Quantum matter describes physical systems specified by two characteristics. The first characteristic is that salient properties of these systems are emergent properties of a quantum many-body system. Here we are using these notions in the same way P. Anderson did in his famous paper More is different. Anderson does not use the word ``emergent'', but he posits that the properties of complex systems cannot be reconstructed from the simple fundamental laws. This is what we mean by emergent. The second characteristic of Quantum Matter is that it describes those systems whose emergent properties are intrinsically quantum. A good example is superconductivity, whose properties are explained by a macroscopic quantum wave-function. The quantum fluctuations and the coherence of this wave-function are fundamental to explain superconductivity. In past twenty years, there has been a flourishing of contexts where our definition applies. The subject of quantum matters includes as subjects of interest Topological phases of matter,
Critical phases of matter and exotic quantum critical points,
State-of-the-art numerical and analytic approaches to the many-body problem, application of modern information and complexity theory to quantum many-body physics, quantum error correction, CFT, and bulk locality in holography and beyond, non-equilibrium phenomena, quantum chaos, scrambling, and complexity in quantum matter and holography.