Spin Ladder Models Research Articles

Energy spectrum and magnetic properties of the decorated spin ladder models of nanomagnets on the base of polymeric transition metal compounds

The work is devoted to the theoretical study of the energy spectrum and low-temperature magnetic properties of the decorated spin-ladder model with the polyacene topology and the three types of the site spins. On the base of cluster expansion technique an approximate analytical treatment of lowest part of the energy spectra of two isomeric ladder structures was given. It is shown that the ladder model with singlet ground state is more stable than its isomeric analog with the macroscopic ground state spin. In addition, the numerical study of field dependence of low-temperature magnetization of 8- spin clusters of both ladder models was performed by means of exact diagonalization method. On the base of these results, it was shown the presence of an intermediate plateau in low-temperature magnetization profile of the above spin ladder models.

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intra-edge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the inter-edge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intra-edge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intra-chain couplings. The results for the critical exponents are compared also to several recent renormalization group calculations for related long-ranged interacting quantum systems.

Symmetry-protected topological orders of one-dimensional spin systems withD2+Tsymmetry

In Liu et al. [Phys. Rev. B 84, 075135 (2011)] we studied eight gapped symmetric quantum phases in $S=1$ spin chains/ladders which respect a discrete spin rotation ${D}_{2}\ensuremath{\subset}SO(3)$ and time reversal $T$ symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of one-dimensional (1D) integer spin systems with ${D}_{2}+T$ symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We show that all the 16 SPT orders can be fully characterized by the physical properties of the symmetry protected degenerate boundary states at the ends of a chain segment. So we can measure and distinguish all the 16 SPT orders experimentally. We also show that all these SPT orders can be realized in $S=1$ spin chain or spin ladder models. The gapped symmetric phases protected by subgroups of ${D}_{2}+T$ are also studied. Again, all these phases can be distinguished by physically measuring their end ``spins.''

Energy-level ordering for frustrated spin ladder models

The Lieb—Mattis theorem about ordering of energy levels is generalized to frustrated antiferromagnetic spin-1/2 ladder model with diagonal and four-spin interaction.

Existence of dimerized phases in frustrated spin ladder models

In the present paper, by using the density-matrix renormalization-group technique, we investigate the existence of dimerized phases in a frustrated spin-1/2 ladder model. By calculating the two-rung localizable entanglement and, in particular, its first-order derivative in the ground state, we show that an intermediate columnar dimerized phase exists indeed in a narrow parameter region between the rung-singlet and the Haldane phases. Furthermore, by introducing an additional interchain next-nearest-neighbor exchange interaction, the stability of this phase can be greatly enhanced and a staggering dimerized phase also appears in the phase diagram. Our results confirm the previous conclusions derived by the bosonization methods.

Topological order, dimerization, and spinon deconfinement in frustrated spin ladders

We consider topological order and dimer order in several frustrated spin ladder models, which are related to higher-dimensional models of current interest; we also address the occurrence of fractionalized phases with deconfined spinon excitations in these models. Combining results obtained with both analytic and numerical methods, we discuss how the occurrence of dimerized or fractionalized phases is dictated by the system's geometry.

Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds

(abbreviated) 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 real compounds. The ground state properties of the integrable two-leg spin-1/2 and the mixed spin-(1/2,1) ladder models at zero temperature are analyzed by means of the Thermodynamic Bethe Ansatz. Solving the TBA equations yields exact results for the critical fields and critical behaviour. The thermal and magnetic properties of the models are investigated in terms of the recently introduced High Temperature Expansion method, which is discussed in detail. It is shown that in the strong coupling limit the integrable spin-1/2 ladder model exhibits three quantum phases: (i) a gapped phase in the regime $H<H_{c1}$, (ii) a fully polarised phase for $H>H_{c2}$, 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 is of the 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 a range of strong coupling ladder compounds. Similar analysis of the mixed spin-(1/2,1) ladder model reveals a rich phase diagram, with a 1/3 and a full saturation magnetisation plateau within the strong antiferromagnetic rung coupling regime. For weak rung coupling, the fractional magnetisation plateau is diminished and a new quantum phase transition occurs. The phase diagram can be directly deduced from the magnetisation curve obtained from the exact result derived from the HTE. The thermodynamics of the spin-orbital model with different single-ion anisotropies is also investigated.

Two-magnon Raman scattering in spin ladders with exact singlet-rung ground state

We suggest a family of spin-ladder models with exact singlet-rung vacuum. In addition to the terms describing interactions along legs and rungs the Hamiltonian has frustration and cyclic terms. Using coordinate Bethe ansatze all one- and two-dimensional states are constructed. The explicit formula for zero-temperature Raman scattering cross section is derived. The corresponding line-shapes are strongly asymmetric and have no more than one van-Hove singularity. The results are in good agreement with experimental data.

Scalar chiral order in spin ladders with four-spin exchanges

We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder. By using the spin-chirality duality transformation, it is found that scalar-chiral-ordered states are exact ground states in a family of spin ladder models. In the scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states. It is also shown that the SU(4)-symmetric model is on a multicritical point surrounded by the staggered dimer, staggered scalar chiral, and gapless phases.

Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter.

Scalar chiral ground states of spin ladders with four-spin exchanges

We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states in a family of spin ladder models. In this scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states and a ${Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ symmetry is fully broken. It is also shown that the SU(4)-symmetric model, which is self-dual under the duality transformation, is on a multicritical point surrounded by the staggered dimer phase, the staggered scalar chiral phase, and the gapless phase.

The extended spin ladder and net models: exact dimer ground state and quantum phase transition

We investigate an extended spin ladder with diagonal frustrated exchanges in a wide parameter regime. By representing the model as a sum of semidefinite positive projection operators, we prove that this model has exactly a dimer ground state. Smoothly changing parameters may lead the model cover several exactly known models. Starting from this ladder model, we proposed two two-dimensional net models with exact ground states. The quantum phase transition of the ground state, due to the change of exchange strengths along perpendicular rungs, is also discussed.

Strongly disordered spin ladders

The effect of quenched disorder on the low-energy properties of various antiferromagnetic spin-ladder models is studied by a numerical strong disorder renormalization-group method and by density-matrix renormalization. For strong enough disorder the originally gapped phases with finite topological or dimer order become gapless. In these quantum Griffiths phases the scaling of the energy, as well as the singularities in the dynamical quantities, are characterized by a finite dynamical exponent, z, which varies with the strength of disorder. At the phase boundaries, separating topologically distinct Griffiths phases the singular behavior of the disordered ladders is generally controlled by an infinite randomness fixed point.

Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

We extend the results of spin ladder models associated with the Lie algebras $su(2^n)$ to the case of the orthogonal and symplectic algebras $o(2^n),\ sp(2^n)$ where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX type rung interactions and applied magnetic field term.

Non-Haldane Spin-Liquid Models with Exact Ground States

We present a family of spin-ladder models which can be solved exactly for the ground state and exhibit non-Haldane spin-liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. 78, 3939 (1997)], and study their excitation spectra using a simple variational Ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.

Magnetic excitations in the spin ladder system (VO)2P2O7

We present the results of elastic and inelastic neutron scattering measurements made on a powder sample of the spin-ladder compound (VO)2P2O7. The elastic scattering measurements made at a temperature of 10 K showed no magnetic structure, consistent with a singlet ground state. The inelastic measurements, also at 10 K, revealed three magnetic modes at 3.5, 6.0, and 14 meV. Theoretical treatments of spin ladder models point to an identification of the 3.5 meV mode as the minimum in the one-magnon dispersion, and the 14 meV mode as the local minimum in the associated two-magnon continuum. However, we have been unable to explain the scattering at 6.0 meV using existing theories of spin ladders.

Absence of superconductivity in the doped antiferromagnetic spin-ladder compound (La,Sr)CuO2.5

A SPIN-½ Heisenberg antiferromagnetic ladder is a model system comprising parallel chains of interacting elemental spins. Spin ladders having an even number of chains have been predicted1a¤-6 to exhibit interesting dynamics, including superconductivity, when unoccupied spin sites are introduced along the chain (that is, when the chains are doped with holes). Spin-ladder models thus provide a novel potential mechanism for high-temperature superconductivity in real materials. But unfortunately materials with spin-ladder structure are quite rare4a-10, and the few known compounds have not previously been doped successfully with holes. Here we report the high-pressure synthesis of a new hole-doped two-chain ladder compound, La1a¤-xSrxCuO2.5. We have observed a marked insulator-to-metal transition in this compound with increased doping, but no superconducting transition down to 5 K. The absence of superconductivity in this material must be reconciled with theoretical predictions based on ideal hole-doped spin-ladder models.