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Physical review. B./Physical review. B

Spin nematic ordering in the spin-1 chain system

Andrei A. Zvyagin, Victor V. Slavin

Published Aug 24, 2022• 11 citations
Publisher

Abstract

We predict the instability of the quantum spin-1 chain material with respect to the spin nematic ordering. For the spin subsystem the spin nematic order parameter is related to the onset of single-ion spin anisotropy. The ordering is caused by the coupling to the elastic subsystem of the crystal or, for spin-1 ultracold bosons in a one-dimensional optical lattice, by the interaction with a Bose-Einstein condensate. Our conclusions are based on the exact integrability of the spin model and on numerical simulations for the nonintegrable cases. Our exact results also describe the behavior of interacting gluons within the lattice toy Yang-Mills-like model, in which spontaneous and field-induced symmetry breaking can be realized.

DOI
10.1103/physrevb.106.054429

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We predict the instability of the quantum spin-1 chain material with respect to the spin nematic ordering. For the spin subsystem the spin nematic order parameter is related to the onset of single-ion spin anisotropy. The ordering is caused by the coupling to the elastic subsystem of the crystal or, for spin-1 ultracold bosons in a one-dimensional optical lattice, by the interaction with a Bose-Einstein condensate. Our conclusions are based on the exact integrability of the spin model and on numerical simulations for the nonintegrable cases. Our exact results also describe the behavior of interacting gluons within the lattice toy Yang-Mills-like model, in which spontaneous and field-induced symmetry breaking can be realized.
Spin-1 chain material is considered. Recently, it was predicted that the spin nematic ordered phase can be realized due to the spin-elastic coupling. In this study we show that the appearance of the spin nematic ordering and phase transitions to such ordered states can be studied using magneto-acoustic experiments. One can observe such phases and phase transitions considering relative changes of the velocity of sound (related to the changes of the elastic modulus of the crystal) as a function of temperature and the external magnetic field. It is shown that those relative changes are proportional to the spin quadrupole susceptibility of the system. The results are obtained using the exact Bethe ansatz solution and Quantum Monte Carlo simulations for several typical values of the biquadratic spin-spin exchange interaction and for various values of the spin-elastic coupling and elastic modules.
We consider the spin-1/2 chain material. It was predicted earlier that the intersite spin nematic order can be realized due to the spin-elastic coupling in such a system. Here we show that intersite spin nematic ordered states can be studied using magnetoelastic and magnetoelectric experiments. Intersite spin nematic phases and phase transitions in spin chain materials can be observed in relative changes of the velocity of sound (related to the changes of the elastic modulus of the crystal), the magnetostriction, and, for noncenter-symmetric systems, the electric permittivity as functions of the temperature and the external magnetic field, since those relative changes are proportional to the spin quadrupole (spin nematic) susceptibility of the system.
We study magnetically stabilized nematic order for spin-one bosons in optical lattices. We show that the Zeeman field-driven quantum phase transitions between non-nematic Mott states and quantum spin nematic Mott states in the weak hopping limit are in the universality class of the ferromagnetic XXZXXZXXZ (S=1∕2)(S=1∕2)(S=1∕2) spin model. We further discuss these transitions as condensation of interacting magnons. The development of O(2) nematic order when external fields are applied corresponds to condensation of magnons, which breaks a U(1) symmetry. Microscopically, this results from a coherent superposition of two non-nematic states at each individual site. Nematic order and spin-wave excitations around critical points are studied and critical behaviors are obtained in a dilute gas approximation. We also find that spin-singlet states are unstable with respect to quadratic Zeeman effects and Ising nematic order appears in the presence of any finite quadratic Zeeman coupling. All discussions are carried out for states in three-dimensional bipartite lattices.
We study a spin-1 Heisenberg model with exchange interaction JJJ, uniaxial single-ion exchange anisotropy DDD, and Zeeman coupling to a magnetic field BBB parallel to the symmetry axis. We compute the (D/J,B/J)(D/J,B/J)(D/J,B/J) quantum phase diagram for square and simple cubic lattices by combining analytical and quantum Monte Carlo approaches, and find a transition between XYXYXY antiferromagnetic and ferronematic phases that spontaneously break the U(1)U(1)U(1) symmetry of the model. In the language of bosonic gases, this is a transition between a Bose-Einstein condensate (BEC) of single bosons and a BEC of pairs. Our work opens up new avenues for measuring this transition in real magnets.
We investigate the Zeeman-field-driven quantum phase transitions between singlet spin liquids and algebraically ordered O(2)O(2)O(2) nematic spin liquids of spin-one bosons in one-dimensional optical lattices. We find that the critical behavior is characterized by condensation of hardcore bosons instead of ideal magnons in high-dimensional lattices. Critical exponents are strongly renormalized by hardcore interactions and critical states are equivalent to the free Fermion model up to the Friedel oscillations. We also find that the algebraically ordered nematic spin liquids close to critical points are fully characterized by the Luttinger-liquid dynamics with Luttinger-liquid parameters magnetically tunable. The Bethe ansatz solution has been applied to determine the critical magnetization and nematic correlations.