy phase is not competitive at this point.…”

“…We also studied the possibility of collinear long-range order formation due to perturbations induced by finite values of Hund's coupling. Within this set of ordered states, linear flavor wave theory (LFWT) [46,47] indicates that only a stripy ordered phase of j = 3/2 moments is stable. However, further VMC computations showed that the QSOL is also stable against the formation of this order.…”

Dimensional crossover in the SU(4) Heisenberg model in the six-dimensional antisymmetric self-conjugate representation revealed by quantum Monte Carlo and linear flavor-wave theory

“…The phase transition from the Néel state during this dimensional crossover will first be assessed by the LFWT by closely following the steps in Ref. [35]. The results of the auxiliary field QMC simulations (free of the sign problem for the current model) will then be presented by considering system sizes up to 40 × 40, showing a small local moment in the 2D model and supporting a continu-ous transition between the Néel state and the VBS state during the dimensional transition.…”

Density matrix renormalization group simulations of SU( N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

“…55,56 Finally, Young's rules could also be used to implement SU (N ) symmetries in tensor networks to study twodimensional SU (N ) Heisenberg models, which could potentially host exotic physical phases. [57][58][59][60][61][62][63][64] Work is currently in progress along these lines.…”