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Register a new userSpin dynamics of the bilinear-biquadratic $S=1$ Heisenberg model on the triangular lattice: a quantum Monte Carlo study
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We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compared to the thermodynamic behavior observed at finite temperatures as well as to Schwinger-boson flavor-wave theory.
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Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg interactions, the spatially emph{completely} anisotropic triangular lattice (SCATL). Using Takahashis modified spin-wave theory, complemented by exact diagonalizations, we find indications that indeed different kinds of order are always separated by disordered phases. Our results further suggest that two gapped non-magnetic phases, identified as distinct in the SATL, are actually continuously connected via the additional anisotropy of the SCATL. Finally, measurements on several materials found magnetic long-range order where calculations on the SATL predict disordered behavior. Our results suggest a simple explanation through the additional anisotropy of the SCATL, which locates the corresponding parameter values in ordered phases. The studied model might therefore not only yield fundamental insight into quantum disordered phases, but should also be relevant for experiments on the quest for spin liquids.
Nematic order is an exotic property observed in several strongly correlated systems, such as the 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 on 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$^o$ rotation -- is an order parameter which can be studied directly in DMRG calculations in two dimensions in different quantum states.
We study the spin-$1/2$ Heisenberg model on the triangular lattice with the antiferromagnetic first ($J_1$) and second ($J_2$) nearest-neighbor interactions using density matrix renormalization group. By studying the spin correlation function, we find a $120^{circ}$ magnetic order phase for $J_2 lesssim 0.07 J_1$ and a stripe antiferromagnetic phase for $J_2 gtrsim 0.15 J_1$. Between these two phases, we identify a spin liquid region characterized by the exponential decaying spin and dimer correlations, as well as the large spin singlet and triplet excitation gaps on finite-size systems. We find two near degenerating ground states with distinct properties in two sectors, which indicates more than one spin liquid candidates in this region. While the sector with spinon is found to respect the time reversal symmetry, the even sector without a spinon breaks such a symmetry for finite-size systems. Furthermore, we detect the signature of the fractionalization by following the evolution of different ground states with inserting spin flux into the cylinder system. Moreover, by tuning the anisotropic bond coupling, we explore the nature of the spin liquid phase and find the optimal parameter region for the gapped $Z_2$ spin liquid.
The zero-temperature properties of the SO(5) bilinear-biquadratic Heisenberg spin chain are investigated by means of a low-energy approach and large scale numerical calculations. In sharp contrast to the spin-1 SO(3) Heisenberg chain, we show that the SO(5) Heisenberg spin chain is dimerized with a two-fold degenerate ground state. On top of this gapful phase, we find the emergence of a non-degenerate gapped phase with hidden (Z$_2$ $times$ Z$_2$)$^2$ symmetry and spin-3/2 edge states that can be understood from a SO(5) AKLT wave function. We derive a low-energy theory describing the quantum critical point which separates these two gapped phases. It is shown and confirmed numerically that this quantum critical point belongs to the SO(5)$_1$ universality class.
The nature of quantum spin liquids is studied for the spin-$1/2$ antiferromagnetic Heisenberg model on a square lattice containing exchange interactions between nearest-neighbor sites, $J_1$, and those between next-nearest-neighbor sites, $J_2$. We perform variational Monte Carlo simulations together with the quantum-number-projection technique and clarify the phase diagram in the ground state together with its excitation spectra. We obtain the nonmagnetic phase in the region $0.4< J_2/J_1le 0.6$ sandwiched by the staggered and stripe antiferromagnetic (AF) phases. Our direct calculations of the spin gap support the notion that the triplet excitation from the singlet ground state is gapless in the range of $0.4 < J_2/J_1 le 0.5$, while the gapped valence-bond-crystal (VBC) phase is stabilized for $0.5 < J_2/J_1 le 0.6$. The VBC order is likely to have the columnar symmetry with a spontaneous symmetry breaking of the $C_{4v}$ symmetry. The power-law behaviors of the spin-spin and dimer-dimer correlation functions in the gapless region are consistent with the emergence of the algebraic quantum-spin-liquid phase (critical phase). The exponent of the spin correlation $langle S(0)S(r)rangle propto 1/r^{z+eta}$ at a long distance $r$ appears to increase from $z+etasim 1$ at $J_2/J_1sim0.4$ toward the continuous transition to the VBC phase at $J_1/J_1sim0.5$. Our results, however, do not fully exclude the possibility of a direct quantum transition between the staggered AF and VBC phases with a wide critical region and deconfined criticality.
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