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arXiv:cond-mat/0511024 · AIP conference proceedings

Possibility of a Two-Component Tomonaga-Luttinger Liquid in Frustrated Integer-Spin Tubes

Masahiro Sato

Published Jan 1, 2006• 0 citations
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Abstract

Uniform‐field effects for frustrated odd‐leg integer‐spin tubes (cylinder type spin systems) are investigated in the weak interchain‐coupling regime. We predict that, as the field exceeds the spin gap, a two‐component Tomonaga‐Luttinger liquid (TLL) appears due to the condensation of the doubly degenerate lowest magnons. Furthermore, it is argued that when the uniform field is so strong that the second lowest magnons are also condensed, the two‐component TLL is destroyed and a new one‐component TLL emerges. This quantum phase transition may be detected as a magnetization cusp.

DOI
10.1063/1.2355072

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Uniform‐field effects for frustrated odd‐leg integer‐spin tubes (cylinder type spin systems) are investigated in the weak interchain‐coupling regime. We predict that, as the field exceeds the spin gap, a two‐component Tomonaga‐Luttinger liquid (TLL) appears due to the condensation of the doubly degenerate lowest magnons. Furthermore, it is argued that when the uniform field is so strong that the second lowest magnons are also condensed, the two‐component TLL is destroyed and a new one‐component TLL emerges. This quantum phase transition may be detected as a magnetization cusp.
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The frustrated three-leg antiferromagnetic spin-12\frac{1}{2}21​ tube with a weak interchain coupling in a magnetic field is investigated by means of Abelian bosonization techniques. It is clearly shown that a vector chiral long-range order and a one-component Tomonaga-Luttinger liquid coexist in a wide magnetic-field region from a state with a small magnetization to a nearly saturated one. The chiral order is predicted to still survive in the intermediate plateau state. We further predict that (even) when the strength of one bond in the three rung couplings is decreased (increased), an Ising-type quantum phase transition takes place and the chirality vanishes (no singular phenomena occur and the chiral order is maintained). Even without magnetic fields, the chiral order would also be present if the spin tube possesses easy-plane anisotropy.
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We develop a theory of spontaneously magnetized Tomonaga-Luttinger (TLL) liquid in geometrically frustrated quasi-one-dimensional quantum magnets by taking an S=1/2S=1/2S=1/2 ferrimagnet on a union-jack lattice as an example. We show that a strong frustration leads to a spontaneous magnetization because of the ferrimagnetic nature of lattice. Due to the ferrimagnetic order, the local magnetization has an incommensurate oscillation with the position. We show that the spontaneously magnetized TLL is smoothly connected to the existence of a Nambu-Goldstone boson in the canted ferrimagnetic phase of a two-dimensional frustrated antiferromagnet.
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The magnetization process of the S = 1 antiferromagnetic chain with the single-ion anisotropy D and the biquadratic interaction is investigated using the numerical diagonalization.Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative D.