Density matrix renormalization group for continuous quantum systems

Dutta, Shovan and Buyskikh, Anton and Daley, Andrew J. and Mueller, Erich J. (2022) Density matrix renormalization group for continuous quantum systems. Physical Review Letters, 128 (23). 230401. ISSN 1079-7114 (

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We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each segment. By combining this mapping with existing numerical density matrix renormalization group routines, we show how one can accurately obtain the ground-state wave function, spatial correlations, and spatial entanglement entropy directly in the continuum. For a prototypical mesoscopic system of strongly interacting bosons we demonstrate faster convergence than standard grid-based discretization. We illustrate the power of our approach by studying a superfluid-insulator transition in an external potential. We outline how one can directly apply or generalize this technique to a wide variety of experimentally relevant problems across condensed matter physics and quantum field theory.