Incommensurate Spin Correlations in Spin-1/2Frustrated Two-Leg Heisenberg Ladders

Abstract

We develop a low-energy effective theory for spin-1/2 frustrated two-leg Heisenberg spin ladders. We obtain a new type of interchain coupling that breaks parity symmetry. In the presence of an XXZ-type anisotropy, this interaction gives rise to a novel ground state, characterized by incommensurate correlations. In the case of a single ladder, this state corresponds to a spin nematic phase. For a frustrated quasi-onedimensional system of infinitely many weakly coupled chains, this state develops true three dimensional spiral order. We apply our theory to recent neutron scattering experiments on Cs2CuCl4.PACS No: 75.10.Jm, 75.40.Gb Quantum spin chains have for a long time attracted the attention of both theorists and experimentalists. One of the main reasons for this continuing fascination is the dominant role played by quantum fluctuations in these systems, which lead to a rich variety of observed physical phenomena. In recent neutron scattering experiments [1] on the quasi one-dimensional frustrated Heisenberg antiferromagnet Cs 2 CuCl 4 , an intriguing type of spiral order was observed. The very existence of such spiral order, which is an incommensurate structure, is puzzling from a theoretical point of view. According to the standard lore, three dimensional ordering of quasi-1D systems results from stabilization of the dominant spin correlations in the underlying 1D constituents. Therefore, 3D spiral order would require strong incommensurate 1D spin correlations. This is in contradiction with the known properties of simple antiferromagnetic Heisenberg chains and ladders, where the only known mechanism for generating incommensurabilities is via external magnetic fields.In the present work we propose a novel mechanism that naturally gives rise to incommensurate correlations in spin ladders and quasi 1D materials in the absence of external fields. Interestingly, we find that this phenomenon occurs in a standard model of two coupled spin-1/2 zig-zag Heisenberg chains, which has attracted much recent interest [2,3].In the bulk of this letter we shall concentrate on this simple frustrated ladder system in order to clearly exhibit the precise nature of the mechanism of incommensurate spin correlations. The application of our results to the quasi 1D case relevant for Cs 2 CuCl 4 is briefly discussed at the end. In what follows we derive the low-energy effective theory for the zig-zag ladder system, which we find to contain a parity-breaking interchain interaction. This "twist term", which was not considered in previous studies, is an operator of conformal spin 1 [5] and has important consequences: We will show that, although it alters the position of phase boundaries already in the spin rotationally invariant (SU(2)) case, it leads to incommensurate correlations only in the presence of an easy plane XXZ anisotropy.The Hamiltonian of the anisotropic zig-zag Heisenberg ladder is

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

“…is the same as the definition of Ref. 17. The inset is the enlarged part where the RG flows to the strong coupling limit can be seen clearly.…”

“…Afterwards, choosing the initial values of a i and b i in the range where J 3 ≫ J 2 , J 1 , we obtain a new solution of the renormalization group equations 17 as shown in Fig. 3, where the RG flows corresponding to H twist go to the strong coupling regime first, which suggests a new phase may come into being.…”

“…As pointed out in Refs. [17,19], it arouses a spin nematic phase in the ground state of the XXZ zigzag spin ladder. Its effect on an isotropic Heisenberg model is still not very clear and needs further investigations.…”

“…The coefficient g LR ∝ −J 3 , and H LR , H JJ and H twist are marginal perturbations with scaling dimension d = 1 17 . H twist is the twist term that is produced by the frustrated inter-chain interactions.…”

“…This parity-breaking operator is marginal in the renormalization group (RG) sense and has a conformal spin 1 18 . Currently, the twist operator is believed to be the origin of incommensurate correlations in XXZ zigzag spin ladders 17,[19][20][21][22] . For an isotropic zigzag spin ladder, the twist operator is proposed to cause dimerization 17 in the ferromagnetic inter-chain coupling region.…”