Recent studies on the frustrated quantum spin chains with easy-plane anisotropy are reviewed. We are particularly interested in novel “chiral ” phases characterized by the spontaneous breaking of the parity symmetry. The ground-state phase diagrams of the chains are discussed. The low-energy properties of one-dimensional quantum spin systems with frustrating interactions have been studied extensively for many years. This is mainly because they exhibit a variety of ground-state phases accompanied with various types of spontaneous symmetry breaking, e.g., the dimer phase with the translational symmetryRecent studies on the frustrated quantum spin chains with easy-plane anisotropy are reviewed. We are particularly interested in novel “chiral ” phases characterized by the spontaneous breaking of the parity symmetry. The ground-state phase diagrams of the chains are discussed. The low-energy properties of one-dimensional quantum spin systems with frustrating interactions have been studied extensively for many years. This is mainly because they exhibit a variety of ground-state phases accompanied with various types of spontaneous symmetry breaking, e.g., the dimer phase with the translational symmetry

Jan 1, 20023 citations

Quantum chiral phases in frustrated easy-plane spin chains

Alexei K. Kolezhuk

The phase diagram of antiferromagnetic spin- $S$ chain with $\mathrm{XY}$ -type anisotropy and frustrating next-nearest-neighbor interaction is studied in the limit of large integer S with the help of a field-theoretical approach. It is shown that the existence of gapless and gapped chiral phases found in recent numerical studies [M. Kaburagi et al., J. Phys. Soc. Jpn. 68, 3185 (1999); T. Hikihara et al., J. Phys. Soc. Jpn. 69, 259 (2000)] is not specific for $S=1,$ but is rather a generic large- $S$ feature. Estimates for the corresponding transition boundaries are obtained, and a sketch of the typical phase diagram is presented. It is also shown that frustration stabilizes the Haldane phase against the variation of the anisotropy.The phase diagram of antiferromagnetic spin-$S$ chain with $\mathrm{XY}$-type anisotropy and frustrating next-nearest-neighbor interaction is studied in the limit of large integer S with the help of a field-theoretical approach. It is shown that the existence of gapless and gapped chiral phases found in recent numerical studies [M. Kaburagi et al., J. Phys. Soc. Jpn. 68, 3185 (1999); T. Hikihara et al., J. Phys. Soc. Jpn. 69, 259 (2000)] is not specific for $S=1,$ but is rather a generic large-$S$ feature. Estimates for the corresponding transition boundaries are obtained, and a sketch of the typical phase diagram is presented. It is also shown that frustration stabilizes the Haldane phase against the variation of the anisotropy.

arXiv:cond-mat/0003427Physical review. B, Condensed matterSep 1, 200036 citations

Ground State Phase Diagram of Frustrated S = 1 X X Z chains: Chiral Ordered Phases

Toshiya Hikihara, Makoto Kaburagi, Hikaru Kawamura +1 more

The ground-state phase diagram of frustrated S=1 XXZ spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied using the infinite-system density-matrix renormalization-group method. We find six different phases, namely, the Haldane, gapped chiral, gapless chiral, double Haldane, Néel, and double Néel (uudd) phases. The gapped and gapless chiral phases are characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κ_l = S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays either exponentially or algebraically. These chiral ordered phases appear in a broad region in the phase diagram for Δ< 0.95, where Δis an exchange-anisotropy parameter. The critical properties of phase transitions are also studied.The ground-state phase diagram of frustrated S=1 XXZ spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied using the infinite-system density-matrix renormalization-group method. We find six different phases, namely, the Haldane, gapped chiral, gapless chiral, double Haldane, Néel, and double Néel (uudd) phases. The gapped and gapless chiral phases are characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κ_l = S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays either exponentially or algebraically. These chiral ordered phases appear in a broad region in the phase diagram for Δ< 0.95, where Δis an exchange-anisotropy parameter. The critical properties of phase transitions are also studied.

arXiv:cond-mat/9910159Journal of the Physical Society of JapanJan 1, 200058 citations

Spin and Chiral Orderings of Frustrated Quantum Spin Chains

Makoto Kaburagi, Hikaru Kawamura, Toshiya Hikihara

Ordering of frustrated S=1/2 and 1 XY and Heisenberg spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied by exact diagonalization and density-matrix renormalization-group methods. It is found that the S=1 XY chain exhibits both gapless and gapped `chiral' phases characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, $κ_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^x$ , whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.Ordering of frustrated S=1/2 and 1 XY and Heisenberg spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied by exact diagonalization and density-matrix renormalization-group methods. It is found that the S=1 XY chain exhibits both gapless and gapped `chiral' phases characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, $κ_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^x$, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.

arXiv:cond-mat/9902002Journal of the Physical Society of JapanOct 1, 199941 citations

Ground-state phase diagrams of frustrated spin-SXXZchains: Chiral ordered phases

Takashi Hikihara, Makoto Kaburagi, Hikaru Kawamura

The ground-state phase diagram of the frustrated spin-S XXZ chain with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied numerically by using the density-matrix renormalization-group method for the cases of $S=1/2,$ $3/2,$ and $2.$ We are particularly interested in the possible gapless and gapped chiral phases, in which the chirality ${\ensuremath{\kappa}}_{l}{=S}_{l}^{x}{S}_{l+1}^{y}\ensuremath{-}{S}_{l}^{y}{S}_{l+1}^{x}$ exhibits a finite long-range order whereas the spin correlation decays either algebraically or exponentially. We show that the gapless chiral phase appears in a broad region of the phase diagram for general S. By contrast, the gapped chiral phase is found for integer S in a narrow region of the phase diagram, while it has not been identified for half-odd integer S within our numerical accuracy. By combining the results with our previous result for $S=1,$ we discuss the S dependence of the phase diagram. The prediction from a bosonization analysis on the decay exponent of the spin correlation is verified.The ground-state phase diagram of the frustrated spin-S XXZ chain with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied numerically by using the density-matrix renormalization-group method for the cases of $S=1/2,$ $3/2,$ and $2.$ We are particularly interested in the possible gapless and gapped chiral phases, in which the chirality ${\ensuremath{\kappa}}_{l}{=S}_{l}^{x}{S}_{l+1}^{y}\ensuremath{-}{S}_{l}^{y}{S}_{l+1}^{x}$ exhibits a finite long-range order whereas the spin correlation decays either algebraically or exponentially. We show that the gapless chiral phase appears in a broad region of the phase diagram for general S. By contrast, the gapped chiral phase is found for integer S in a narrow region of the phase diagram, while it has not been identified for half-odd integer S within our numerical accuracy. By combining the results with our previous result for $S=1,$ we discuss the S dependence of the phase diagram. The prediction from a bosonization analysis on the decay exponent of the spin correlation is verified.

arXiv:cond-mat/0010283Physical review. B, Condensed matterApr 11, 200193 citations

Ground-State Phases of Anisotropic Mixed Diamond Chains with Spins 1 and 1/2

Kazuo Hida

The ground-state phases of anisotropic mixed diamond chains with spins 1 and 1/2 are investigated. Both single-site and exchange anisotropies are considered. We find the phases consisting of an array of uncorrelated spin-1 clusters separated by singlet dimers. Except in the simplest case where the cluster consists of a single $S=1$ spin, this type of ground state breaks the translational symmetry spontaneously. Although the mechanism leading to this type of ground state is the same as that in the isotropic case, it is nonmagnetic or paramagnetic depending on the competition between two types of anisotropy. We also find the Néel, period-doubled Néel, Haldane, and large- $D$ phases, where the ground state is a single spin cluster of infinite size equivalent to the spin-1 Heisenberg chain with alternating anisotropies. The ground-state phase diagrams are determined for typical sets of parameters by numerical analysis. In various limiting cases, the ground-state phase diagrams are determined analytically. The low-temperature behaviors of magnetic susceptibility and entropy are investigated to distinguish each phase by observable quantities. The relationship of the present model with the anisotropic rung-alternating ladder with spin-1/2 is also discussed.The ground-state phases of anisotropic mixed diamond chains with spins 1 and 1/2 are investigated. Both single-site and exchange anisotropies are considered. We find the phases consisting of an array of uncorrelated spin-1 clusters separated by singlet dimers. Except in the simplest case where the cluster consists of a single $S=1$ spin, this type of ground state breaks the translational symmetry spontaneously. Although the mechanism leading to this type of ground state is the same as that in the isotropic case, it is nonmagnetic or paramagnetic depending on the competition between two types of anisotropy. We also find the Néel, period-doubled Néel, Haldane, and large-$D$ phases, where the ground state is a single spin cluster of infinite size equivalent to the spin-1 Heisenberg chain with alternating anisotropies. The ground-state phase diagrams are determined for typical sets of parameters by numerical analysis. In various limiting cases, the ground-state phase diagrams are determined analytically. The low-temperature behaviors of magnetic susceptibility and entropy are investigated to distinguish each phase by observable quantities. The relationship of the present model with the anisotropic rung-alternating ladder with spin-1/2 is also discussed.

arXiv:1408.3890Journal of the Physical Society of JapanOct 28, 20146 citations

The phase diagram of antiferromagnetic spin-

S

chain with

\mathrm{XY}

-type anisotropy and frustrating next-nearest-neighbor interaction is studied in the limit of large integer S with the help of a field-theoretical approach. It is shown that the existence of gapless and gapped chiral phases found in recent numerical studies [M. Kaburagi et al., J. Phys. Soc. Jpn. 68, 3185 (1999); T. Hikihara et al., J. Phys. Soc. Jpn. 69, 259 (2000)] is not specific for

S=1,

but is rather a generic large-

S

feature. Estimates for the corresponding transition boundaries are obtained, and a sketch of the typical phase diagram is presented. It is also shown that frustration stabilizes the Haldane phase against the variation of the anisotropy.

κ_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^x

, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.

S=1/2,

3/2,

and

2.

We are particularly interested in the possible gapless and gapped chiral phases, in which the chirality ${\ensuremath{\kappa}}_{l}{=S}_{l}^{x}{S}_{l+1}^{y}\ensuremath{-}{S}_{l}^{y}{S}_{l+1}^{x}$ exhibits a finite long-range order whereas the spin correlation decays either algebraically or exponentially. We show that the gapless chiral phase appears in a broad region of the phase diagram for general S. By contrast, the gapped chiral phase is found for integer S in a narrow region of the phase diagram, while it has not been identified for half-odd integer S within our numerical accuracy. By combining the results with our previous result for

S=1,

we discuss the S dependence of the phase diagram. The prediction from a bosonization analysis on the decay exponent of the spin correlation is verified.

S=1

spin, this type of ground state breaks the translational symmetry spontaneously. Although the mechanism leading to this type of ground state is the same as that in the isotropic case, it is nonmagnetic or paramagnetic depending on the competition between two types of anisotropy. We also find the Néel, period-doubled Néel, Haldane, and large-

D

phases, where the ground state is a single spin cluster of infinite size equivalent to the spin-1 Heisenberg chain with alternating anisotropies. The ground-state phase diagrams are determined for typical sets of parameters by numerical analysis. In various limiting cases, the ground-state phase diagrams are determined analytically. The low-temperature behaviors of magnetic susceptibility and entropy are investigated to distinguish each phase by observable quantities. The relationship of the present model with the anisotropic rung-alternating ladder with spin-1/2 is also discussed.