The spin nematic phase, characterized by long-range order of spin quadrupole moments in the absence of dipolar magnetism, presents a significant challenge for conventional experimental detection. We propose a novel method to detect this elusive order in quantum magnets with an illustration in the spin-1 triangular lattice Mott insulator. By integrating out the phonon degrees of freedom, we obtain a phase diagram with substantially enlarged regions for the spin-nematic and spin-nematic-supersolid phases. We then demonstrate that through the spin-lattice coupling, the emergence of spin nematic order imprints a distinctive signature onto the phonon spectra, providing a clear spectroscopic signature for the quadrupolar order accessible via Raman or inelastic X-ray scattering. Our formalism offers a direct and powerful method to uncover the hidden spin nematicity, opening a new pathway for diagnosing multipolar orders in quantum magnets.
The spin nematic phase, characterized by long-range order of spin quadrupole moments in the absence of dipolar magnetism, presents a significant challenge for conventional experimental detection. We propose a novel method to detect this elusive order in quantum magnets with an illustration in the spin-1 triangular lattice Mott insulator. By integrating out the phonon degrees of freedom, we obtain a phase diagram with substantially enlarged regions for the spin-nematic and spin-nematic-supersolid phases. We then demonstrate that through the spin-lattice coupling, the emergence of spin nematic order imprints a distinctive signature onto the phonon spectra, providing a clear spectroscopic signature for the quadrupolar order accessible via Raman or inelastic X-ray scattering. Our formalism offers a direct and powerful method to uncover the hidden spin nematicity, opening a new pathway for diagnosing multipolar orders in quantum magnets.
In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.
Nematic order is an exotic property observed in several strongly correlated systems, such as iron-based superconductors. Using large-scale density matrix renormalization group (DMRG) techniques, we study at zero temperature the nematic spin liquid that competes with spin dipolar and quadrupolar orders. We use these nematic orders to characterize different quantum phases and quantum phase transitions. More specifically, we study a spin-1 bilinear-biquadratic Heisenberg model on the square lattice with couplings beyond nearest neighbors. We focus on parameter regions around the highly symmetric SU(3) point where the bilinear and biquadratic interactions are equal. With growing further-neighbor biquadratic interactions, we identify different spin dipolar and quadrupolar orders. We find that the DMRG results for cylindrical geometries correctly detect nematicity in different quantum states and accurately characterize the quantum phase transitions among them. Therefore, spin-driven nematicity, here defined as the spontaneous breaking of the lattice invariance under a ${90}^{\ensuremath{\circ}}$ rotation, is an order parameter which can be studied directly in DMRG calculations in two dimensions in different quantum states.
Motivated by the lack of an obvious spectroscopic probe to investigate nonconventional order such as quadrupolar orders in spin S>21 systems, we present a theoretical approach to inelastic light scattering for spin-1 quantum magnets in the context of a two-band Hubbard model. In contrast to the S=21 case, where the only type of local excited state is a doubly occupied state of energy U, several local excited states with occupation up to four electrons are present. As a consequence, we show that two distinct resonating scattering regimes can be accessed depending on the incident photon energy. For $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{in}}\ensuremath{\lesssim}U$, the standard Loudon-Fleury operator remains the leading term of the expansion as in the spin-21 case. For $\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{in}}\ensuremath{\lesssim}4U$, a second resonant regime is found with a leading term that takes the form of a biquadratic coupling $\ensuremath{\sim}{({\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{j})}^{2}$. Consequences for the Raman spectra of S=1 magnets with magnetic or quadrupolar order are discussed. Raman scattering appears to be a powerful probe of quadrupolar order.
Motivated by advances in pump-probe experiments and light-driven phenomena, we theoretically study the impact of pumped and driven phonons in Mott insulators which host multipole moments, thus going beyond conventional dipolar magnetism. As a case study, we examine pseudospin-1/2 Mott insulators hosting quadrupolar and octupolar moments, and investigate the effect of resonantly exciting E_{g} phonon modes which couple linearly to the quadrupoles. We show that this leads to multipolar precession, with the backaction resulting in pseudochiral phonon dynamics in the octupolar ordered phase. We further study the impact of a short-time two-phonon drive, showing that it can induce the buildup of octupolar order or even switch its sign on picosecond timescales. Our results are obtained using a Monte Carlo code incorporating phonons, molecular dynamics simulations to numerically integrate the coupled spin-phonon equations of motion, and analytical Floquet theory. Our work shows how driven phonons can probe and control hidden orders in solids.
The dynamics of magnetic moments coupled to phonons is of great interest for understanding spin transport in solids as well as for our ability to control magnetism via tailored phonon modes. For spin S>1/2, spin-orbit coupling permits an unusual linear coupling of phonons to quadrupolar moments, so that phonons act as a dynamical transverse field for the spins. Here, we develop a generalized SU(N) spin-phonon Monte Carlo and molecular dynamics technique to simulate the equilibrium and nonequilibrium properties of such spin-orbital-phonon coupled Mott insulators, and apply it to a spin-1 model with competing XY antiferromagnet (AFM) and quadrupolar paramagnet (QPM) phases which is relevant to the Mott insulator Ba2FeSi2O7. We uncover a rich variety of dynamical phenomena in this system induced by linear or chiral phonon drives, including the generation of a uniform magnetization in the QPM and AFM, strengthening of Néel order and gapping of the AFM Nambu-Goldstone mode by Floquet-Ising anisotropy, a non-equilibrium QPM to AFM transition, and creation of Floquet copies of transverse and longitudinal spin waves. Our work is relevant for driven spin-1 magnets, such as Ba2FeSi2O7, and we highlight broader implications for nonequilibrium multipolar magnetism.
Spinon-Induced Phonon Dynamics in Chiral and π-Flux Quantum Spin Liquids
Quantum spin liquids (QSLs) are magnetic phases that evade long-range order down to the lowest temperatures due to strong quantum fluctuations. Their lack of conventional order parameters, however, makes experimental identification challenging. In this work, we investigate how distinct QSL phases affect phonon dynamics through spinon-phonon coupling. By computing the phonon self-energy, we show that the phonon spectrum remains unrenormalized by spinon interactions, while sound attenuation and phonon thermal conductivity exhibit distinct signatures of the underlying QSL phase. These response functions therefore provide experimentally accessible fingerprints for distinguishing different QSL backgrounds. Remarkably, we find that a chiral QSL coupled to phonons does not generate a phonon thermal Hall effect despite explicitly breaking time-reversal symmetry. Our results establish phonon transport as a potential probe for identifying and characterizing quantum spin liquids.