Extended Diamond Chain

Quantum phase with spontaneous translational symmetry breaking in an extended dimaond chain  Phys. Rev. B 112, 094420  (2025) 

New Frontiers in 1D Quantum Systems Enabled by Triangular Units 

—Topological Quantum Phases and Spontaneous Symmetry Breaking in an Extended Diamond Chain—

 Triangular units with geometric frustration are fascinating building blocks in quantum spin systems, capable of generating quantum states that cannot be realized in conventional spin lattices. In 1D systems, where quantum fluctuations are particularly strong, the interplay between frustration and reduced dimensionality provides an ideal setting for the emergence of novel quantum phases closely linked to topology and symmetry. In this study, we successfully realized a new quantum spin model, the extended diamond chain, in which triangular units are connected along a 1D lattice through molecular design.

This spin lattice can be regarded as an extension of the conventional diamond chain, incorporating multiple competing interactions that introduce magnetic frustration. Magnetization measurements and theoretical analyses revealed that the ground state is a nonmagnetic spin-gapped phase. Furthermore, the low-energy effective model can be mapped onto a nonlinear sigma model, demonstrating that the ground state belongs to a symmetry-protected topological (SPT) phase equivalent to the Haldane phase. These results provide experimental evidence that topological quantum phases can emerge in 1D frustrated systems built from triangular units.

 At higher magnetic fields, we discovered an unusual quantum phase above the one-half magnetization plateau, characterized by spontaneous symmetry breaking (SSB) of the translational symmetry. This phase can be understood as a state in which spins spontaneously dimerize due to frustration-induced effective next-nearest-neighbor interactions. The coexistence of a spin gap and field-induced spontaneous symmetry breaking is rare in 1D quantum systems, making the extended diamond chain a unique experimental realization of this phenomenon.

 These findings establish the extended diamond chain as a new platform for exploring quantum many-body phenomena arising from the interplay between topological order and spontaneous symmetry breaking. More broadly, they demonstrate how lattice topology and frustration can be harnessed to engineer previously unexplored quantum states in low-dimensional magnetic systems.