Bethe String States and quantum spin dynamics


The real frequency response at high energy is a hard-core problem of condensed matter physics. On the other hand, 1D integrable models due to their exact solvability provide reliable reference points for studying quantum and thermodynamic correlations. Although the low energy fractional excitations are often well understood, exploring quantum dynamics in these systems remains challenging in the gapless regime, especially at intermediate and high energies.

Bethe string states and dynamics spin responses

In quantum spin systems, a single spin's flip proporgates through coupling with neighboring spins, wihch is called a "magnon" excitation. In a ferromagnet, there exists an effective attraction between magnons, which leads to bound states of magnons, denoted as "string states" by H. Bethe. In one-dimensional antiferromagnet, there are thermdynamically large number of flipped spins, hence the string states become an essentially many-body problem. An n-string states means that n magnons form a bound state, and they further collide with other magnons in the scattering states. Furthermore, the interaction among magnons in antiferromaggnet is repulsive, hence, string states do not appear at the ground state but show up as excited states, which can be detected through spin spectroscopy measurements.

Based on the algebraic Bethe ansatz formalism, we study spin dynamics in the antiferromagnetic spin-1/2 XXZ chain with the Ising anisotropy via the form-factor formulae [Ref. 1] . The dynamic spin structure factors (DSF) are calculated and contributions from various excitations at different energy scales are identified under the guidance of sum rules. In particular, string states - complex magnon bound states merged in the sea of scattering states of unbound magons are of particular interest. The S+-(q,\omega) spectra separate into low, intermediate and high energy branches. The low energy branches are dominated by fractional excitations, reflecting antiferromagnetic quantum fluctuations. In contrast, the two-string and three-string states govern the quantum spin dynamics at intermediate and high energies close to the quantum criticality, which are multi-particle inter-band excitations based on the commensurate Neel ordered background.

Experiment detection of the (many-body) string states

Experimental realization and identification of string states in condensed-matter systems remains a challenge up to date. We have collaborated with A. Loidl's group providing theory support to their ESR measurement on the dynamic spin structure measurement on the 1D XXZ chain SrCo2V2O8 [Ref 2.] . The bound states (strings) and fractional magnetic excitations (psinons and antipsinons) are observed in the field-induced critical regime, which are precisely described by the Bethe ansatz.

For a non-technical report, please see UC San Diego Physicists Apply Pencil, Paper and Sociology to Breakthrough Research .


References and talks

  • 1. Wang Yang, Jianda Wu, Shenglong Xu, Zhe Wang Congjun Wu, "Quantum spin dynamics of the axial antiferromagnetic spin-1/2 XXZ chain in a longitudinal magnetic field",
    arXiv:1702.01854    .

  • 2. Zhe Wang, Jianda Wu, Wang Yang, Anup Kumar Bera, Dmytro Kamenskyi, A.T.M. Nazmul Islam, Shenglong Xu, Joseph Matthew Law, Bella Lake, Congjun Wu , Alois Loidl, "Experimental Observation of Bethe Strings", Nature 554, 219 (2018).

  • Talk: Quantum Spin Dynmaics from Bethe Strings .


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    Last modified: Oct 16, 2018.