# Holographic Non-Hermitian Lattices and Junctions with PT-Restoring RG Flows

**Authors:** Daniel Arean, David Garcia-Fariña  
**arXiv:** [2410.13584](https://arxiv.org/abs/2410.13584)  
**Date:** 2024-10-17  
**Summary page:** https://www.summarizepaper.com/en/paper/2410.13584v1/

## Key points

- Exploration of inhomogeneous non-Hermitian strongly coupled holographic field theories
- Focus on lattice system with inflow/outflow of matter and junction setup with Hermitian and non-Hermitian components
- Introduction of complex external gauge field leading to spontaneous PT symmetry breaking
- Emergence of imaginary current indicating departure from unitary evolution
- Flow towards PT-unbroken fixed point in the infrared (IR) regime
- Proposal of IR PT-symmetry restoration concept
- Detailed examination of non-Hermitian junction within framework
- Investigation of IR PT restoration in other inhomogeneous systems
- Exploration of non-Hermitian deformations around quantum critical points using holography

## Summary

In this work, we explore the construction and analysis of inhomogeneous non-Hermitian strongly coupled holographic field theories. Our focus is on two specific models: a lattice system with inflow/outflow of matter at each site, and a junction setup featuring both Hermitian and non-Hermitian components. By introducing a complex external gauge field, we uncover solutions that exhibit spontaneous PT symmetry breaking, indicating a departure from unitary evolution. This broken PT symmetry is associated with the emergence of an imaginary current within the system. Furthermore, our investigation extends to the infrared (IR) regime, revealing that these solutions ultimately flow towards a PT-unbroken fixed point. We propose the concept of IR PT-symmetry restoration, similar to previous perturbative studies. Moving forward, there are several avenues for further exploration. Firstly, we suggest a more detailed examination of the non-Hermitian junction within our framework to better understand its phenomenology and potential connections to real-world condensed matter systems. Additionally, it would be valuable to investigate whether IR PT restoration is a common feature across various inhomogeneous systems beyond our current models. Moreover, an exciting direction for future research involves exploring non-Hermitian deformations around quantum critical points using holography as a tool to study their effects within strongly coupled systems. By expanding our understanding of inhomogeneous non-Hermitian systems and their implications for fundamental physics phenomena like quantum criticality and symmetry restoration, we aim to contribute valuable insights to the field of theoretical physics.