Density-Matrix Renormalization Group for Continuous Quantum Systems

Abstract

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.

Main paper: 7 pages, 5 figures; Supplement: 13 pages, 5 figures

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• Realizing multiband states with ultracold dipolar quantum simulators
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Probing non-Gaussian correlations through entanglement generation in a many-body quantum system
• Diminished quantum depletion and correlated droplets in one-dimensional dipolar Bose gas
• Fractal Path Strategies for Efficient 2D DMRG Simulations