Quantum State Engineering in Spin-Ladder Platforms

　Spin ladders are quantum spin models consisting of coupled one-dimensional spin chains and represent a fundamental class of quantum many-body systems that bridge the gap between one and two dimensions. In spin-1/2 antiferromagnetic ladders, the ground state depends sensitively on the number of legs: even-leg ladders exhibit a quantum nonmagnetic state with a finite spin gap, whereas odd-leg ladders realize a gapless quantum-critical state. This topology-dependent behavior makes spin ladders an ideal platform for exploring the crossover between strong quantum fluctuations and classical magnetic orde. 

  Rather than treating spin ladders as fixed model systems, our research aims to actively engineer quantum states by introducing additional degrees of freedom through molecular design. By controlling exchange interactions, magnetic anisotropy, spin size, and randomness, we create and manipulate novel quantum phases that go beyond conventional ladder physics. From the perspective of “ladder structures × additional degrees of freedom,” we develop a new framework for quantum-state engineering, where quantum many-body states are designed and realized through bottom-up molecular material design.

1. Realization of a random-singlet state by introducing bond randomness  Phys. Rev. B  111, 134430 (2025)

 A spin-1/2 two-leg ladder is one of the most fundamental quantum spin models, exhibiting a nonmagnetic quantum ground state with a finite spin gap formed by singlet pairs across the ladder rungs. When randomness is introduced into the exchange interactions, however, the spin gap can collapse, giving rise to a random-singlet (RS) state consisting of singlet pairs formed over widely varying and often long distances. Such a disorder-driven quantum-critical state has been predicted theoretically for decades.

 In this study, we introduced bond randomness into a spin-ladder system through molecular design by randomly incorporating regioisomers of radical molecules into the crystal structure. This approach enabled us to control the exchange interactions at the molecular level and transform an otherwise uniform spin-gapped ladder into a disorder-dominated quantum-critical state.

 Magnetization measurements revealed gapless, continuous magnetization accompanied by a Curie contribution, while specific-heat measurements exhibited anomalous temperature dependence. These observations are in excellent agreement with theoretical predictions for the RS state and provide compelling experimental evidence for a bond-randomness-induced RS phase.

 This work demonstrates that disorder, traditionally regarded as an unavoidable imperfection, can instead be transformed into a controllable design parameter through molecular engineering. It represents a realization of quantum-state engineering using disorder, opening a new route toward the creation and control of emergent quantum phases.

2. Quantum–Classical Hybrid Design: Embedding Classical Degrees of Freedom into a Quantum Ladder   Phys. Rev. B  112, 224419 (2025)

 Spin-1/2 two-leg ladders are prototypical quantum magnetic systems characterized by strong quantum fluctuations, exhibiting a variety of quantum many-body phenomena such as spin gaps and quantum-critical behavior. Despite extensive theoretical studies, little is known experimentally about how robust these quantum states remain when coupled to external degrees of freedom or classical spins in real materials.

In this study, we designed and synthesized a hybrid-spin (three-leg) ladder in which a chain of high-spin Mn²⁺ ions (S = 5/2) is embedded between two quantum spin-1/2 radical chains forming a two-leg ladder. This molecular architecture creates a strongly coupled system consisting of a quantum spin ladder and a nearly classical spin chain. By embedding classical degrees of freedom directly into a quantum system, we established a unique experimental platform for testing the stability of quantum fluctuations themselves.

 Magnetization and specific-heat measurements revealed that the characteristic quantum properties of a pure spin-1/2 ladder—including the spin gap and low-dimensional quantum-critical behavior—are completely suppressed. Instead, the system exhibits long-range magnetic order that can be described by classical spin-wave and mean-field theories. These results provide direct evidence that the introduction of classical degrees of freedom effectively weakens quantum fluctuations, driving the system from a quantum phase toward a classical magnetic state.

 This work demonstrates that spin size can serve as a powerful design parameter for controlling the strength and stability of quantum fluctuations. It represents the first experimental realization of a hybrid-spin ladder designed to test the robustness of quantum ladder states and opens a new direction for quantum-state engineering based on spin-ladder architectures.

3. Engineering Ising-Type Quantum States through Magnetic Anisotropy  Phys. Rev. B  112, 014430 (2025)

 In one-dimensional spin systems, exchange anisotropy plays a crucial role in determining the nature of the ground state and excitation spectrum. In particular, in systems with strong Ising anisotropy, weak interchain interactions confine spinons, transforming the excitation continuum into a series of discrete energy levels known as a Zeeman ladder. Despite the fundamental importance of such phenomena, material platforms in which strong exchange anisotropy can be systematically designed and controlled at the molecular level remain rare.

 In this study, we created a new ladder-based quantum spin architecture, termed the hexagonal-plaquette chain, through molecular design. By combining organic radicals with Co²⁺ ions possessing strong spin–orbit coupling, we realized a unique one-dimensional structure composed of edge-sharing hexagonal plaquettes. We further demonstrated that the low-energy degrees of freedom of this system can be perturbatively mapped onto an effective spin-1/2 Ising chain.

 Molecular-orbital calculations and ESR measurements revealed strongly anisotropic g tensors and exchange interactions, providing direct evidence that the hexagonal-plaquette chain intrinsically hosts strong Ising-type magnetic anisotropy. Specific-heat measurements further indicated the presence of an anisotropy-induced excitation gap and signatures of discrete excitations arising from spinon confinement by weak interchain couplings, consistent with the formation of a Zeeman-ladder spectrum.

 This work demonstrates how crystal-field effects and spin–orbit coupling can be incorporated as design parameters to engineer magnetic anisotropy and realize a new quantum spin model based on ladder architectures. The hexagonal-plaquette chain represents a concrete example of anisotropy engineering, where quantum states are designed through the extension and deformation of ladder structures, opening new opportunities for quantum-state engineering in molecular quantum materials.