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arXiv:2011.11901

Ground state properties and exact thermodynamics of a 2-leg anisotropic spin ladder system

Sk Saniur Rahaman, Shaon Sahoo, Manoranjan Kumar

Published Nov 24, 2020• 0 citations
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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 $S$ or $σ$-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 $Cv(T)$, $χ(T)$ and $S(T)$ are also calculated using the transfer matrix method for different phase. The magnetic gap in the SRFM and the SLFM can be notice from $χ(T)$ and $Cv(T)$ curves.

DOI
10.48550/arxiv.2011.11901

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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.
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.
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.
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.
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Abstract In this work, we consider a frustrated two‐leg spin‐1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin‐1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non‐collinear ferrimagnetic (NCF), , antiferromagnetic and dimer phases. The quantum phase diagram is constructed for the Heisenberg spin‐1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the stability of phase and calculate the pitch angle in the NCF phase.
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