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arXiv:cond-mat/0106260 · Physical Review Letters

Spinons in a Crossed-Chains Model of a 2D Spin Liquid

Oleg A. Starykh, Rajiv R. P. Singh, Gregory Levine

Published Apr 4, 2002• 46 citations
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Abstract

Using the random phase approximation, we show that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a "sliding Luttinger liquid." In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.

DOI
10.1103/physrevlett.88.167203

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Using the random phase approximation, we show that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a "sliding Luttinger liquid." In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.
Exact diagonalizations indicate that the effective one-dimensional behavior (sliding Luttinger liquid phase) of the frustrated spin-1/2 crossed chain model, predicted by Starykh, Singh, and Levine [Phys. Rev. Lett. 88, 167203 (2002)], persists for a wide range of interchain couplings. The extension of the other phases (plaquette valence bond crystal and N\'eel long-range order) is made precise. The coexistence region of these two phases, proposed by Sachdev and Park [Ann. Phys. (N.Y.) 298, 58 (2002)], has at most a very narrow width.
Exact diagonalizations indicate that the effective 1-dimensional behavior (sliding Luttinger liquid phase) of the frustrated spin-1/2 crossed chain model, predicted by Starykh, Singh and Levine [Phys. Rev. Lett. 88, 167203 (2002)], persists for a wide range of transverse couplings. The extension of the other phases (plaquette valence bond crystal and Néel long range order) is precised. No clear indication of a coexistence of these two phases is found, at variance with a suggestion of Sachdev and Park (cond-mat/0108214).
We study quantum disordered ground states of the two-dimensional Heisenberg-Kitaev model on the triangular lattice using a Schwinger boson approach. Our aim is to identify and characterize potential gapped quantum spin liquid phases that are stabilized by anisotropic Kitaev interactions. For antiferromagnetic Heisenberg and Kitaev couplings and sufficiently small spin SSS, we find three different symmetric Z2{Z}_{2}Z2​ spin liquid phases, separated by two continuous quantum phase transitions. Interestingly, the gap of elementary excitations remains finite throughout the transitions. The first spin liquid phase corresponds to the well-known zero-flux state in the Heisenberg limit, which is stable with respect to small Kitaev couplings and develops ${120}^{\ensuremath{\circ}}$ order in the semiclassical limit at large SSS. In the opposite Kitaev limit, we find a different spin liquid ground state, which is a quantum disordered version of a magnetically ordered state with antiferromagnetic chains, in accordance with results in the classical limit. Finally, at intermediate couplings, we find a spin liquid state with unusual spin correlations. Upon spinon condensation, this state develops Bragg peaks at incommensurate momenta in close analogy to the magnetically ordered Z2 vortex crystal phase, which has been analyzed in recent theoretical works.
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.
Using a recently proposed perturbative numerical renormalization-group algorithm, we explore the connection between quantum criticality and the emergence of Luttinger liquid physics in t−Jt-Jt−J chains coupled by frustrated interactions. This study is built on an earlier finding that at the maximally frustrated point, the ground state of weakly-coupled Heisenberg chains is disordered, the transverse exchanges being irrelevant. This result is extended here to transverse couplings up to J⊥=0.6J_{\perp}=0.6J⊥​=0.6, and we argue that it may also be valid at the isotropic point. A finite size analysis of coupled Heisenberg chains in the vicinity of the maximally frustrated point confirms that the transverse spin-spin correlations decay exponentially while the longitudinal ones revert to those of decoupled chains. We find that this behavior persists upon moderate hole doping $x \alt 0.75$. For larger doping, the frustration becomes inactive and the quantum critical point is suppressed.