Chitoshi Yasuda

Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice

The S = ½ and S= I two-dimensional quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice are investigated by the quantum Monte Carlo method. By finite-size-scaling analyses on the correlation lengths, the ground-state phase diagram parametrized by strengths of the dimerization and of the spatial anisotropy is determined much more accurately than the previous works. It is confirmed that the quantum critical phenomena on the phase boundaries belong to the same universality class as that of the classical three-dimensional Heisenberg model. Furthermore, for S= 1, we show that all the spin-gapped phases, such as the Haldane and dimer phases, are adiabatically connected in the extended-parameter space, though they are classified into different classes in terms of the string order parameter in the one-dimensional, i.e., the zero-interchain-coupling, case.

Bond-dilution effects on two-dimensional spin-gapped Heisenberg antiferromagnets

Abstract Bond-dilution effects on spin-1/2 spin-gapped Heisenberg antiferromagnets of coupled alternating chains on a square lattice are investigated by means of the quantum Monte Carlo method. It is found that, in contrast with the site-diluted system having an infinitesimal critical concentration, the bond-diluted system has a finite critical concentration of diluted bonds, xc, above which the system is in an antiferromagnetic (AF) long-range ordered phase. In the disordered phase below xc, plausibly in the concentration region significantly less than xc, the system has a spin-gap due to singlet pairs of induced magnetic moments reformed by the AF interactions through the two-dimensional shortest paths.

Site-dilution-induced antiferromagnetic long-range order in a two-dimensional spin-gapped Heisenberg antiferromagnet

Effects of the site dilution on spin-gapped Heisenberg antiferromagnets with

Plaquette-singlet solid state and topological hidden order in a spin-1 antiferromagnetic Heisenberg ladder

S=1/2

Dilution Effects on Two-Dimensional Heisenberg Antiferromagnets with Non-Magnetic Spin-Gapped Ground State

and S=1 on a square lattice are investigated by means of the quantum Monte Carlo method. It is found that effective magnetic moments induced around the diluted sites exhibit the antiferromagnetic long-range order in the medium of spin-singlet pairs. Their microscopic structure is examined in detail and important roles of the higher dimensionality than one on the phenomenon are discussed.

Bond-Dilution-Induced Quantum Phase Transitions in Heisenberg Antiferromagnets

Ground-state properties of the spin-1 two-leg antiferromagnetic ladder are investigated precisely by means of the quantum Monte Carlo method. It is found that the correlation length along the chains and the spin gap both remain finite regardless of the strength of interchain coupling, i.e., the Haldane state and the spin-1 dimer state are connected smoothly without any quantum phase transitions between them. We propose a plaquette-singlet solid state, which qualitatively describes the ground state of the spin-1 ladder quite well, and also a corresponding topological hidden order parameter. It is shown numerically that the new hidden order parameter remains finite up to the dimer limit, though the conventional string order defined on each chain vanishes immediately when infinitesimal interchain coupling is introduced.

Spin Dependence of the Critical Concentration for the Neel State of 2D Impure Heisenberg Antiferromagnets.

Dilution effects on spin-½ quantum Heisenberg antiferromagnets with a non-magnetic spin-gapped ground state are studied by means of the quantum Monte Carlo simulation. In the site-diluted system, an antiferromagnetic long-range order (AF-LRO) is induced at an infinitesimal concentration of dilution due to an effective coupling J m n between induced magnetic moments. In the bond-diluted case, on the other hand, the AF-LRO is not induced up to a certain concentration of dilution due to singlet pairs reformed by an AF coupling J a f between the edge spins of the diluted bond through the two-dimensional shortest paths. The competition between J m n and J a f yields peculiar phenomena in the bond-diluted system.

Quantum Phase Transition in Antiferromagnetic Heisenberg Chains Coupled to Phonons

Bond-dilution effects on the ground state of the square-lattice antiferromagnetic Heisenberg model, consisting of coupled bond-alternating chains, are investigated by means of quantum Monte Carlo simulation. It is found that, when the ground state of the nondiluted system is a nonmagnetic state with a finite spin gap, a sufficiently weak bond dilution induces a disordered state with a mid-gap in the original spin gap, and under a strong bond dilution an antiferromagnetic long-range order emerges. While the site-dilution-induced long-range order is induced by an infinitesimal concentration of dilution, there exists a finite critical concentration in the case of bond dilution. We argue that this essential difference is due to the occurrence of two types of effective interactions between induced magnetic moments in the case of bond dilution, and that the antiferromagnetic long-range-ordered phase does not appear until the magnitudes of the two interactions become comparable.

Order-Disorder Transition of a Two-Dimensional Spin 1/2 Heisenberg Antiferromagnet with Nonmagnetic Impurities

The spin-wave theory and the coherent potential approximation are applied to a spin S Heisenberg antiferromagnet with nonmagnetic impurities on square lattice. The impurity effects are taken into account by substituting S (1- x ) for S and using the coherent potential approximation to the exchange interaction, where x is the impurity concentration. At T =0 for S =1/2 the critical impurity concentration x c of the Neel state is 0.303 and the percolation threshold x p is 0.500. The ground state in x c < x < x p is the disordered state with the spin gap. For S ≥1 the long range Neel order vanishes at x p =0.500. These results explain qualitatively the experimental results of La 2 Cu 1- x Mg x O 4 ( S =1/2) and K 2 Mn 1- x Mg x F 4 ( S =5/2). The difference of x c between these materials is caused by the decrease in the magnitude of the effective spin with impurity doping. The spin gap is expected to be observed for La 2 Cu 1- x Mg x O 4 in x c < x < x p at low temperatures.

Theory of diluted magnetic semiconductors: A minimal model

We develop an analytical approach based on a unitary transformation to investigate S =1/2 antiferromagnetic Heisenberg chains coupled to phonons, and find a new quantum phase transition at zero temperature. Although the usual phase transition occurs depending on the strengths of the spin–spin and spin–phonon interactions, the phase transition in the present work is induced by a change in the geometrical structure of the spin–phonon interaction. The magnetic properties of the phase transition can be understood in relation to a phase transition that has already been found in the frustrated J 1 – J 2 model.