# Anomalies and entanglement renormalization

## TL;DR

This paper investigates 't Hooft anomalies in discrete symmetries within (1+1)D lattice models using multiscale entanglement renormalization ansatz (MERA), deriving topological constraints and numerically analyzing critical phases.

## Contribution

It introduces a MERA class optimized for anomalous symmetries and demonstrates its effectiveness in studying protected gapless phases and duality transformations.

## Key findings

- Numerical conformal data for all projective representations of anomalous symmetries.
- Identification of a protected gapless phase along a symmetric critical line.
- Implementation of a duality transformation between critical lines using the new MERA class.

## Abstract

We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line. Conformal data is obtained for all irreducible projective representations of each anomalous symmetry twist, corresponding to definite topological sectors. It is numerically demonstrated that this line is a protected gapless phase. Finally, we implement a duality transformation between a pair of critical lines using our subclass of MERA.