Thermodynamic properties of an alternating-spin (1/2,1) two-leg ladder

Most complex networks serve as conduits for various dynamical processes, ranging from mass transfer by chemical reactions in the cell to packet transfer on the Internet. We collected data on the time dependent activity of five natural and technological networks, finding evidence of orders of magnitude differences in the fluxes of individual nodes. This dynamical inhomogeneity reflects the emergence of localized high flux regions or hot spots, carrying an overwhelming fraction of the networks activity. We find that each system is characterized by a unique scaling law, coupling the flux fluctuations with the total flux on individual nodes, a result of the competition between the systems internal collective dynamics and changes in the external environment. We propose a method to separate these two components, allowing us to predict the relevant scaling exponents. As high fluctuations can lead to dynamical bottlenecks and jamming, these findings have a strong impact on the predictability and failure prevention of complex transportation networks.Received: 25 October 2003, Published online: 17 February 2004PACS: 89.75.-k Complex systems - 89.75.Da Systems obeying scaling laws - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion     

Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder

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.     

Perturbative study of thermodynamic properties for the two-leg spin ladder

We apply finite-temperature perturbation theory to study thermodynamic properties of the two-leg antiferromagnetic spin ladder in the strong interchain coupling limit. The internal energy, specific heat and uniform susceptibility are calculated analytically by third-order perturbation expansions. At zero temperature, the present method results in the same ground state energy as that obtained by the strong coupling expansion without temperature. At finite-temperature, we obtain a peak in the specific heat and a broad maximum in the uniform susceptibility. The results agree quite well with experimental data for the material Cu₂(C₅H₁₂N₂)₂Cl₄ and the numerical data of 8-order series expansion theory.     

Topological phases of the two-leg Kitaev ladder

We study the phase diagram of the two-leg Kitaev model. Different topological phases can be characterized by either the number of Majorana modes for a deformed chain of the open ladder, or by a winding number related to the ‘h  -loop’ in the momentum space. By adding a three-spin interaction term to break the time-reversal symmetry, two originally different phases are glued together, so that the number of Majorana modes reduce to 0 or 1, namely, the topological invariant collapses to _Z2$Z_2$ from an integer Z. These observations are consistent with a recent general study [S. Tewari, J.D. Sau, arXiv:1111.6592v2].     

Thermodynamic properties of the spin-1/2 antiferromagnetic ladder under magnetic field

Specific heat (C_V) measurements in the spin-1/2 Cu₂(C₂H₁₂N₂)₂Cl₄ system under a magnetic field up to H =8.25 T are reported and compared to the results of numerical calculations based on the 2-leg antiferromagnetic Heisenberg ladder. While the temperature dependences of both the susceptibility and the low-field specific heat are accurately reproduced by this model, deviations are observed above the critical field H_C1 at which the spin gap closes. In this Quantum High Field phase, the contribution of the low-energy quantum fluctuations are stronger than in the Heisenberg ladder model. We argue that this enhancement can be attributed to dynamical lattice fluctuations. Finally, we show that such a Heisenberg ladder, for H > H C1, is unstable, when coupled to the 3D lattice, against a lattice distortion. These results provide an alternative explanation for the observed low temperature ( K-0.8 K) phase (previously interpreted as a 3D magnetic ordering) as a new type of incommensurate gapped state. Received: 23 July 1998 / Accepted: 24 August 1998     

Concurrence and entanglement entropy in a dimerised spin-1/2 two-leg ladder

We consider isotropic spin-1/2 two-leg ladders with dominant spatially-modulated rung exchanges. We study the effect of a uniform magnetic field on the ground state phase diagram of the model using perturbation theory and the numerical Lanczos method. The ground state phase diagram consists of two gapless Luttinger liquid (LL) and three gapped phases. Numerically, we calculate the concurrence between two spins and the entanglement entropy between legs. Numerical experiment shows that the gapless LL phases are fundamentally different. In the first LL phase, only spins on rungs are entangled, but in the second LL phase the spins on legs are long-distance entangled. Therefore, the concurrence between spins on legs can be considered as a function to distinguish the LL phases.     

A two-leg spin ladder model for fumarate-bridged chain-like polymer of Cu(II)

In this paper, the transfer matrix renormalization group method is used to study the thermodynamic and the magnetic properties of a novel one-dimensional fumarate-bridged Cu(II) chain by a two kinds of models. One simplified model is that of the dominant ferromagnetic and antiferromagnetic alternating chain, which is only in rough agreement with the experimental results. Further research shows a possible mechanism of alternating strong ferromagnetic and weak antiferromagnetic interaction among one chain. Considering the weak antiferromagnetic interaction existing in the actual materials, we propose a two-leg spin ladder model with intrachain ferromagnetic and weak interchain antiferromagnetic interaction. The obtained theoretical results are in quite good agreement with experimental curves, which indicates the two-leg spin ladder model is appropriate to describe the fumarate-bridged chain-like polymer of Cu(II).     

Field-induced Tomonaga-Luttinger liquid phase of a two-leg spin-1/2 ladder with strong leg interactions

We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an S=1/2 two-leg spin ladder in the strong-leg regime.     

Thermodynamic properties of a spin half ladder system

A complete dimerized state exists for one kind of two-leg spin half ladders, which has local antiferromagnetic ordering and frustration effect at the same time. The system’s low-lying excitations can be obtained exactly which enables us to calculate thermodynamic quantities such as specific heat and magnetic susceptibility at low temperatures. Our results also show that the subset energy spectrum is a good approximation to the whole spectrum even for the usual two-leg spin half ladder without frustration.     

Thermodynamic properties of a spin half ladder system

A complete dimerized state exists for one kind of two-leg spin half ladders, which has local antiferromagnetic ordering and frustration effect at the same time. The system’s low-lying excitations can be obtained exactly which enables us to calculate thermodynamic quantities such as specific heat and magnetic susceptibility at low temperatures. Our results also show that the subset energy spectrum is a good approximation to the whole spectrum even for the usual two-leg spin half ladder without frustration.     

Orbital effect of a magnetic field on two-leg Hubbard ladder

By setting up the relevant recursion relations and by doing exact and approximate calculations, we show that there is no critical dimension in a self-avoiding random walk on a simplex fractal. Received: 6 April 1998 / Revised: 4 August 1998 / Accepted: 26 August 1998     

两腿XXZ自旋梯子模型的量子相变与量子临界现象

对于无限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络(TN)算法数值模拟出基态波函数,首次尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

Phase diagram of interacting fermionic two-leg ladder with pair hopping

We study the phase diagram of the interacting fermionic two-leg ladder, which is featured by pair hopping and interactions of singlet and triplet superconducting channels. By using Abelian bosonization method, we obtain the full phase diagram of our model. The superconducting triplet pairing phase is characterized by a fractional edge spin and interpreted as two Kitaev chains under the mean filed approximation. The pair hopping will give rise to spin-density-wave(SDW)orders and can also support Majorana edge modes in spin channel. At half filling, the resulting Majorana-SDW phase shows additional fractionalization in charge channel, and can be interpreted as two Su–Schrieffer–Heeger(SSH) chains in the mean field regime.     

The ground state of the two-leg Hubbard ladder a density-matrix renormalization group study

We present density-matrix renormalization group results for the ground state properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an insulating spin-gapped system, exhibiting a crossover from a spin liquid to a band insulator as a function of the interchain hopping matrix element. When the system is doped, there is a parameter range in which the spin gap remains. In this phase, the doped holes from singlet pairs and the pair field and the “4k_F” density correlations associated with pair-density fluctuations decay as power laws, while the “2k_F” charge density wave correlations decay exponentially. We discuss the behavior of the exponents of the pairing and density correlations within this spin-gapped phase. Additional one-band Luttinger liquid phases which occur in the large interband hopping regime are also discussed.     

Intermediate dimensional character of charge transfer excitation modes in a two-leg cuprate ladder

Collective charge modes in the cuprate ladder compound Sr₁₄Cu₂₄O₄₁ are studied over the one-dimensional Brillouin zone using resonant inelastic X-ray scattering. Low energy (2-4 eV) spectral weight across the Mott gap is dominated by a broad, dispersive feature containing two distinct peaks that may be interpreted as independent modes. Details of low energy dispersion, intensity distribution across the Brillouin zone and peak composition fall between the characteristic spectra of quasi-1D (e.g. SrCuO₂) and -2D cuprates (e.g. Nd₂CuO₄). We demonstrate that dispersion and splitting between the two observed modes can be understood in a variant of the strong coupling limit (Hubbard-U?t) with a single band Hubbard model.     

Entanglement in (1/2,1) Mixed-Spin XY Model with Long-Range Interaction

In this study, we investigate entanglement in a two mixed-spin (1/2,1) XY Heisenberg spin system under an applied magnetic field by considering the long-range interaction with an inverse-square function. The spin-spin coupling constant is considered as a function of the distance between spins. We also discuss the temperature and magnetic field dependence of the thermal entanglement in this system for this interaction. The numerical results show that, in the presence of the long-range interaction, thermal entanglement between spins has a rich behavior dependent upon the interaction strength, temperature and magnetic field. We find that for less than a critical distance there are entanglement plateaus dependent upon the distance between spins, whereas above the critical distance the entanglement can exhibit sudden death.     

Trilayer Bethe lattices in the form of spin-(1/2,3/2,1/2)

The critical behaviors of the trilayer Bethe lattice in the form of spin-(1/2,3/2,1/2) with the exterior two layers consisting of spin-1/2 and the interior one having only spin-3/2 Ising spins are studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic bilinear exchange interactions between the nearest-neighbor spins. The ground-state phase diagrams are calculated and it is found that the model presents six different ground state phase configurations. The thermal variations of the order-parameter and free energy are investigated, therefore, topologically different phase diagrams of the model are obtained. It is found that the model exhibits second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3, 4 and 6 and, the reentrant behavior for q=4 and 6, respectively.     

High temperature thermal conductivity of two-leg spin-1/2 ladders

Based on numerical simulations, a study of the high temperature, finite frequency, thermal conductivity kappa(omega) of spin-1/2 ladders is presented. The exact diagonalization and a novel Lanczos technique are employed. The conductivity spectra, analyzed as a function of rung coupling, point to a nondiverging dc limit but to an unconventional low frequency behavior. The results are discussed in perspective with recent experiments indicating a significant magnetic contribution to the energy transport in quasi-one-dimensional compounds.