Progress of Theoretical Physics Supplement

Chiral Order in Spin-SXY Chains

Thierry Jolicoe ur, P. Lecheminant

Published Jan 1, 2002• 3 citations

Abstract

We consider the issue of chiral ordering in spin chains for an arbitrary value of the spins S. By use of bosonization according to a scheme developped by H.-J. Schulz, we obtain a phase diagram of the chain with XY exchange couplings between the nearest and the next-to-nearest neighbors. We obtain a satisfactory picture including a so-called chiral spin nematic phase which is gapless, has long-range chiral order and incommensurate spin correlations. We perform a stability analysis of this phase and point out that this analysis is in conflict with existing DMRG results that show a difference between integer and half-integer spin cases.

DOI: 10.1143/ptps.145.23

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Progress of Theoretical Physics Supplement

Chiral Order in Spin-SXY Chains

Thierry Jolicoe ur, P. Lecheminant

Published Jan 1, 2002• 3 citations

Publisher

Abstract

DOI: 10.1143/ptps.145.23

Related papers

Chiral order in spin-S XY chains

Th. Jolicœur, P. Lecheminant

We consider the issue of chiral ordering in spin chains for an arbitrary value of the spins S. By use of bosonization according to a scheme developped by H.-J. Schulz, we obtain the phase diagram of the chain with XY exchange between nearest and next-to-nearest neighbors. We obtain a satisfactory picture including a chiral spin nematic phase which is gapless, has long-range chiral order and incommensurate spin correlations. We perform a stability analysis of this phase and point out that this analysis is in conflict with existing DMRG results that shows a difference between integer and half-integer spin case.We consider the issue of chiral ordering in spin chains for an arbitrary value of the spins S. By use of bosonization according to a scheme developped by H.-J. Schulz, we obtain the phase diagram of the chain with XY exchange between nearest and next-to-nearest neighbors. We obtain a satisfactory picture including a chiral spin nematic phase which is gapless, has long-range chiral order and incommensurate spin correlations. We perform a stability analysis of this phase and point out that this analysis is in conflict with existing DMRG results that shows a difference between integer and half-integer spin case.

arXiv:cond-mat/0204160Apr 7, 20020 citations

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

Takashi Hikihara, Makoto Kaburagi, Hikaru Kawamura

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Takashi Hikihara, Makoto Kaburagi, Hikaru Kawamura

The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25

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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

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.

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.

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.