# Bridging Perturbative Expansions with Tensor Networks

## TL;DR

This paper introduces a tensor network framework that reformulates perturbative expansions in quantum many-body systems, enabling better interpolation across phase transitions and revealing order parameters for topological phases.

## Contribution

It presents a novel tensor network approach to perturbative expansions, connecting them with entanglement properties and phase transition indicators in quantum systems.

## Key findings

- Tensor networks effectively interpolate perturbative expansions.
- Constructed perturbative entanglement Hamiltonians with spectral insights.
- Tensor networks reveal order parameters for topological phase transitions.

## Abstract

We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This approach leads to classes of tensor-network states parametrized by few parameters with a clear physical meaning, while still providing excellent variational energies. We also demonstrate how to construct perturbative expansions of the entanglement Hamiltonian, whose eigenvalues form the entanglement spectrum, and how the tensor-network approach gives rise to order parameters for topological phase transitions.