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Quantum dimer phases in a frustrated spin ladder

T. Vekua, A. Honecker

Published Jan 24, 2006• 0 citations
OpenAlex

Abstract

The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.

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The phase diagram of a frustrated $S=1∕2$ antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and in-chain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.

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Exact columnar dimer ground state and quantum phase transitions in a frustrated coupled spin ladder model

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arXiv:2602.13406•Feb 13, 2026•0 citations
The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
The phase diagram of a frustrated S=1∕2S=1∕2S=1∕2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and in-chain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
We study the ground-state phase diagram of a spin-12\frac{1}{2}21​ frustrated XXZ ladder, in which two antiferromagnetic chains are coupled by competing rung and diagonal interactions, ${J}_{\ensuremath{\perp}}$ and ${J}_{\ifmmode\times\else\texttimes\fi{}}$. Previous studies on the isotropic model have revealed that a fluctuation-induced effective dimer attraction between the legs stabilizes the columnar dimer (CD) phase in the highly frustrated regime ${J}_{\ensuremath{\perp}}\ensuremath{\approx}2{J}_{\ifmmode\times\else\texttimes\fi{}}$, especially for ferromagnetic ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}<0$. By means of effective field theory and numerical analyses, we extend this analysis to the XXZ model, and we obtain a rich phase diagram. The diagram includes four gapped featureless phases with no symmetry breaking: the rung singlet (RS) and Haldane phases as well as their twisted variants, the RS* and Haldane* phases, which are all distinct in the presence of certain symmetries. Significantly, the Haldane-CD transition point in the isotropic model turns out to be a crossing point of two transition lines in the XXZ model, and the stripe N\'eel and RS* phases appear between these lines. This indicates a nontrivial interplay between the effective dimer attraction and the exchange anisotropy. In the easy-plane regime, the four featureless phases and two critical phases are found to compete in a complex manner depending on the signs of ${J}_{\ensuremath{\perp},\ifmmode\times\else\texttimes\fi{}}$.
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.
The ground-state properties of spin-1/2 ladders are studied, emphasizing the role of frustration and ring exchange coupling. We present a unified field theory for ladders with general coupling constants and geometry. Rich phase diagrams can be deduced by using a renormalization group calculation for ladders with in-chain next-nearest-neighbor interactions and plaquette ring exchange coupling. In addition to established phases such as Haldane, rung singlet, and dimerized phases, we also observe a surprising instability towards an incommensurate phase for weak interchain couplings, which is characterized by an exotic coexistence of self-consistent ferromagnetic and antiferromagnetic order parameters.
The spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Néel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.
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.