Magnetization plateaus as insulator-superfluid transitions in quantum spin systems

We study the magnetization process in two-dimensional S=1/2 spin systems, to discuss the appearance of a plateau structure. The following three cases are considered: (1) the Heisenberg antiferromagnet and multiple-spin exchange model on the triangular lattice, (2) Shastry-Sutherland type lattice, [which is a possible model for SrCu2(BO3)2,] (3) 1/5-depleted lattice (for CaV4O9). We find in these systems that magnetization plateaus can appear owing to a transition from superfluid to a Mott insulator of magnetic excitations. The plateau states have CDW order of the excitations. The magnetizations of the plateaus depend on components of the magnetic excitations, range of the repulsive interaction, and the geometry of the lattice.Comment: 5 pages, RevTeX, 7 figures, note and reference adde

Dilute-Bose-Gas Approach to ground state phases of 3D quantum helimagnets under high magnetic field

We study high-field phase diagram and low-energy excitations of three-dimensional quantum helimagnets. Slightly below the saturation field, the emergence of magnetic order may be mathematically viewed as Bose-Einstein condensation (BEC) of magnons. The method of dilute Bose gas enables an unbiased quantitative analysis of quantum effects in three-dimensional helimagnets and thereby three phases are found: cone, coplanar fan and an attraction-dominant one. To investigate the last phase, we extend the usual BEC approach so that we can handle 2-magnon bound states. In the case of 2-magnon BEC, the transverse magnetization vanishes and long-range order occurs in the quadrupolar channel (spin-nematic phase). As an application, we map out the phase diagram of a 3D helimagnet which consists of frustrated J1-J2 chains coupled by an interchain interaction J3.Comment: 4pages, 3figures, International Conference on Magnetism (ICM) 2009 (Karlsruhe, Germany, July 26-31, 2009)

Quantum fluctuations in quantum lattice-systems with continuous symmetry

We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems at $T=0$. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show quantum fluctuations. For the one-dimensional systems, it is shown that the ground state is invariant under the continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than $|r|^{-d+1}$ whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice-systems having not-too-long-range interactions.Comment: 14 pages. To appear in J.Stat.Phy

Quantum melting of incommensurate domain walls in two dimensions

Quantum fluctuations of periodic domain-wall arrays in two-dimensional incommensurate states at zero temperature are investigated using the elastic theory in the vicinity of the commensurate-incommensurate transition point. Both stripe and honeycomb structures of domain walls with short-range interactions are considered. It is revealed that the stripes melt and become a stripe liquid in a large-wall-spacing (low-density) region due to dislocations created by quantum fluctuations. This quantum melting transition is of second order and characterized by the three-dimensional XY universality class. Zero-point energies of the stripe and honeycomb structures are calculated. As a consequence of these results, phase diagrams of the domain-wall solid and liquid phases in adsorbed atoms on graphite are discussed for various domain-wall masses. Quantum melting of stripes in the presence of long-range interactions that fall off as power laws is also studied. These results are applied to incommensurate domain walls in two-dimensional adsorbed atoms on substrates and in doped antiferromagnets, e.g. cuprates and nickelates.Comment: 11 pages, 5 figure

Field-induced phase transitions in a Kondo insulator

We study the magnetic-field effect on a Kondo insulator by exploiting the periodic Anderson model with the Zeeman term. The analysis using dynamical mean field theory combined with quantum Monte Carlo simulations determines the detailed phase diagram at finite temperatures. At low temperatures, the magnetic field drives the Kondo insulator to a transverse antiferromagnetic phase, which further enters a polarized metallic phase at higher fields. The antiferromagnetic transition temperature $T_c$ takes a maximum when the Zeeman energy is nearly equal to the quasi-particle gap. In the paramagnetic phase above $T_c$, we find that the electron mass gets largest around the field where the quasi-particle gap is closed. It is also shown that the induced moment of conduction electrons changes its direction from antiparallel to parallel to the field.Comment: 7 pages, 6 figure

Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density

We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0< n < 1.75) electron density when the interactions are sufficiently strong. Quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the inter-orbital interaction U'-J is attractive. At quarter-filling (n=1), the insulating ferromagnetic state appears accompanying orbital quasi-long-range order. For low densities (n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative to stabilize the ferromagnetic order and this long-range order is robust against variation of the band-dispersion. A partially polarized state appears in the density region 1.68<n<1.75 and phase separation occurs for n just below the half-filling (n=2).Comment: 16 pages, 16 figures, final version, references adde

Magnetic Phase Diagram of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange

We study the spin-1/2 two-leg Heisenberg ladder with four-spin ring exchanges under a magnetic field. We introduce an exact duality transformation which is an extension of the spin-chirality duality developed previously and yields a new self-dual surface in the parameter space. We then determine the magnetic phase diagram using the numerical approaches of the density-matrix renormalization-group and exact diagonalization methods. We demonstrate the appearance of a magnetization plateau and the Tomonaga-Luttinger liquid with dominant vector-chirality quasi-long-range order for a wide parameter regime of strong ring exchange. A "nematic" phase, in which magnons form bound pairs and the magnon-pairing correlation functions dominate, is also identified.Comment: 18pages, 7 figure

Chern-Simons Theory for Magnetization Plateaus of Frustrated J1J_1-J2J_2 Heisenberg model

The magnetization curve of the two-dimensional spin-1/2 $J_1$-$J_2$ Heisenberg model is investigated by using the Chern-Simons theory under a uniform mean-field approximation. We find that the magnetization curve is monotonically increasing for $J_2/J_1 < 0.267949$, where the system under zero external field is in the antiferromagnetic N\'eel phase. For larger ratios of $J_2/J_1$, various plateaus will appear in the magnetization curve. In particular, in the disordered phase, our result supports the existence of the $M/M_{\rm sat}=1/2$ plateau and predicts a new plateau at $M/M_{\rm sat}=1/3$. By identifying the onset ratio $J_2/J_1$ for the appearance of the 1/2-plateau with the boundary between the N\'eel and the spin-disordered phases in zero field, we can determine this phase boundary accurately by this mean-field calculation. Verification of these interesting results would indicate a strong connection between the frustrated antiferromagnetic system and the quantum Hall system.Comment: RevTeX 4, 4 pages, 3 EPS figure

Fractional S^z excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag XXZ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying $S^z=\pm 1/3$ and its bound state of $S^z=\pm 2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain-walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.Comment: 13 pages, 15 figure

Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice

Combined with Laughlin's argument on the quantized Hall conductivity, Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number, on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength and particle statistics (bose/fermi), a finite excitation gap is possible only when the particle number per unit cell of the groundstate is an integer.Comment: 4 pages in REVTE