Continuous matrix product states with periodic boundary conditions and an application to atomtronics

TL;DR

This paper develops a new time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions, enabling efficient simulation of atomtronic systems like rotating Bose gases with barriers.

Contribution

It introduces a variational algorithm for continuous matrix product states with periodic boundaries, including boundary degrees of freedom for impurity problems, with improved computational efficiency.

Findings

Successfully applied to an atomtronic Bose gas in a ring trap.

Allows for spectral cutoff in transfer matrix, enhancing efficiency.

Demonstrates applicability to quantum impurity problems.

Abstract

We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system - an interacting Bose gas rotating in a ring shaped trap in the presence of a localised barrier potential.