# O(3) nonlinear sigma model in 1+1 dimensions with matrix product states

## TL;DR

This paper uses matrix product states to numerically analyze the O(3) nonlinear sigma model in 1+1 dimensions, revealing its spectral properties, entanglement scaling, and phase transitions at nonzero chemical potential.

## Contribution

It demonstrates the effectiveness of tensor network methods in studying the O(3) nonlinear sigma model, including phase structure and continuum limit behavior, without sign problem issues.

## Key findings

- Reproduced the analytical mass gap at zero chemical potential.
- Found entanglement entropy scaling consistent with central charge 2.
- Mapped phase transitions at nonzero chemical potential with high precision.

## Abstract

We numerically study the spectral properties, the entanglement and the zero-temperature phase structure at nonvanishing chemical potential of the O(3) nonlinear sigma model. Using matrix product states, a particular kind of one-dimensional tensor network state, we show that we are able to reach the asymptotic scaling regime and to reproduce the analytical predictions for the mass gap at vanishing chemical potential. In addition, we study the scaling of the entanglement entropy towards the continuum limit obtaining a central charge consistent with 2. Moreover, our approach does not suffer from the sign problem and we also explore the phase structure of the model for nonzero chemical potential and map out the location of the transitions between different charge sectors with high precision.