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arXiv:cond-mat/0111177 · Physical review. B, Condensed matter

Magnetization and dimerization profiles of the cut two-leg spin ladder

P. Lecheminant, E. Orignac

Published Apr 18, 2002• 49 citations
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Abstract

The physical properties of the edge states of the cut two-leg spin ladder are investigated by means of the bosonization approach. By carefully treating boundary conditions, we derive the existence of spin-1/2 edge states in the spin ladder with a ferromagnetic rung exchange and for the open spin-1 Heisenberg chain. In contrast, such states are absent in the antiferromagnetic rung coupling case. The approach, based on a mapping onto decoupled semi-infinite off-critical Ising models, allows us to compute several physical quantities of interest. In particular, we determine the magnetization and dimerization profiles of the cut two-leg spin ladder and of the open biquadratic spin-1 chain in the vicinity of the $\mathrm{SU}{(2)}_{2}$ Wess-Zumino-Novikov-Witten critical point.

DOI
10.1103/physrevb.65.174406

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The physical properties of the edge states of the cut two-leg spin ladder are investigated by means of the bosonization approach. By carefully treating boundary conditions, we derive the existence of spin-1/2 edge states in the spin ladder with a ferromagnetic rung exchange and for the open spin-1 Heisenberg chain. In contrast, such states are absent in the antiferromagnetic rung coupling case. The approach, based on a mapping onto decoupled semi-infinite off-critical Ising models, allows us to compute several physical quantities of interest. In particular, we determine the magnetization and dimerization profiles of the cut two-leg spin ladder and of the open biquadratic spin-1 chain in the vicinity of the SU(2)2\mathrm{SU}{(2)}_{2}SU(2)2​ Wess-Zumino-Novikov-Witten critical point.
We investigate the ground-state phase diagram and critical properties of the S=1/2S=1/2S=1/2 two-leg Heisenberg spin ladder system with a negative four-spin interaction using a numerical exact diagonalization method. Using the perturbation theory in the strong negative rung-coupling limit, we derive an S=1S=1S=1 bilinear-biquadratic chain as an effective model. We discuss the ground-state phase diagram in this limit. Next we numerically determine a phase boundary between the rung singlet phase and the columnar dimer (CD) phase by the phenomenological renormalization group method, and one between the CD phase and the Haldane phase by the twisted boundary condition method. We confirm that the phase transition between the CD phase and the Haldane phase is of second order and this universality class is described by the k=2k=2k=2 SU(2)SU(2)SU(2) Wess-Zumino-Novikov-Witten nonlinear $\ensuremath{\sigma}$ model, calculating the central charge and scaling dimensions.
The ground-state phase diagram of a Heisenberg $\text{spin}\ensuremath{-}\frac{1}{2}$ system on a two-leg ladder with rung alternation is studied by combining analytical approaches with numerical simulations. For the case of ferromagnetic leg exchanges a unique ferrimagnetic ground state emerges, whereas for the case of antiferromagnetic leg exchanges several different ground states are stabilized depending on the ratio between exchanges along legs and rungs. For the more general case of a honeycomb-ladder model for the case of ferromagnetic leg exchanges besides the usual rung-singlet and saturated ferromagnetic states we obtain a ferrimagnetic Luttinger liquid phase with both linear and quadratic low-energy dispersions and ground-state magnetization continuously changing with system parameters. For the case of antiferromagnetic exchanges along legs, different dimerized states including states with additional topological order are suggested to be realized.
We study a phase transition and critical properties of the quantum spin ladder system with a four-spin interaction. We determine a phase boundary between a rung singlet and a staggered dimer phases numerically. This phase transition is of a second order in the weak-coupling region. We confirm that this universality class is described by the k=2k=2k=2 SU(2) Wess-Zumino-Witten model, analyzing the central charge and scaling dimensions. In the strong-coupling region, phase transition becomes of a first order.
The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus is proportional to the excitation gap at given magnetization and scales as   , where  is the amplitude of rung exchange modulation and the critical
We study boundary rung defects in n-leg quantum spin ladders with SU(2n)\mathrm{SU}{(2}^{n})SU(2n) leg symmetry. The rung interactions are parametrized by two coupling parameters J and ${J}^{\ensuremath{'}}$ interpolating between the uniform spin tube ${(J}^{\ensuremath{'}}=J)$ and the open spin ladder ${(J}^{\ensuremath{'}}=0).$ The rung defect at the edge of the ladder has rung coupling parameters Jd{J}_{d}Jd​ and ${J}_{d}^{\ensuremath{'}}.$ The conditions for the integrability of the model are investigated as a function of n, J, ${J}^{\ensuremath{'}},$ Jd,{J}_{d},Jd​, and ${J}_{d}^{\ensuremath{'}},$ and the Bethe Ansatz equations for the exact solution are derived. The boundary quantum critical behavior is discussed. The conditions for the formation of a local moment (boundary bound state due to the defect) are studied. In the absence of a magnetic field such a bound state is only possible for even-legged spin tubes, while for odd-legged ladders a bound state can only occur in a large magnetic field. Depending on the parameters of the host this local moment may be screened in analogy to the Kondo effect.
We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin that is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba4Ir3O10{\mathrm{Ba}}_{4}{\mathrm{Ir}}_{3}{\mathrm{O}}_{10}Ba4​Ir3​O10​. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong rung coupling a gapped dimerized phase related to competing symmetry sectors in Hilbert space that ultimately results in frustration-driven spin-Peierls transition. In the weak rung-coupling regime, the system is uniform yet shows a gapped spinon continuum together with a sharp coherent low-energy branch that renders the system critical overall. In either case, the additional rung spin quickly gets sidelined and nearly decouples once its bare coupling to the ladder drops somewhat below the direct Heisenberg coupling of the legs.