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arXiv:1509.04062 · Physical Review B

Ground-state phases of a rung-alternated spin−12 Heisenberg ladder

Fatemeh Amiri, Gaoyong Sun, H.-J. Mikeska, T. Vekua

Published Nov 20, 2015• 16 citations
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Abstract

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.

DOI
10.1103/physrevb.92.184421

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The ground-state phase diagram of a Heisenberg spin\ensuremath−12\text{spin}\ensuremath{-}\frac{1}{2}spin\ensuremath−21​ 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.
Ground-state and finite-temperature properties of S=1/2S=1/2S=1/2 Heisenberg ladders with a ferromagnetic leg, an antiferromagnetic leg, and antiferromagnetic rungs are studied. It is shown that a partial ferrimagnetic phase extends over a wide parameter range in the ground state. The numerical results are supported by an analytical calculation based on a mapping onto the nonlinear σσσ model and a perturbation calculation from the strong-rung limit. It is shown that the partial ferrimagnetic state is a spontaneously magnetized Tomonaga--Luttinger liquid with incommensurate magnetic correlation, which is confirmed by a DMRG calculation. The finite-temperature magnetic susceptibility is calculated using the thermal pure quantum state method. It is suggested that the susceptibility diverges as T−2T^{-2}T−2 in the ferrimagnetic phases as in the case of ferromagnetic Heisenberg chains.
We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either SSS or σσσ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both SSS and σσσ-type of spins are anti-ferromagnetically aligned with each other, two nearest SSS spins along the rung form an anisotropic singlet bond whereas two nearest σσσ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like Cv(T)Cv(T)Cv(T), χ(T)χ(T)χ(T) and S(T)S(T)S(T) are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from χ(T)χ(T)χ(T) and Cv(T)Cv(T)Cv(T) curves.
We explore the ground-state phase diagram of the S=1/2S=1/2S=1/2 two-leg ladder with different leg interactions. The xyxyxy and zzz components of the leg interactions between nearest-neighbor spins in the aaa (bbb) leg are respectively denoted by Jl,aJ_{{\rm l},a}Jl,a​ and ΔlJl,aΔ_{\rm l} J_{{\rm l},a}Δl​Jl,a​ (Jl,bJ_{{\rm l},b}Jl,b​ and ΔlJl,bΔ_{\rm l} J_{{\rm l},b}Δl​Jl,b​). On the other hand, the xyxyxy and zzz components of the uniform rung interactions are respectively denoted by ΓrJrΓ_{\rm r} J_{\rm r}Γr​Jr​ and JrJ_{\rm r}Jr​. In the above, ΔlΔ_{\rm l}Δl​ and ΓrΓ_{\rm r}Γr​ are the XXZXXZXXZ-type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when Jl,aJl,b<0J_{{\rm l},a} J_{{\rm l},b}<0Jl,a​Jl,b​<0 irrespective of the sign of JrJ_{\rm r}Jr​. The phase diagram on the ΔlΔ_{\rm l}Δl​ (∣Δl∣≤1.0|Δ_{\rm l}| \leq 1.0∣Δl​∣≤1.0) versus Jl,bJ_{{\rm l},b}Jl,b​ (−2.0≤Jl,b≤3.0-2.0\leq J_{{\rm l},b}\leq 3.0−2.0≤Jl,b​≤3.0) plane in the case where Jl,a=0.2J_{{\rm l},a}=0.2Jl,a​=0.2, Jr=−1.0J_{\rm r}=-1.0Jr​=−1.0, and Γr=0.5Γ_{\rm r} = 0.5Γr​=0.5 is determined numerically. We employ the physical consideration, and the level spectroscopy and phenomenological renormalization-group analyses of the numerical date obtained by the exact diagonalization method. The resultant phase diagram contains the ferromagnetic, Haldane, N{é}el, nematic Tomonaga-Luttinger liquid (TLL), partial ferrimagnetic, and XY1XY1XY1 phases. Interestingly enough, the nematic TLL phase appears in the strong-rung unfrustrated region as well as in the strong-rung frustrated one. We perform the first-order perturbational calculations from the strong rung coupling limit to elucidate the characteristic features of the phase diagram. Furthermore, we make the density-matrix renormalization-group calculations for some physical quantities such as the energy gaps, the local magnetization, and the spin correlation functions to supplement the reliability of the phase diagram.
A frustrated two‐legged spin‐1/2 ladder featuring alternating Ising and isotropic Heisenberg exchange interactions on the rungs is investigated, while Ising exchanges are present along the legs and diagonals. This model exhibits the following four ground‐state phases: (i) stripe rung ferromagnet (SRFM), (ii) anisotropic antiferromagnet, (iii) dimer, and (iv) stripe leg ferromagnet. In this work, different magnetization plateaus are analyzed by studying the spin density, quantum fidelity, and quantum concurrence in the presence of longitudinal and transverse magnetic fields. The exact diagonalization and transfer matrix methods are used to solve the model Hamiltonian. In the presence of a longitudinal field, the discrete magnetization plateaus appear at 0, 1/2, and 1 of the saturation value across all phases [(i)–(iv)]. Interestingly, in the presence of an externally applied transverse field, the SRFM phase [(i)] exhibits a continuous change in magnetization. The other three phases [(ii)–(iv)] show both discrete jump and continuous change in magnetization in different limits of the transverse field.
Abstract We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropic S -type or discrete anisotropic σ -type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both S and σ -type of spins are anti-ferromagnetically aligned with each other, two nearest S spins along the rung form an anisotropic singlet bond whereas two nearest σ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heat C v ( T ), magnetic susceptibility χ ( T ) and thermal entropy S ( T ) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed from χ ( T ) and C v ( T ) curves.
Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.