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Alternatively, one can represent Eq. (3) also in terms of real fields (Equation presented) and (Equation presented), defined as (Equation presented) [14]. In the (Equation presented) representation, Eq. (3) coincides with the corresponding quadratic part of the exchange Hamiltonian (2) of Ref. [14]. We also note that Ref. [14] has further replaced the bond-dependent terms by their average [see Eq. (3) of Ref. [14]]; we do not use that approximation here.
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Alternatively, one can represent Eq. (3) also in terms of real fields (Equation presented) and (Equation presented), defined as (Equation presented) [14]. In the (Equation presented) representation, Eq. (3) coincides with the corresponding quadratic part of the exchange Hamiltonian (2) of Ref. [14]. We also note that Ref. [14] has further replaced the bond-dependent terms by their average [see Eq. (3) of Ref. [14]]; we do not use that approximation here.
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