Continuous matrix product states for coupled fields: Application to Luttinger Liquids and quantum simulators

TL;DR

This paper introduces a new method for constructing continuous matrix product states for coupled quantum fields, enabling better analysis of Luttinger liquids and proposing a quantum simulation architecture.

Contribution

It presents a novel scheme for cMPS of coupled fields based on dissipative dynamics, extending the applicability of cMPS to complex quantum systems.

Findings

Validated the method with DMRG results for Lieb-Liniger models

Characterized Luttinger liquid behavior using the new cMPS approach

Proposed a circuit QED setup as a quantum simulator for coupled fields

Abstract

A way of constructing continuous matrix product states (cMPS) for coupled fields is presented here. The cMPS is a variational \emph{ansatz} for the ground state of quantum field theories in one dimension. Our proposed scheme is based in the physical interpretation in which the cMPS class can be produced by means of a dissipative dynamic of a system interacting with a bath. We study the case of coupled bosonic fields. We test the method with previous DMRG results in coupled Lieb Liniger models. Besides, we discuss a novel application for characterizing the Luttinger liquid theory emerging in the low energy regime of these theories. Finally, we propose a circuit QED architecture as a quantum simulator for coupled fields.