Nearly Deconfined Spinon Excitations in The Square-Lattice Spin-1/2 Heisenberg Antiferromagnet
Update: 2018-02-24 10:06:28      Author:

The anomaly in the excitation spectrum around the wave-vector (π,0) in experimental realizations of the 2D spin-1/2 Heisenberg spin model, such as CFTD, is a long-standing issue, which is also reproduced in calculations with the Heisenberg model. It is manifested as a suppression of the excitation energy and an associated enhancement of spectral weight in the continuum above the spin-wave (magnon) peak. The physical reasons behind the anomaly have been debated over the past 20 years or so, and in the last few years the interest in the issue has heated up further as new high-resolution neutron scattering experiments have been carried out [1]. The main question is whether the anomaly is caused simply by more or less standard multi-magnon excitation processes [2], or whether there are more exotic reasons such as deconfinement of spinons [1]. On the other hand, the recently improved analytic continuation (SAC) method [3] enables people to study the spectral anomaly in greater details than previously. Most importantly, it provides an unbiased way to extract the energy and amplitude of the leading δ-function (magnon pole) contribution to the dynamic spin structure factor.

Recently, Hui Shao and Stefano Chesi of CSRC, Yan Qi Qin and Zi Yang Meng from IOP, Sylvain Capponi from University of Toulouse, and Anders Sandvik from Boston University, have used the improved SAC method to investigate the spin excitation spectral functions of the spin-1/2 square-lattice Heisenberg antiferromagnet [4], and, as shown in Fig. 1, the results are in excellent agreement with recent neutron scattering experiment on CFTD. Moreover, the abnormal reduction of the excitation energy at (π,0) is found together with a reduction of the magnon weight. Upon turning on a competing four-spin interaction which brings the system to a critical point with deconfined spinon excitations, they observe a rapid reduction of the magnon weight to zero (see Fig. 2 left). This, along with an effective model of the excitations - one magnon or two spinons (see Fig.2 right), brings to the picture of nearly deconfined spinons at (π,0) - a precursor to deconfined quantum criticality. This work bridges the two interpretations (magnons versus spinons), by elucidating the so far neglected role of the interplay between the magnon pole and the continuum above it. Furthermore, it is the first study of the dynamics of the J-Q model and the evolution of its excitation spectrum upon approaching the deconfined quantum-critical point, where hitherto unknown aspects of the spinon deconfinement mechanism remains uncovered.


Fig. 1: Comparison of the SAC results on the spin-1/2 square-lattice Heisenberg antiferromagnet and the new neutron scattering experiments carried out on CFTD. Left panel: spectral functions at two wave vectors; Right panel: single-magnon dispersion along a representative path of the BZ.


Fig. 2: Left panel: size dependence of the excitation energy (a) and the relative weight of the magnon pole (b) at q=(π,0) close to the Heisenberg limit of the J-Q model; Right panel: (a) dispersions of the bare excitations and (b) the lowest energy of the mixed spinon-magnon system obtained with the dispersions in (a).



[1]      B. D. Piazza et al., Nat. Phys. 11, 62 (2015).

[2]      M. Powalski et al., arXiv:1701.04730 (2017).

[3]      A.W. Sandvik, Phys. Rev. B 57, 10287 (1998); H. Shao and A. W. Sandvik, in progress.

[4]      H. Shao, Y. Qin, S. Capponi, S. Chesi, Z. Meng, and A. W. Sandvik, Phys. Rev. X 7, 041072 (2017).

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