Asymmetric spin-1/2 two-leg ladders

Abstract

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_\perp. This model is characterized by a gap Δin the spectrum of spin excitations. We show that in the large J_\perp 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 Δ~ J_\perp. The second class appears for a strong asymmetry of the coupling along legs, κJ_|| << J_\perp << J_|| and is characterized by two energy scales: the exponentially small spin gap Δ~ J_\perp \exp(-J_|| / J_\perp), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange ~ J_\perp^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.

18 pages, 11 figures

References in corpus (28)

• Many-Body Physics with Ultracold Gases
• Correlated Electrons in High Temperature Superconductors
• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Bosonization and Strongly Correlated Systems
• DMRG and periodic boundary conditions: a quantum information perspective
• Dimerization and Incommensurate Spiral Spin Correlations in the Zigzag Spin Chain: Analogies to the Kondo Lattice
• Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
• On the Field-Induced Gap in Cu Benzoate and Other S=1/2 Antiferromagnets
• The Loop Algorithm
• Cluster algorithms for general-S quantum spin systems
• Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain
• Finite-lattice extrapolations for a Haldane gap antiferromagnet
• The ALPS project: open source software for strongly correlated systems
• Indirect RKKY interaction in any dimensionality
• Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain
• Efficient Matrix Product State Method for periodic boundary conditions
• Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg Model on the ladder
• Field-induced Antiferromagnetism and the Kondo Insulator-to-Metal Transition
• Massive triplet excitations in a magnetized anisotropic Haldane spin chain
• DMRG study of the Bond Alternating \textbf{S}=1/2 Heisenberg ladder with Ferro-Antiferromagnetic couplings
• Spin Gap in Chains with Hidden Symmetries
• A Luttinger Liquid Coupled to a Quantum Spin Bath: Flow Equation Approach to the Kondo Necklace Model
• Jordan-Wigner approach to dynamic correlations in spin-ladders
• Ferrimagnetic mixed-spin ladders in weak and strong coupling limits
• Bosonization for Wigner-Jordan-like Transformation : Backscattering and Umklapp-processes on Fictitious Lattice
• Spin gap and string order parameter in the ferromagnetic Spiral Staircase Heisenberg Ladder: a quantum Monte Carlo study
• Susceptibilities and Spin Gaps of Weakly-coupled Spin Ladders
• Centipede ladder at quarter filling

Cited by in corpus (11)

• Constrained sampling method for analytic continuation
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Incommensurate correlations in the anisotropic triangular Heisenberg lattice
• Phase diagram of the Hubbard-Kondo lattice model from variational cluster approximation
• Heisenberg Necklace Model in Magnetic Field
• Spin nematic states in antiferromagnets containing ferromagnetic bonds
• Phase diagram of a frustrated asymmetric ferromagnetic spin ladder
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Fractional spin excitations and conductance in the spiral staircase Heisenberg ladder
• Kondo spin liquid in Kondo necklace model: Classical disordered phase versus symmetry-protected topological state
• Spiral magnetism and chiral superconductivity in Kondo-Hubbard triangular lattice model