Charge density waves in strongly correlated electron systems

Strong electron correlations are at the heart of many physical phenomena of current interest to the condensed matter community. Here we present a survey of the mechanisms underlying such correlations in charge density wave (CDW) systems, including the current theoretical understanding and experimental evidence for CDW transitions. The focus is on emergent phenomena that result as CDWs interact with other charge or spin states, such as magnetism and superconductivity. In addition to reviewing the CDW mechanisms in 1D, 2D, and 3D systems, we pay particular attention to the prevalence of this state in two particular classes of compounds, the high temperature superconductors (cuprates) and the layered transition metal dichalcogenides. The possibilities for quantum criticality resulting from the competition between magnetic fluctuations and electronic instabilities (CDW, unconventional superconductivity) are also discussed.