Low-energy excitations in two-leg and three-leg quantum spin ladders

Ichinose, Ikuo; Kayama, Yasuyuki

doi:10.1016/s0550-3213(98)00207-7

Cited by 4 publications

(5 citation statements)

References 17 publications

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“…The comparison between Eqs. (27) and (22) elucidates the relation ξ r (H = 0) −2 = ξ r (H) −2 + H 2 /c 2 at T = 0. Thus, one can see that new dispersions ǫ z r (k) restore the Zeeman splitting at T = 0.…”

Section: Zeeman Splitting In Ladders and Tubesmentioning

confidence: 74%

“…We investigate the low-energy excitations more quantitatively by solving the SPE (22). As we will see in Figs.…”

Section: A No-field Casementioning

confidence: 99%

“…As far as we know, there are only two spin-tube-like materials 17,18 even now. However, odd-leg tubes with an AF rung coupling 19,20,21,22,23,24,25 have attracted considerable interest at least theoretically, because such tubes possess the frustration along the rung. It is known that at least for the strong rung-coupling regime, odd-leg AF-rung spin-1 2 tubes take doubly degenerate and gapful GSs with the one-site translational symmetry along the chain breaking.…”

Section: Introductionmentioning

confidence: 99%

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N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

Sato

2005

Phys. Rev. B

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We investigate the low-energy properties, especially the low-energy excitation structures, of N -leg integer-spin ladders and tubes with an antiferromagnetic (AF) intrachain coupling. In the odd-leg tubes, the AF rung coupling causes the frustration. To treat all ladders and tubes systematically, we apply Sénéchal's method [Phys. Rev. B 52, 15319 (1995)], based on the nonlinear sigma model, together with a saddle-point approximation. This strategy is valid in the weak interchain (rung) coupling regime. We show that all frustrated tubes possess six-fold degenerate spin-1 magnon bands, as the lowest excitations, while other ladders and tubes have a standard triply degenerate bands. We also consider effects of four kinds of Zeeman terms: uniform, staggered only along the rung, only along the chain, or both directions. The above prediction of the no-field case implies that a sufficiently strong uniform field yields a two-component Tomonaga-Luttinger liquid (TLL) due to the condensation of doubly degenerate lowest magnons in frustrated tubes. In contrast, the field induces a standard one-component TLL in all other systems. This is supported by symmetry and bosonization arguments based on the Ginzburg-Landau theory. The bosonization also suggests that the two-component TLL vanishes and a one-component TLL appears, when the uniform field becomes larger for the second lowest magnon bands to touch the zero-energy line. This transition could be observed as a cusp singularity in the magnetization process. When the field is staggered only along the rung direction, it is implied that the lowest doubly-degenerate bands fall down with the field increasing in all systems. For final two cases where the fields are staggered along the chain, it is showed that at least in the weak rung-coupling region, the lowest-excitation gap grows with the field increasing, and no critical phenomena occurs. Furthermore, for the ladders of the final two cases, we predict that the inhomogeneous magnetization along the rung occurs, and the frustration between the field and the rung coupling can induce the magnetization pointing to the opposite direction to the field. All the analyses suggest that the emergence of the doubly degenerate transverse magnons and the single longitudinal one is universal for the one-dimensional AF spin systems with a weak staggered field.

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Section: Zeeman Splitting In Ladders and Tubesmentioning

confidence: 74%

“…We investigate the low-energy excitations more quantitatively by solving the SPE (22). As we will see in Figs.…”

Section: A No-field Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

Sato

2005

Phys. Rev. B

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“…However, in the present case, it is conceivable that "kinetic terms" of the gauge field appear effectively from the high-energy modes. For 1D quantum spin models, this possibility is realized [5]. The form of the continuum Lagrangian (8) is essential in order to solve the "constraints" on holons and spinons.…”

mentioning

confidence: 99%

Comment on “Confinement of Slave Particles in U(1) Gauge Theories of Strongly Interacting Electrons”

Ichinose

Matsui

2001

Phys. Rev. Lett.

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“…The determination of the charge e, or the parameter k, was attempted in [4] following the argument of [1]. More recently Berruto et al have examined the correspondence between the spin chain model and the two-flavor lattice Schwinger model and have found that both model have the low energy excitation spectrum of the same pattern.…”

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confidence: 99%

AntiferromagneticS=12Heisenberg chain and the two-flavor massless Schwinger model

Hosotani

1999

Phys. Rev. B

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Abstract. An antiferromagnetic S = 1 2Heisenberg chain is mapped to the two-flavor massless Schwinger model at θ = π. The electromagnetic coupling constant and velocity of light in the Schwinger model are determined in terms of the Heisenberg coupling and lattice spacing in the spin chain system.In the previous paper [1] we have shown that an S = 1 2 spin chaincorresponds to the two-flavor massless Schwinger model (two-dimensional QED) in a uniform background charge density:Here ℓ is the lattice spacing in the spin chain model. The coupling constant e and velocity of light c are related to J and ℓ by e = k J/ℓ and c = 2ℓJ/πh, where k is a constant of O(1) left undetermined. The Schwinger model contains one more parameter. Its ground state is the θ vacuum. The value of θ also remained undetermined. In this Letter we shall show that k ∼ 2.225 and θ = π with the aid of the result from the Bethe ansatz.[2] The correspondence between the spin chain and Schwinger model has been noticed by many authors.[3] Deductive derivation was achieved in ref. [1].The original spin degree is tranformed to the flavor index of the Dirac field ψ, whereas the odd-even site index of the lattice becomes the spin degree of the Dirac field. The finiteness of the lattice spacing ℓ must be taken into account in establishing the correspondence. In the naive continuum limit ℓ → 0 with c kept fixed, the charge e diverges as 1/ℓ and all massive modes of the Schwinger model decouple. These massive modes play an important role when the correspondence is applied to the spin ladder problem.The determination of the charge e, or the parameter k, was attempted in [4] following the argument of [1]. More recently Berruto et al have examined the correspondence between the spin chain model and the two-flavor lattice Schwinger model and have found that both model have the low energy excitation spectrum of the same pattern. [5]

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Low-energy excitations in two-leg and three-leg quantum spin ladders

Cited by 4 publications

References 17 publications

N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

N-leg integer-spin ladders and tubes in commensurate external fields: Nonlinear sigma model approach

Comment on “Confinement of Slave Particles in U(1) Gauge Theories of Strongly Interacting Electrons”

AntiferromagneticS=12Heisenberg chain and the two-flavor massless Schwinger model

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