Weakly disordered spin ladders

2002

We study antiferromagnetic two-leg spin-1/2 ladders with strong bond randomness, using the real space renormalization group method. We find the low-temperature spin susceptibility of the system follows non-universal power laws, and the ground state spin-spin correlation is short-ranged. Our results suggest that there is no phase transition when the bond randomness increases from zero; for strong enough randomness the system is in a Griffith region with divergent spin susceptibility and short-range spin-spin correlation.

2012

One-dimensional (1D) spin chains have been extensively studied over the years both experimentally and theoretically. Spin chains are good approximations to the magnetism of diverse inorganic and organic crystals. They are simple manybody quantum systems, well suited for computational studies, 1 with some exactly known properties and rich ground-state (GS) phase diagrams. Solid-state studies focus broadly on magnetic properties, instabilities, and phase transitions that limit 1D behavior at low temperature.

Journal of physics. Condensed matter : an Institute of Physics journal, 2016

The spin-1/2 chain with isotropic exchange J 1, J 2 > 0 between first and second neighbors is frustrated for either sign of J 1 and has a singlet ground state (GS) for J 1/J 2 ⩾ -4. Its rich quantum phase diagram supports gapless, gapped, commensurate (C), incommensurate (IC) and other phases. Critical points J 1/J 2 are evaluated using exact diagonalization and density matrix renormalization group calculations. The wave vector q G of spin correlations is related to GS degeneracy and obtained as the peak of the spin structure factor S(q). Variable q G indicates IC phases in two J 1/J 2 intervals, [-4, - 1.24] and [0.44, 2], and a C-IC point at J 1/J 2 = 2. The decoupled C phase in [-1.24, 0.44] has constant q G = π/2, nondegenerate GS, and a lowest triplet state with broken spin density on sublattices of odd and even numbered sites. The lowest triplet and singlet excitations, E m and E σ , are degenerate in finite systems at specific frustration J 1/J 2. Level crossing e...

Nuclear Physics B, 1999

The influence of non-magnetic doping on the thermodynamic properties of two-leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero-modes) in the framework of a generalized Dirac model. The low-temperature thermodynamic properties are dominated by these zero-modes. We use the single-fermion density of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder. In particular, we find that the magnetic susceptibility χ diverges at T-->0 as 1/Tln 2(1/T), and the specific heat behaves as C~1/ln 3(1/T). The predictions on magnetic susceptibility are consistent with the most recent results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic susceptibility induced in the system by such defects.

Physical Review B

The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five-and seven-membered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction (J 2 = 1) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (J 1) along the rungs. As a function of J 1 , the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of various gs properties such as spin gap, spin-spin correlations, spin density, and bond order reveal that the system has four distinct phases, namely, the AF phase at small J 1 ; the ferrimagnetic phase with gs spin S G = n for 1.44 < J 1 < 4.74 and with S G = 2n for J 1 > 5.63, where n is the number of unit cells; and a reentrant nonmagnetic phase at 4.74 < J 1 < 5.44. The system also shows the presence of spin current at specific J 1 values due to simultaneous breaking of both reflection and spin parity symmetries.

Physical Review B, 1996

We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains. It is shown that the system always has a spectral gap. For the case of identical chains the model in the continuous limit is equivalent to 4 decoupled noncritical Ising models. For this case we obtain the exact expressions for the asymptotics of spin-spin correlation functions. When the chains have different exchange integrals the spectrum at low energies is well described by the O(3) nonlinear sigma model. We discuss the topological order parameter related to the gap formation and give a detailed description of the dynamical magnetic susceptibility.

2010

We consider asymmetric spin-1/2 two-leg ladders with non-equal antiferromagnetic (AF) couplings J and κJ along legs (κ ≤ 1) and ferromagnetic rung coupling, J ⊥ . This model is characterized by a gap ∆ in the spectrum of spin excitations. We show that in the large J ⊥ limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at κ = 1, admits a linear scaling for the spin gap ∆ ∼ J ⊥ . The second class appears for a strong asymmetry of the coupling along legs, κJ J ⊥ J and is characterized by two energy scales: the exponentially small spin gap ∆ ∼ J ⊥ exp(−J /J ⊥ ), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ∼ J 2 ⊥ /J . We report numerical results obtained by exact diagonalization, density matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetry. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.

Physica A: Statistical Mechanics and its Applications, 2004

We investigate the Hamiltonian dynamics of two low-dimensional quantum spin systems in a random ÿeld, at the inÿnite-temperature limit: the XY chain and the two-leg XY ladder with interchain Ising interactions. We determine the longitudinal spin autocorrelation functions of the spin-1 2 XY chain and ladder in the presence of disordered ÿelds by using the method of recurrence relations. The ÿrst six basis vectors for the chain and the ÿrst four basis vectors for the ladder of the dynamic Hilbert spaces of z j (t), as well as the corresponding recurrents and moments of the time-dependent autocorrelation function, are analytically computed for bimodal distributions of the ÿelds. We did ÿnd a remarkable result in the disordered models. Cases with a fraction of p sites under ÿeld BB and a fraction of 1 − p sites under the ÿeld BA have the same longitudinal dynamics as those with p sites under ÿeld BA and 1 − p sites under the ÿeld BB. We also ÿnd that both the XY chain and the two-leg XY ladder with Ising interchain coupling in the presence of random ÿelds are sensitive to the percentage of disorder but not to the intensity of the ÿelds.

Physical review. B, Condensed matter, 1991

The model that we study is a two-XY-quantum-spin-chain system with Ising interchain magnetic interaction. This model, referred to as the spin-ladder model, is used as a first step to model the thermodynamic properties of low-dimensional spin system. Similarities between the spin-ladder model and the one-dimensional Hubbard model are used in our analysis. As a consequence we can qualitatively understand the heat capacity and spin susceptibilty and show that both measurements are necessary to analyze a spin-ladder system. We also show that the strong-interchain-coupling limit of the spin-ladder model is equivalent to a one-chain spin Heisenberg Hamiltonian. Furthermore, the spin-Peierls transition is investigated for small (~I/2J~&& 1) and large (~I/2J~)) 1) interchain coupling, and we show its occurrence at relatively small spin-phonon coupling (A, 0.6). From the results obtained for the smalland large-interchain-interaction limits, we propose the conjecture that the in-phase dimerization persists for all values of the interaction parameter at zero temperature.

Physical Review A, 2010

We observe signatures of disorder-induced order in 1D XY spin chains with an external, sitedependent uni-axial random field within the XY plane. We numerically investigate signatures of a quantum phase transition at T = 0, in particular an upsurge of the magnetization in the direction orthogonal to the external magnetic field, and the scaling of the block-entropy with the amplitude of this field. Also, we discuss possible realizations of this effect in ultra-cold atom experiments.