フラストレートしたスピン梯子系の磁気相図

Frustrated spin ladders show magnetization plateaux depending on the rung-exchange interaction and frustration defined by the ratio of first and second neighbor exchange interactions in each chain. This paper reports on its magnetic phase diagram. Using the variational matrix-product state method, we accurately determine phase boundaries. Several kinds of magnetization plateaux are induced by the frustration and the strong correlation among quasiparticles on a lattice. The appropriate description of quasiparticles and their relevant interactions are changed by a magnetic field. We find that the frustration differentiates the triplet quasiparticle from the singlet one in kinetic energy.Frustrated spin ladders show magnetization plateaux depending on the rung-exchange interaction and frustration defined by the ratio of first and second neighbor exchange interactions in each chain. This paper reports on its magnetic phase diagram. Using the variational matrix-product state method, we accurately determine phase boundaries. Several kinds of magnetization plateaux are induced by the frustration and the strong correlation among quasiparticles on a lattice. The appropriate description of quasiparticles and their relevant interactions are changed by a magnetic field. We find that the frustration differentiates the triplet quasiparticle from the singlet one in kinetic energy.

arXiv:1707.04946Physical review. B./Physical review. BApr 30, 201810 citations

Magnetization plateaus by reconstructed quasispinons in a frustrated two-leg spin ladder under a magnetic field

貴則杉本, 森道康, 貴巳遠山 +1 more

The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu2PO6.The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu2PO6.

Physical Review BSep 1, 20150 citations

フラストレートした量子スピン梯子系における再構築された擬スピンによる磁化プラトー

Takanori Sugimoto, Michiyasu Mori, Takami Toyama +1 more

The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu $_{2}$ PO $_{6}$ .The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaux in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaux are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasi-spinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaux at 1/3 and 2/3 can be associated with the array of quasi-spinons such as soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful to understand magnetization curves in BiCu$_{2}$PO$_{6}$.

Sep 1, 20150 citations

Magnetization plateaux and jumps in frustrated four-leg spin tubes in magnetic fields

H. D. Rosales, Marcelo Arlego, F. A. Gómez Albarracín

We study the ground state phase diagram of a frustrated spin-1/2 four-leg tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: density matrix renormalization group (DMRG), a low-energy effective Hamiltonian (LEH) and a Hartree variational approach (HVA). We find that in the limit of weakly interacting plaquettes, singlet and triplet states play an important role in the formation of magnetization plateaux. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong- coupling expansion, by an XXZ spin-1/2 chain in a magnetic field. These results are consistent with the DMRG and HVA calculations.We study the ground state phase diagram of a frustrated spin-1/2 four-leg tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: density matrix renormalization group (DMRG), a low-energy effective Hamiltonian (LEH) and a Hartree variational approach (HVA). We find that in the limit of weakly interacting plaquettes, singlet and triplet states play an important role in the formation of magnetization plateaux. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong- coupling expansion, by an XXZ spin-1/2 chain in a magnetic field. These results are consistent with the DMRG and HVA calculations.

Journal of Physics Conference SeriesDec 8, 20141 citation

Effects of frustration on magnetic excitations in a two-leg spin-ladder system

Takanori Sugimoto, Michiyasu Mori, Takami Tohyama +1 more

We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearest-neighbor bonds in the leg direction, and on the nearest-neighbor bonds in the rung direction. A dynamical spin correlation function at zero temperature is calculated using the dynamical density-matrix renormalization-group method for possible magnetic phases, i.e., columnar-dimer and rung-singlet phases. The columnar-dimer phase is characterized by multispinon excitations with a spin gap, whereas the rung-singlet phase is dominated by the triplet excitation in the rung direction. One major difference found between these two phases appears in the spectral weight of magnetic excitations, in particular, the bonding and antibonding modes in the rung direction. Therefore, we can distinguish one phase from the other by the difference in the spectral weight. Furthermore, we examine the effect of frustration on both modes in the rung-singlet phase with a perturbation theory from the strong coupling limit. The antibonding mode is shown to be stable against frustration, and a wave number with minimum excitation energy is shifted from being commensurate to being incommensurate. In contrast, the bonding mode is merged into the continuum excitation of multiple triplet excitations by increasing frustration. By comparing our results with inelastic neutron scattering experiments for BiCu ${}_{2}$ PO ${}_{6}$ , the magnitude of the magnetic exchange interactions and the ground state will be determined.We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearest-neighbor bonds in the leg direction, and on the nearest-neighbor bonds in the rung direction. A dynamical spin correlation function at zero temperature is calculated using the dynamical density-matrix renormalization-group method for possible magnetic phases, i.e., columnar-dimer and rung-singlet phases. The columnar-dimer phase is characterized by multispinon excitations with a spin gap, whereas the rung-singlet phase is dominated by the triplet excitation in the rung direction. One major difference found between these two phases appears in the spectral weight of magnetic excitations, in particular, the bonding and antibonding modes in the rung direction. Therefore, we can distinguish one phase from the other by the difference in the spectral weight. Furthermore, we examine the effect of frustration on both modes in the rung-singlet phase with a perturbation theory from the strong coupling limit. The antibonding mode is shown to be stable against frustration, and a wave number with minimum excitation energy is shifted from being commensurate to being incommensurate. In contrast, the bonding mode is merged into the continuum excitation of multiple triplet excitations by increasing frustration. By comparing our results with inelastic neutron scattering experiments for BiCu${}_{2}$PO${}_{6}$, the magnitude of the magnetic exchange interactions and the ground state will be determined.

arXiv:1301.4740Physical Review BApr 24, 201311 citations

Magnetization Process of anS=1 Frustrated Spin Ladder

Kiyomi Okamoto, Kouichi Okunishi, Tôru Sakai

We investigate, at T =0, the magnetization process of the S =1 frustrated two-leg spin ladder having the leg interaction ( J ), the rung interaction ( J 0 ) and the diagonal interaction ( J d ), especially focusing on the appearance and the disappearance of the magnetization plateaux. We use the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data and the DMRG. When J d =0, the M s /2 plateau ( M s is the saturation magnetization) appears for J 0 / J > 1.463. Then there is no M s /2 plateau for the so-called isotropic case J = J 0 . In case of J d > 0, J d helps the M s /2 plateau. And also, the M s /4 and (3/4) M s plateaux appear when J d is sufficiently large. These two plateaux are associated with the spontaneous breaking of the translation symmetry along the leg direction. We show the plateau phase diagram on the J d versus J plane, and also the magnetic phase diagram on the H versus J d plane for fixed J .We investigate, at T =0, the magnetization process of the S =1 frustrated two-leg spin ladder having the leg interaction ( J ), the rung interaction ( J 0 ) and the diagonal interaction ( J d ), especially focusing on the appearance and the disappearance of the magnetization plateaux. We use the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data and the DMRG. When J d =0, the M s /2 plateau ( M s is the saturation magnetization) appears for J 0 / J > 1.463. Then there is no M s /2 plateau for the so-called isotropic case J = J 0 . In case of J d > 0, J d helps the M s /2 plateau. And also, the M s /4 and (3/4) M s plateaux appear when J d is sufficiently large. These two plateaux are associated with the spontaneous breaking of the translation symmetry along the leg direction. We show the plateau phase diagram on the J d versus J plane, and also the magnetic phase diagram on the H versus J d plane for fixed J .

Journal of the Physical Society of JapanJan 1, 20053 citations

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, the magnitude of the magnetic exchange interactions and the ground state will be determined.