Signature of Néel order in exact spectra of quantum antiferromagnets on finite lattices

Abstract

We show how the broken symmetries of the Neel state are embodied in the exact spectrum of the triangular Heisenberg antiferromagnet on finite lattices as small as N = 21 (spectra up to N = 36 have been computed). We present the first numerical evidence of an extensive set of low-lying levels that are below the softest magnons and collapse to the ground state in the thermodynamic limit, This set of quantum states represents the quantum counterpart of the classical Neel ground state.We develop an approach relying on the symmetry analysis and finite-size scaling and we provide new arguments in favor of an ordered ground state for the S = 2 triangular Heisenberg model. PACS numbers: 75.10.Jm, 75.30.Kz, 75.40. Mg In the last decades, a large amount of work has been devoted to the understanding of the quantum ground state of two-dimensional antiferromagnets.In the early seventies, Anderson launched a debate on the possible existence of a "resonating valence bond" (RVB) state which could represent an alternative to the Neel antiferromagnetic state [1]. The first candidate to be considered was the spin-2 Heisenberg antiferromagnet on the triangular lattice:where the sum runs over Erst neighbor pairs. A variational RVB state was proposed to be more stable than the Neel state [2]. From the spin-wave analysis, it was later concluded that quantum fiuctuations were insufficient to destabilize Neel's classical state [3]; perturbative approaches led to the same conclusion and variational ones did not weaken it [4,5]. However, exact results of diagonalization on small periodic samples up to N = 27 were extrapolated and gave the opposite result [6,7]. But in the above numerical studies, the spin-liquid hypothesis was not really explored, nor was the Neel long-range order (NLRO) assumption convincingly discarded. Usually NLRO is checked on the finite-size scaling of the ground-state energy and magnetization [8,9]. The magnon dispersion relation being linear in k, the leading finite-size correction to the ground-state energy per particle F is O(N~) and that for the magnetization modulus per particle M is O(N t 2) (M~i s defined in[10]). Figure 1 shows the values of E~and M~for small periodic samples. We present the results for the erst calculation of the N = 36 sample, a calculation made possible by using all the symmetries of the Hamiltonian and the lattice. We find (2S, S~)ss = -0.3735823(1) and Mss = 0.400575(1). Prom the values, it is clear that the magnetization modulus does not extrapolate to zero in the N~oo limit; but, it is difficult to assert that the finite-size sealing of the ground-state energy behaves as N~. Therefore, no de6nite conclusion can be drawn from the ground-state evaluations on small samples. In this Letter we show how the hypothesis of NLRO implies a list of drastic conditions on the symmetries, dynamics, and the finite-size scaling of an extensive [O(Ns~~)] set of low-lying levels of the spectrum. Some of these conditions are new, others go back to Anderson's seminal paper on antiferromagnets [11] or ...

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