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arXiv:1307.5945 · Europhysics Letters (EPL)

Honeycomb Heisenberg spin ladder: Unusual ground state and thermodynamic properties

Yang Zhao, Wei Li, Bin Xi, Shi-Ju Ran, Yuan-Yuan Zhu, Bing-Wu Wang, Song Gao, Gang Su

Published Dec 1, 2013• 5 citations
arXivHTMLPDF

Abstract

The unusual ground state and thermodynamic properties of spin-(1/2) two-leg honeycomb (HC) spin ladder are systematically studied by jointly utilizing various analytical and numerical methods. The HC spin ladder is found to exhibit behaviors dramatically different from those of the conventional square spin ladder. A strong relevant term and a half saturation magnetization plateau that can be attributed to the formation of diluted dimer states are observed in the HC ladder, both of which are absent in the square ladder. The ground state phase diagram of the HC spin ladder is identified, and the thermodynamic properties of the specific heat and susceptibility for different couplings are thoroughly explored, where two kinds of excitations are unveiled. Our calculated result is well fitted to the experimental data of the two-leg HC spin ladder compound [Cu 2 L 1 (N 3 ) 4 ] n .

DOI
10.1209/0295-5075/104/57009

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The unusual ground state and thermodynamic properties of spin-(1/2) two-leg honeycomb (HC) spin ladder are systematically studied by jointly utilizing various analytical and numerical methods. The HC spin ladder is found to exhibit behaviors dramatically different from those of the conventional square spin ladder. A strong relevant term and a half saturation magnetization plateau that can be attributed to the formation of diluted dimer states are observed in the HC ladder, both of which are absent in the square ladder. The ground state phase diagram of the HC spin ladder is identified, and the thermodynamic properties of the specific heat and susceptibility for different couplings are thoroughly explored, where two kinds of excitations are unveiled. Our calculated result is well fitted to the experimental data of the two-leg HC spin ladder compound [Cu 2 L 1 (N 3 ) 4 ] n .
This article considers recent advances in the investigation of the thermal and magnetic properties of integrable spin ladder models and their applicability to the physics of strong coupling ladder compounds. For this class of compounds the rung coupling J ⊥ is much stronger than the coupling J ∥ along the ladder legs. The ground state properties of the integrable two-leg spin- and the mixed spin-() ladder models at zero temperature are analysed by means of the Thermodynamic Bethe Ansatz (TBA). Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are discussed in terms of the recently introduced High Temperature Expansion (HTE) method, which is reviewed in detail. In the strong coupling region the integrable spin- ladder model exhibits three quantum phases: (i) a gapped phase in the regime , (ii) a fully polarized phase for , and (iii) a Luttinger liquid magnetic phase in the regime H c1<H<H c2. The critical behaviour in the vicinity of the critical points H c1 and H c2 is of Pokrovsky-Talapov type. The temperature-dependent thermal and magnetic properties are directly evaluated from the exact free energy expression and compared to known experimental results for the strong coupling ladder compounds (5IAP)2CuBr4· 2H2O, Cu2(C5H12N2)2Cl4, (C5H12N)2CuBr4, BIP-BNO and [Cu2(C2\O 2)(C10H8N2)2)](NO3)2. Similar analysis of the mixed spin-() ladder model reveals a rich phase diagram, with a and a full saturation magnetization plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetization plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetization curve obtained from the exact result derived from the TBA and HTE. The results are applied to the mixed ferrimagnetic ladder compound PNNBNO. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also discussed. For this model single-ion anisotropy can trigger different quantum phase transitions within the spin and orbital degrees of freedom, with magnetization plateaux arising from different spin and orbit Landé g-factors.
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.
The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J>0 in the armchair direction and ferromagnetic interaction J^{'}<0 in the zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio Q_{2} and spin stiffness ρ in two directions for various coupling ratios α=J^{'}/J under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point α_{c}=-0.93. Through the finite-size scaling analysis on Q_{2}, ρ_{x}, and ρ_{y}, we determined the critical exponent related to the correlation length ν to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing α. A phase diagram in the coupling ratio α-magnetic field h plane is obtained, where four phases, including dimerized, stripe, canted stripe, and polarized, are identified. It is also unveiled that the temperature dependence of the specific heat C(T) for different α's intersects precisely at one point, similar to that of liquid ^{3}He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of Q_{2}, ρ, and C(T) are carefully analyzed. The susceptibility is compared with the experimental data to give the magnetic parameters of both compounds.
We investigate the low-temperature phase diagram of the exactly solved su (4) two-leg spin ladder as a function of the rung coupling and magnetic field H by means of the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases, while in the presence of a strong magnetic field there is no singlet ground state for ferromagnetic rung coupling. For antiferromagnetic rung coupling, there is a gapped phase in the regime H < H c1 , a fully polarized gapped phase for H > H c2 and a Luttinger liquid magnetic phase in the regime H c1 < H < H c2 . The critical behaviour derived using the TBA is consistent with the existing experimental, numerical and perturbative results for the strong coupling ladder compounds. This includes the spin excitation gap and the critical fields H c1 and H c2 , which are in excellent agreement with the experimental values for the known strong coupling ladder compounds (5IAP) 2 CuBr 4 ·2H 2 O, Cu 2 (C 5 H 12 N 2 ) 2 Cl 4 and (C 5 H 12 N) 2 CuBr 4 . In addition we predict the spin gap for the weak coupling compounds with , such as (VO) 2 P 2 O 7 , and also show that the gap opens for arbitrary .
Using the recently developed transfer-matrix renormalization group method, we have studied the thermodynamic properties of two-leg antiferromagnetic ladders in a magnetic field. Based on different magnetization behaviors, we found a disordered spin liquid, the Luttinger liquid, spin-polarized phases, and a classical regime. Our calculations in the Luttinger liquid regime suggest that both the divergence of the NMR relaxation rate and the anomalous specific heat behavior observed on Cu2(C5H12N2)2Cl4 are due to a quasi-one-dimensional effect rather than three-dimensional ordering.
Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung.The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations.Both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and threequarters of the saturation magnetization.