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.
We study a spin-half frustrated coupled ladder system, in which ladders with leg, rung, and diagonal interactions are linked via nearest-neighbor coupling. By introducing a leg-symmetric inter-ladder interaction that connects the left-to-left and right-to-right legs of adjacent ladders, the model is found to possess an exact dimer ground state, characterized by a product of two-spin singlets forming a columnar dimer phase. We analyze this model using bond-operator mean-field theory (BOMFT) and the density matrix renormalization group (DMRG) to probe the phase transitions that occur as one traverses the coupling space. The BOMFT reveals three distinct phases: a double-stripe ordered phase, a Néel ordered phase, and a quantum disordered dimerized phase. The critical points for the transitions are at $ J_1 = -0.81 $ (double-stripe to dimerized) and at $ J_1 = 2.81 $ (dimerized to Néel phase). Further, the DMRG results corroborate the exact ground state and refine the critical points to $ J_1 = -0.79 $ and $ J_1 = 2.29 $ for the respective transitions. Additionally, another transition is identified as the Néel order vanishes for $ J_1 \ge 4.5 $. The model can alternatively be represented as a network of orthogonal zigzag and fully frustrated spin ladders, offering a structural framework conducive to quantum materials engineering.
Abstract In this work, we consider a frustrated two‐leg spin‐1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin‐1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non‐collinear ferrimagnetic (NCF), , antiferromagnetic and dimer phases. The quantum phase diagram is constructed for the Heisenberg spin‐1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the stability of phase and calculate the pitch angle in the NCF phase.
The frustrated ladder with alternate ferromagnetic(F) exchange
−JF and AF exchange
JA to first neighbors and F exchange
−JL to second neighbors is studied by exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations in systems of
2N spins-1/2 with periodic boundary conditions. The ground state is a singlet
(S=0) and the singlet-triplet gap
εT is finite for the exchanges considered. Spin-1/2 string correlation functions
g1(N) and
g2(N) are defined for an even number
N of consecutive spins in systems with two spins per unit cell; the ladder has string order
g2(∞)>0 and
g1(∞)=0. The minimum
N∗ of
g2(N) is related to the range of ground-state spin correlations. Convergence to
g2(∞) is from below, and
g1(N) decreases exponentially for
N≥N∗. Singlet valence bond (VB) diagrams account for the size dependencies. The frustrated ladder at special values of
JF,
JL and
JA reduces to well-known models such as the spin-1 Heisenberg antiferromagnet and the
J1−J2 model, among others. Numerical analysis of ladders matches previous results for spin-1 gaps or string correlation functions and extends them to spin-1/2 systems. The nondegenerate singlet ground state of ladder is a bond-order wave, a Kekulé VB diagrams at
JL=JF/2≤JA, that is reversed on interchanging
−JF and
JA. Inversion symmetry is spontaneously broken in the dimer phase of the
J1−J2 model where the Kekulé diagrams are the doubly degenerate ground states at
J2/J1=1/2.
We investigate a frustrated four-leg spin-1/2 ladder using density matrix renormalization group calculations. The uniform system displays three regimes: short-range antiferromagnetic legs, short-range ferromagnetic legs, and an effective spin-2 Heisenberg chain, separated by a crossover and a first-order transition. The spin-2 regime is confirmed through its finite string order parameter, edge-localized excitations, and excellent agreement with a projected Sr = 2 effective Hamiltonian. Recasting the model as two frustrated two-leg ladders coupled by rung and diagonal interactions, we track how the trivial and Haldane phases of an isolated ladder evolve as interladder couplings are introduced. The resulting phase diagrams reveal crossover and first-order lines whose locations are captured by the spin-2 projection and show how singlet- and triplet-dominated regimes reorganize when two ladders merge into a four-leg structure, clarifying the emergence of effective spin-1 versusspin-2 behavior.
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.
Abstract Ladders with 2 N spins-1/2 and singlet ( S = 0) ground states are studied numerically using exact diagonalization and density matrix renormalization group (DMRG) calculations. The curvatures E ″ ( s ) of states with the lowest energy E ( s ) at spin s = S / N ≤ 1 are obtained in the thermodynamic limit. All states have E ″ ( s ) > 0 in two phases, one with strong F exchange J F in rungs, the other with strong F exchange J L in legs. The Dimer phase with frustrated F exchanges has one or more states with E ″ ( s ) < 0. All three phases have finite gaps to the lowest triplet state. The ladder at J F → ∞ is adiabatically connected to the spin-1 Heisenberg AF chain, and at J L → ∞ to the J 1 − J 2 model.