Entanglement Continuous Unitary Transformations

TL;DR

Entanglement-CUT (eCUT) is a tensor network-based method that approximates continuous unitary transformations to analyze quantum many-body Hamiltonians by truncating entanglement, enabling the extraction of low-energy physics.

Contribution

The paper introduces entanglement-CUT (eCUT), a non-perturbative tensor network scheme for approximating flow equations in quantum many-body systems, including higher dimensions.

Findings

Successfully applied to 1D quantum Ising model

Effective in extracting quasiparticle gaps

Potential for generalization to higher dimensions

Abstract

Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second quantization. Yet, one of their main challenges is how to approximate the infinitely-many coupled differential equations that are produced throughout this flow. Here we show that tensor networks offer a natural and non-perturbative truncation scheme in terms of entanglement. The corresponding scheme is called "entanglement-CUT" or eCUT. It can be used to extract the low-energy physics of quantum many-body Hamiltonians, including quasiparticle energy gaps. We provide the general idea behind eCUT and explain its implementation for finite 1d systems using the formalism of matrix product operators. We also present proof-of-principle results for the spin-1/2 1d quantum Ising model and the 3-state quantum Potts model in a transverse field. Entanglement-CUTs can also be generalized to higher dimensions and to the thermodynamic limit.