Spontaneous symmetry breaking is one of the central concepts in physics. Spontaneous breaking of continuous symmetry is especially of great interest because it is accompanied by the Nambu-Goldstone (NG) boson and closely related to the dimensionality of the system. Generally the Mermin-Wagner theorem prevents the one-dimensional (1D) and 2D systems from breaking the continuous symmetry. For instance, in 1D ferromagnet, the spontaneous magnetization exists only at zero temperature, where a non-relativistic NG boson is generated. On the other hand, in 1D quantum antiferromagnet, the true long-range antiferromagnetic order is absent even at zero temperature. Such a disordered ground state is well described by the Tomonaga-Luttinger liquid (TLL). Here one may deem that the strong quantum fluctuation dynamically transforms the NG boson into the TLL. Thus the TLL and the NG boson of the antiferromagnetic order shares a feature: both of them possess the relativistic dispersion. This is in contrast to the non-relativistic dispersion of the NG boson of the ferromagnetic order. In this sense, it would be counterintuitive to find a TLL structure compatible with the spontaneous ferromagnetic order.
In my presentation, I will show that quasi-1D frustrated quantum antiferromagnets indeed allow the TLL compatible with the spontaneous ferromagnetic order, that is, the spontaneously magnetized TLL. Here the geometrical frustration plays a central role. The geometrical frustration induces the ferromagnetic instability of the TLL keeping the antiferromagnetic fluctuation intact. Our theory explains recently obtained numerical results on the "union-jack" antiferromagnet [T. Shimokawa and H. Nakano, J. Korean Phys. Soc. 63, 591 (2013)].
We study nonlinear effects on the excitation spectra, and frequency dependent spin and thermal conductivities of square lattice Heisenberg antiferromagnets (SLHAFs) by nonlinear spin-wave theory . SLHAFs are known to have the collinear Neel structure at zero-magnetic field, and noncollinear canted states in finite fields. It is pointed out that a rotonlike minimum appears on the acoustic mode in high fields as a result of strong three-magnon interactions that appear only in noncollinear arrangement of spins . The roton softens rapidly with simultaneous sharpening as the field increases . This roton feature should affect thermal and transport properties. We calculate the frequency dependent spin and thermal conductivities by linear response theory , and confirm that f-sum rules are satisfied. We also study off-diagonal parts of the coupled transport. We compare the spin conductivity calculated within linear spin-wave theory, and the one calculated including \(1/S\) corrections. We find that qualitative difference in AC spin conductivity in high fields: a two-magnon sideband appears due to the strong nonlinear interactions. We also study the integrated intensity \(I_0\) of the thermal conductivity. The theoretical formula of \(I_0\) is always zero for the collinear classical spins . However, \(I_0\) becomes finite in zero-field by the presence of the instantaneous noncollinearity due to the quantum fluctuations.
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The recent determination of the phase diagram of the spin 1/2 triangular XXZ model in a magnetic field has shown the existence of the non-classical \(\pi\)-coplanar state in the easy-plane, high-field region. The first-order boundary between this \(\pi\)-coplanar and the 0-coplanar states (also called "\(\psi\)" and "V" states) can in principle be calculated by solving a three-magnon scattering problem field-theoretically. We address this problem in the Faddeev equation approach and try to compare with the existing numerical results.
Recent theoretical studies suggest that the quenched randomness in the exchange interaction might produce the randomness-induced quantum spin-liquid state, the valence bond-glass (VBG) or the random-singlet state. Our exact diagonalization studies have revealed that such randomness-induced quantum spin-liquid state is realized not only in the S=1/2 antiferromagnetic Heisenberg model on the triangular lattice, but also in that on the kagome lattice. We calculate the dynamical structure factor of both the triangular and kagome lattices to investigate the dynamical properties of their VBG state. We shall also discuss the relationship between the our calculation results and the the inelastic-neutron-scattering measurements on the kagome antiferromagnet Herbertsmithite.
Recent theoretical studies reveal the presence of the multiple-Q order in the classical Heisenberg model on the triangular lattice under magnetic fields. Especially, the triple-Q state corresponds to the so-called "skyrmion lattice" state which is stabilized by the frustration effect of the symmetric exchange interactions. Because of the symmetric nature of the interaction, both skyrmions and anti-skyrmions are allowed, in contrast to the skyrmion-latice system stabilized via the anti-symmetric Dzyaloshinskii-Moriya interaction. In order to study whether such multiple-Q orders and the skyrmion-lattice state are ever realized on other lattices, we treat here the J1-J2 classical Heisenberg model on the honeycomb lattice, having the three-fold rotational symmetry as in the case of the triangular lattice. We reveal the presence of several multiple-Q orders in the honeycomb model, while its phase structure is considerably different from that in the triangular model. Comparison is then made with the multiple-Q order and the skyrmion-lattice state of the corresponding triangular-lattice model.
With the help of some physical considerations, we numerically determine the ground-state phase diagram of an \(S=1/2\) ladder with uniform isotropic leg and alternating anisotropic rung interactions. We denote by \(J_l\) the interaction constant of the leg interaction, and by \(J_r\) and \(J_r'\) those of the rung interactions which are alternating. When the sign of \(J_r\) is different from that of \(J_r'\), the present ladder system has a frustration. In this study, we treat the case where \(J_l=0.2\) (antiferromagnetic), \(J_r=1\) (antiferromagnetic) and \(J_r'<0\) (ferromagnetic). The obtained phase diagrams show that when the anisotropy of the rung interactions is of the \(XY\)-type, the Neel phase appears, and that when it is of the Ising-type, the Haldane phase appears. These are contrary to the usual situation, and are called 'the inversion phenomena concerning the interaction anisotropy'.
We study dynamical properties of the honeycomb-lattice iridate Na\(_2\)IrO\(_3\). An interesting point of this material is that the interactions between magnetic moments of Ir ions contain the Kitaev-type anisotropy in addition to the Heisenberg-type interaction . To explain the origin of magnetic orderings observed [2,3], effective models have been discussed [2,4,5] in the viewpoint of the effects of farther neighbor interactions and anisotropy. We carry out numerical exact diagonalization to evaluate dynamical structure factors for these effective models. Comparing the numerical results with the inelastic-neutron-scatterings experiments , we discuss the characteristics of each effective model.
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