Many-Body String Excitations in the Antiferromagnetic Ising Spin Chain Compound BaCo2V2O8
Z. Wang, Y. Kohama, and K. Kindo
The one-dimensional (1D) spin-1/2 Heisenberg-Ising model is the paradigmatic model for the study of quantum phase transitions and spin dynamics. However, the realization of this spin model in a solid-state material and its study are quite challenging. Several criteria must be fulfilled simultaneously: 1. the intrachain coupling should be dominant over the interchain coupling. 2. A significant Ising-like anisotropy should be present. 3. The required experimental conditions, such as high magnetic fields, should be available.
These criteria were found to be realized in the spin-1/2 Heisenberg-Ising chain antiferromagnetic material BaCo2V2O8. Our recent work has revealed a unique quantum critical behaviors under a strong transverse magnetic field (B⊥c) of 40 T , which is characteristic for the transverse-field Ising quantum critical point. In contrast, in an applied longitudinal field (B//c), the phase diagram of the Heisenberg-Ising antiferromagnetic chain is completely different. Two phase transitions can be induced, and the different phases are characterized by different quantum spin excitations. In this work, we performed high-resolution terahertz spectroscopy and magnetocaloric-effect (MCE) measurements in BaCo2V2O8 as a function of temperature and applied longitudinal magnetic field . We found characteristic features revealing the field-induced quantum phase transitions, and observed the characteristic spin dynamics for the various phases. In particular, many-body string excitations as well as low-energy fractional excitations  were identified in the field-induced gapless phase, by comparing to the Bethe-Ansatz calculations . Moreover, approaching the field-induced quantum phase transition from higher field, we observed a dominant contribution of the higher-energy string states than the lower-lying fractional excitations, in contrast to the conventional belief.
Figure 1(a) shows the MCE data, T(B), measured at different initial temperatures. The T(B) starting from 1.7 K at zero field reaches a minimum at the critical field (Bc) of 3.8 T, following by a slight increase towards higher fields. Before the temperature jump above the saturation fields of 22.9 T, the MCE detect a weak minimum at about 19.5 T. The weak minimum corresponds to the half-saturated magnetization as seen in Figure 1(b) and possibly reflects commensurate fluctuations. In down-sweeping data, the T(B) curve matches with the up-sweeping curve, except for a (irreversible) heating effect at the phase boundary. At higher temperatures, the anomalies at the critical and the half-saturated fields broaden and smear out, whereas the minimum at saturation fields remains and becomes the dominant feature. These observations qualitatively agree with the calculated phase diagram for the 1D Heisenberg-Ising model, confirming that the BaCo2V2O8 is a suitable system for investigating the string and the additional fractional magnetic excitations. This conclusion is also checked by the magnetization data, which shows quantitatively agreement with the 1D Heisenberg-Ising model (Red curve in Fig.1(b)).
We investigated the dynamical properties with THz transmission spectra in the applied longitudinal magnetic field. These data are available in Ref.  which tracked the field dependence of exotic spin excitations, i.e., many-body string and fractional excitations. We have revealed their selection rule in the vicinity of a field induced QCP in the Ising-like spin-½ chain compound. While the gapped fractional excitations are dominant in the 3D ordered state, we found that the high-energy string excitations plays an important role in quantum critical dynamics, which is consistent with Bethe-Ansatz calculations .
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