Continuous Matrix Product States for Inhomogeneous Quantum Field Theories: a Basis-Spline Approach

TL;DR

This paper introduces a spline-based parametrization for continuous matrix product states (cMPS), enabling efficient ground state optimization of inhomogeneous quantum field theories, demonstrated on Lieb-Liniger bosons in a periodic potential.

Contribution

It presents a novel spline-based cMPS parametrization and regauging techniques, extending ground-state optimization to inhomogeneous systems.

Findings

Successful implementation of inhomogeneous cMPS optimization

Application to Lieb-Liniger bosons in a periodic potential

First practical approach for non-translational invariant Hamiltonians

Abstract

Continuous Matrix Product States (cMPS) are powerful variational ansatz states for ground states of continuous quantum field theories in (1+1) dimension. In this paper we introduce a novel parametrization of the cMPS wave function based on basis-spline functions, which we coin spline-based MPS (spMPS), and develop novel regauging techniques for inhomogeneous cMPS. We extend a recently developed ground-state optimization algorithm for translational invariant cMPS [M. Ganahl, J. Rinc\'on, G.Vidal. Phys.Rev.Lett. 118,220402 (2017)] to the case of inhomogeneous cMPS and, as proof-of-principle, use it to obtain the ground-state of a gas of Lieb-Liniger bosons in a periodic potential. The proposed method provides a first working implementation of a cMPS optimization for non-translational invariant continuous Hamiltonians.