Berneviget al.Reply:

Abstract

Bernevig et al. Reply:We provide a Reply to the preceding Comment [1] by Greiter and Schuricht (GS). Let us first stress that there is no doubt about the mathematical correctness of our derivation. We now show that our interpretation of the physics of spinons is correct. Against the existence of spinon attraction, GS recall that spinons constitute an ''ideal gas of half fermions'' [2]. In reality, spinons feel a statistical interaction associated with a rule for progressively filling single-particle states. The fully dressed S matrix for spinons [3] in the Haldane-Shastry model (HSM) [4] takes the trivial form S i times the identity I. (This is well known and we derived it on p. 9 of the second paper of Ref. [5], which is equivalent to computing the S matrix associated with exchange statistics of semions-which can also be done by asymptotic Bethe ansatz -there is an extra i in our formula: it comes from a misprint in the final version of the Letter.) Triviality of the S matrix means that spinons are alleged asymptotic states of the HSM. Their long-distance behavior is not affected by their dynamical short-range attraction. In our Letter, we explicitly show the short-distance effects of the interaction on two-spinon wave functions [5]. We now consider the points raised by GS separately.GS claim our interpretation of the p mn e i as twospinon relative wave function is ambiguous, because the p mn 's are defined by expanding the (overcomplete) set of states in the (basis of) energy eigenfunctions mn . This statement is false. In real space, spinons are nonlocal excitations, with typical size of the order of the lattice step [5]. The 's should be thought of as the lattice version of two-particle coherent states. The overcompleteness of the 's is, therefore, the lattice version of the usual overcompleteness of coherent states. Two spinons at the same site correspond to a localized spin-1 excitation, unambiguously described by z 1 ; . . . ; z N=2ÿ1 [5]. The physical meaning of p mn 1 as the probability enhancement when the two spinons are at the same site (and form the spin-1 excitation) is hence absolutely unambiguous, at odds to GS's statement that the jp mn j 2 's ''cannot be interpreted as probability distribution.'' We also find a similar short-range attraction between a spinon and a holon (in the supersymmetric t ÿ J model with 1=r 2 interaction) although the states of a localized spinon and a localized holon do not form an overcomplete set [5]. We wish to remark that using overcomplete sets of states to treat nonlocal excitations as quantum-mechanical particles is in fact widely used for Laughlin quasiholes, a fact which Greiter correctly and explicitly points out in a prior publication [6]. The spinon situation is no different.GS assert that ''the second argument of [Bernevig, Giuliano, and Laughlin] is that the last term in their expression for the energy of the two-spinon states represents 'a negative interaction contribution that becomes negligibly small in the thermodynamic limit'.'' We clearly state that th...

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