# Effective dimension reduction with mode transformations: Simulating two-dimensional fermionic condensed matter systems

## TL;DR

This paper introduces a novel approach for simulating two-dimensional fermionic systems by combining mode transformations with matrix-product states, enabling higher accuracy in capturing ground states and phase transitions.

## Contribution

It demonstrates that applying fermionic mode transformations enhances the effectiveness of matrix-product states for 2D fermionic models, surpassing traditional local embedding limitations.

## Key findings

- Matrix-product states effectively describe ground states with low entanglement in 2D fermionic systems.
- Mode transformations reduce entanglement, improving simulation accuracy.
- Successful simulation of a phase transition in a 10x10 lattice of spinless fermions.

## Abstract

Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected entangled pair states aimed at simulating the physics of two-dimensional models. In this work, we advocate the paradigm that for two-dimensional fermionic models, matrix-product states are still applicable to significantly higher accuracy levels than direct embeddings into one-dimensional systems allow for. To do so, we exploit schemes of fermionic mode transformations and overcome the prejudice that one-dimensional embeddings need to be local. This approach takes the insight seriously that the suitable exploitation of both the manifold of matrix-product states and the unitary manifold of mode transformations can more accurately capture the natural correlation structure. By demonstrating the residual low levels of entanglement in emerging modes, we show that matrix-product states can describe ground states strikingly well. The power of the approach is exemplified by investigating a phase transition of spin-less fermions for lattice sizes up to 10x10.