$Q$-Deformed Rainbows: a Universal Simulator of Free Entanglement Spectra

TL;DR

This paper introduces a spin chain model capable of simulating any free fermion entanglement spectrum by tuning magnetic fields, using $q$-deformed singlets to generate diverse quantum correlations.

Contribution

It presents a universal entanglement spectrum simulator based on a position-dependent XX spin chain with $q$-deformed singlet states, enabling precise control over quantum correlations.

Findings

Successfully reproduces arbitrary free fermion entanglement spectra.

Demonstrates versatility with examples including homogeneous and prime-based correlations.

Provides a practical method for generating tailored entanglement structures.

Abstract

The behaviour of correlations across a bipartition is an indispensable tool in diagnosing quantum phases of matter. Here we present a spin chain with position-dependent XX couplings and magnetic fields, that can reproduce arbitrary structure of free fermion correlations across a bipartition. In particular, by choosing appropriately the strength of the magnetic fields we can obtain any single particle energies of the entanglement spectrum with high fidelity. The resulting ground state can be elegantly formulated in terms of $q$-deformed singlets. To demonstrate the versatility of our method we consider certain examples, such as a system with homogeneous correlations and a system with correlations that follow a prime number decomposition. Hence, our entanglement simulator can be easily employed for the generation of arbitrary entanglement spectra with possible applications in quantum technologies and condensed matter physics.