The spin nematic phase, which is a kind of multipole phases, has attracted a lot of interest in the field of the strongly correlated electron systems, as well as the quantum spin liquid phase. Using the numerical exact diagonalization, the density matrix renormalization group (DMRG) calculation, and the finite-size scaling analysis, it is found that some spin nematic and spin liquid phases appear in the anisotropic and/or frustrated quantum spin systems. In our previous work, quasi-one-dimensional quantum spin systems with the easy-axis anisotropy in magnetic field are theoretically investigated using the numerical exact diagonalization, the density matrix renormalization group (DMRG) and the finite-size scaling analysis[1]. It was found that a field-induced nematic phase appears at some critical field in the anisotropic spin ladder and the mixed spin chain. The nematic phase is characterized by the power-law decay in the correlation function of the second-order spin moment. In addition at some higher critical field a quantum phase transition can occur to the conventional field-induced Tomonaga-Luttinger liquid. Several typical magnetization curves calculated by DMRG are presented. We will also propose an experiment to observe these field-induced transitions by NMR measurements. The field-induced incommensurate order observed in azurite, which is modeled by the distorted diamond chain, by the recent NMR measurement will be also discussed. Recently the field-induced nematic phase was observed on the frustrated spin ladder system[2,3]. So we study on a frustrated spin ladder system[4], using the numerical diagonalization and DMRG. As a result, it is found that several exotic quantum phases, including the spin-nematic liquid phase. We also report some exact eigen states of the present model. [1] T. Sakai, T. Tonegawa and K. Okamoto, Physica Status Solidi B 247 (2010) 583.[2] N. Buttgen et al., Phys. Rev B 90, (2014) 134401.[3] K. Nawa et al., J. Phys. Soc. Jpn., 82 (2013) 094709.[4] T. Hikihara, T. Tonegawa, K. Okamoto and T. Sakai, J. Phys. Soc. Jpn. 86 (2017) 054709.
We study a spin-1 Heisenberg model with exchange interaction
J, uniaxial single-ion exchange anisotropy
D, and Zeeman coupling to a magnetic field
B parallel to the symmetry axis. We compute the
(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
XY antiferromagnetic and ferronematic phases that spontaneously break the
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.
When quantum effects are small, Heisenberg antiferromagnets have a Néel ordered ground state, but strong zero-point fluctuations can lead to new ‘‘exotic’’ spin-liquid ground states without long-range Néel order. These effects are strongest in low dimensions and frustrated systems, and always occur in one dimension. The nature of the new ground state can depend on whether the microscopic spins have integer or half-integer S. As an example of such systems the rich phase diagram of the one-dimensional S=1 Heisenberg antiferromagnet with additional biquadratic exchange and uniaxial on-site anisotropy will be discussed in detail.
We discuss spin-
21 one-dimensional (1D) and quasi-1D magnets with competing ferromagnetic nearest-neighbor
J1 and antiferromagnetic next-nearest-neighbor
J exchange interactions in a strong magnetic field
H. It is well known that, due to attraction between magnons, quantum phase transitions (QPTs) take place at
H=Hs from the fully polarized phase to the nematic phase if
J>∣J1∣/4. Such a transition at
J>0.368∣J1∣ is characterized by a softening of the two-magnon bound-state spectrum. Using a bond-operator formalism we propose a bosonic representation of the spin Hamiltonian containing, aside from bosons describing one-magnon spin-1 excitations, a boson describing spin-2 excitations whose spectrum coincides at $H\ensuremath{\ge}{H}_{s}$ with the two-magnon bound-state spectrum obtained before. The presence of the bosonic mode in the theory that softens at
H=Hs makes the QPT consideration substantially standard. In the 1D case at
H<Hs, we find an expression for the magnetization which well describes existing numerical data. Expressions for spin correlators are obtained which coincide with those derived before, either in the limiting case of $J\ensuremath{\gg}|{J}_{1}|$ or using a phenomenological theory. In quasi-1D magnets, we find that the boundary in the
H-
T plane between the fully polarized and the nematic phases is given by ${H}_{s}(0)\ensuremath{-}{H}_{s}(T)\ensuremath{\propto}{T}^{3/2}$. Simple expressions are obtained in the nematic phase for static spin correlators, spectra of magnons and the soft mode, magnetization, and the nematic order parameter. All static two-spin correlation functions are short ranged with the correlation length proportional to
1/ln(1+∣J1∣/J). Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel.
The magnetization process of the S = 1/2 two-dimensional magnet where ferromagnetic dimers connected by the antiferromagnetic bond on the Shastry-Sutherland lattice is investigated using the numerical diagonalization of a finite-size cluster. We introduce the easy-axis anisotropy at the intradimer ferromagnetic interaction and consider the external magnetic field along the easy axis. It is found that the two-magnon bound state appears at higher magnetization regions for sufficiently large anisotropy. Base on the previous studies of several one-dimensional systems and the present calculation of the spin correlation function, the spin nematic order perpendicular to the external field is expected to occur in this two-magnon bound phase.
A spin-1/2 magnetic system with the ferromagnetic and antiferromagnetic interactions on the Shastry-Sutherland lattice is investigated using the numerical diagonalization of finite-size clusters. The easy-axis anisotropy is introduced at the ferromagnetic bond of the present system and the magnetization process in the external magnetic field parallel to the axis is studied. As a result, the field-induced two-magnon bound phase is found at higher magnetization region than half the saturation. Base on the analogy to the previous study on the spin ladder system, the spin nematic order perpendicular to the external field would be expected to appear in this two-magnon bound phase.