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Abstract: We explore the small-temperature regime in the deconfined phase of massive fundamental matter at finite baryon number density coupled to the 3+1 dimensional N = 4 SYM theory. In this setting, we can demonstrate a new type of non-trivial temperature-independent scaling solutions for the probe brane embeddings. Focusing mostly on matter supported in 2+1 dimensions, the thermodynamics indicate that there is a quantum liquid with interesting density-dependent low-temperature physics. We also comment about 3+1 and 1+1 dimensional systems, where we further find for example a new thermodynamic instability. ar X i