Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice

Shi-Ju Ran,1 Wei Li,2 Shou-Shu Gong,2,3 Andreas Weichselbaum,4 Jan von Delft,4 and Gang Su5,6,*

1ICFO–Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

2Department of Physics, Key Laboratory of Micro-nano Measurement-Manipulation and Physics (Ministry of Education), and International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China 3National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA

4Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-University, Munich 80333, Germany

5School of Physical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100049, China

6Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

We explore the frustrated spin-1/2 Heisenberg model on the star lattice with antiferromagnetic (AF) couplings inside each triangle and ferromagnetic (FM) intertriangle couplings (Je < 0), and calculate its magnetic and thermodynamic properties. We show that the FM couplings do not sabotage the magnetic disordering of the ground state due to the frustration from the AF interactions inside each triangle, but trigger a fully gapped inversion-symmetry-breaking trimerized valence bond crystal (TVBC) with emergent spin-1 degrees of freedom. We discover that with strengthening Je, the system exhibits a universal scaling behavior either with or without a magnetic field h: the order parameter, the five critical fields that separate the Je-h ground-state phase diagram into six phases, and the excitation gap obtained by low-temperature specific heat, all depend exponentially on Je. Our work implies that the spin-1 VBCs can be stabilized by introducing small FM couplings in the geometrically frustrated spin-1/2 systems.