It is a salient experimental fact that a large fraction of candidate spin liquid materials freeze as the temperature is lowered. The question naturally arises whether such freezing is intrinsic to the spin liquid (disorder-free glassiness) or extrinsic, in the sense that a topological phase simply coexists with standard freezing of impurities. Here, we demonstrate a surprising third alternative, namely that freezing and topological liquidity are inseparably linked. The topological phase reacts to the introduction of disorder by generating degrees of freedom of a new type (along with interactions between them), which in turn undergo a freezing transition while the topological phase supporting them remains intact.
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