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Tb$_2$Ti$_2$O$_7$, a two singlet spin-liquid pyrochlore

The pyrochlore compound \tbti\ is known to remain in a spin-liquid state down to the lowest attainable temperature (0.05\,K), whereas current theories predict it should order into an antiferromagnetic structure. A number of models have been developed in order to resolve this discrepancy, but they could not obtain a spin-liquid ground state. We present here an explanation for the lack of magnetic order in \tbti\ based on the presence of a Jahn-Teller-like distortion from the local trigonal symmetry and on the physics of the two-singlet system coupled by exchange.