Density-Matrix Renormalization Group for Continuous Quantum Systems

TL;DR

This paper presents a new method that adapts matrix product state techniques to continuous quantum systems, enabling accurate analysis of ground states, correlations, and entanglement directly in the continuum.

Contribution

It introduces a practical framework combining space segmentation and basis functions with DMRG routines for continuous systems, improving convergence and applicability.

Findings

Faster convergence than grid-based methods for bosonic systems

Accurate computation of ground states and correlations in continuum

Application to superfluid-insulator transition in external potential

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.