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arXiv:1212.1767 · Physical Review B

Low-energy effective theory and two distinct critical phases in a spin- 12 frustrated three-leg spin tube

Yang Zhao, Shou-Shu Gong, Yongjun Wang, Gang Su

Published Dec 7, 2012• 6 citations
arXivHTMLPDF

Abstract

Motivated by the crystal structures of [(CuCl${}_{2}$tachH)${}_{3}$Cl]Cl${}_{2}$ and Ca${}_{3}$Co${}_{2}$O${}_{6}$, we develop a low-energy effective theory using the bosonization technique for a spin-$\frac{1}{2}$ frustrated three-leg spin tube with trigonal prism units in two limit cases. The features obtained with the effective theory are numerically elucidated by the density matrix renormalization group method. Three different quantum phases in the ground state of the system, say, one gapped dimerized phase and two distinct gapless phases, are identified, where the two gapless phases are found to have the conformal central charge $c=1$ and $\frac{3}{2}$, respectively. Spin gaps, spin and dimer correlation functions, and the entanglement entropy are obtained. In particular, it is disclosed that the critical phase with $c=\frac{3}{2}$ is the consequence of spin frustrations, which might belong to the SU(2)${}_{k=2}$ Wess-Zumino-Witten-Novikov universality class, and is induced by the twist term in the bosonized Hamiltonian density.

DOI
10.1103/physrevb.86.224406

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We investigate quantum phase transitions of the S=12S=\frac{1}{2}S=21​ three-leg antiferromagnetic spin tube with asymmetric interchain (rung) exchange interactions. On the basis of the electron tube system, we propose a useful effective theory to give the global phase diagram of the asymmetric spin tube. In addition, using other effective theories we raise the reliability of the phase diagram. The density-matrix renormalization-group and the numerical diagonalization analyses show that the finite spin gap appears in a narrow region around the rung-symmetric line, in contrast to a recent paper by Nishimoto and Arikawa, [Phys. Rev. B 78, 054421 (2008)]. The numerical calculations indicate that this global phase diagram obtained by use of the effective theories is qualitatively correct. In the gapless phase on the phase diagram, the numerical data are fitted by a finite-size scaling in the c=1c=1c=1 conformal field theory. We argue that all the phase transitions between the gapful and gapless phases belong to the Berezinskii-Kosterlitz-Thouless universality class.
We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.
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We study the ground-state phase diagram of a frustrated spin-1/2 four-leg tube. Using a variety of complementary techniques, namely, density matrix renormalization group, exact diagonalization, Schwinger boson mean-field theory, quantum Monte Carlo, and series expansion, we explore the parameter space of this model in the regime of all-antiferromagnetic exchange. In contrast to unfrustrated four-leg tubes, we uncover a rich phase diagram. Apart from the Luttinger liquid fixed point in the limit of decoupled legs, this comprises several gapped ground states, namely, a plaquette, an incommensurate, and an antiferromagnetic quasispin-2 chain phase. The transitions between these phases are analyzed in terms of total energy and static structure factor calculations and are found to be of (weak) first order. Despite the absence of long-range order in the quantum case, remarkable similarities to the classical phase diagram are uncovered, with the exception of the icommensurate regime, which is strongly renormalized by quantum fluctuations. In the limit of large leg exchange, the tube exhibits a deconfinement crossover from gapped magnon-like excitations to spinons.