Zero modes, bosonization, and topological quantum order: The Laughlin state in second quantization

Fractional Quantum Hall (FQH) wave functions are usually obtained in a first-quantized language, using special properties of analyticity of the lowest Landau level (LLL) wave functions. Unfortunately, this formalism is not directly applicable to several systems different from the LLL, such as the recently discovered fractional Chern insulators. Introducing a second-quantized formalism represents an important step towards a new understanding of FQH wave functions in terms of the guiding center degrees of freedom only. In this paper, the authors present several applications of the formalism, including an explicit derivation of the second-quantized version of Read's string order parameter for the Laughlin state.