  Quantum materials exhibiting magnetic frustration are connected to diverse
phenomena including high-Tc superconductivity, topological order and quantum
spin liquids (QSLs). A QSL is a quantum phase (QP) related to a
quantum-entangled fluid-like state of matter. Previous experiments on QSL
candidate materials are usually interpreted in terms of a single QP, although
theories indicate that many distinct QPs are closely competing in typical
frustrated spin models. Here we report on combined temperature-dependent muon
spin relaxation and specific heat measurements for the triangular-lattice QSL
candidate material 1T-TaS2 that provide evidence for competing QPs. The
measured properties are assigned to arrays of individual QSL layers within the
layered charge density wave structure of 1T-TaS2 and their characteristic
parameters can be interpreted as those of distinct Z2 QSL phases. The present
results reveal that a QSL description can extend beyond the lowest
temperatures, offering a new perspective in the search for novel quantum
materials.
