[Paper Review] Dynamics of charge-imbalance-resolved entanglement negativity after a quench in a free-fermion model

Gilles Parez, Riccarda Bonsignori+1 more|arXiv (Cornell University)|Feb 10, 2022

Quantum many-body systems139 references50 citations

TL;DR

This paper investigates the time evolution of charge-imbalance-resolved entanglement negativity after a quantum quench in a free-fermion chain, using charged moments and Fourier transforms to resolve entanglement across symmetry sectors. It finds perfect equipartition of negativity in the scaling limit at early and late times, and proposes a quasiparticle picture conjecture for charged Rényi logarithmic negativities applicable to generic integrable models.

ABSTRACT

The presence of a global internal symmetry in a quantum many-body system is reflected in the fact that the entanglement between its subparts is endowed with an internal structure, namely it can be decomposed as sum of contributions associated to each symmetry sector. The symmetry resolution of entanglement measures provides a formidable tool to probe the out-of-equilibrium dynamics of quantum systems. Here, we study the time evolution of charge-imbalance-resolved negativity after a global quench in the context of free-fermion systems, complementing former works for the symmetry-resolved entanglement entropy. We find that the charge-imbalance-resolved logarithmic negativity shows an effective equipartition in the scaling limit of large times and system size, with a perfect equipartition for early and infinite times. We also derive and conjecture a formula for the dynamics of the charged R\'enyi logarithmic negativities. We argue that our results can be understood in the framework of the quasiparticle picture for the entanglement dynamics, and provide a conjecture that we expect to be valid for generic integrable models.

Motivation & Objective

• To understand the non-equilibrium dynamics of entanglement in quantum many-body systems with global U(1) symmetry.
• To resolve entanglement measures—specifically negativity—into charge-imbalance sectors to probe symmetry-resolved entanglement.
• To extend the quasiparticle picture of entanglement dynamics to charged Rényi logarithmic negativities.
• To provide analytical formulas and conjectures for the dynamics of symmetry-resolved entanglement in free-fermion models.
• To lay a foundation for generalizing these results to interacting integrable models.

Proposed method

• Uses charged moments Nn(α) of the partially transposed density matrix to resolve entanglement by charge imbalance.
• Expresses charged moments in terms of two-point correlation matrices in free-fermion systems.
• Applies Fourier transforms to charged moments at quadratic order in α to extract charge-imbalance-resolved logarithmic negativity.
• Derives analytical expressions and conjectures for charged Rényi logarithmic negativities En(α) via exact computation and numerical validation.
• Proposes a quasiparticle picture conjecture for En(α) based on the dynamics of entangled quasiparticle pairs across subsystems.
• Validated results against ab initio numerical computations for two distinct quench protocols: Néel and dimer states.

Experimental results

Research questions

• RQ1 How does the charge-imbalance-resolved entanglement negativity evolve in time after a global quench in a free-fermion chain?
• RQ2 What is the role of symmetry resolution in the dynamics of entanglement negativity, particularly in the scaling limit?
• RQ3 Can the quasiparticle picture be generalized to describe the dynamics of charged Rényi logarithmic negativities?
• RQ4 Does equipartition of entanglement hold across charge-imbalance sectors in the long-time and early-time limits?
• RQ5 What is the structure of the charged Rényi logarithmic negativity for arbitrary n and α in free-fermion models?

Key findings

• The charge-imbalance-resolved logarithmic negativity exhibits perfect equipartition at early and infinite times in the scaling limit.
• At intermediate times, equipartition is broken at order ∆q²/ℓ, with deviations matching numerical results under |∆q| ≪ ℓ.
• The charged Rényi logarithmic negativities En(α) are analytically computed for n=1 and conjectured for general n.
• The conjectured form of En(α) generalizes the quasiparticle picture to symmetry-resolved entanglement, with α-dependent kernels ϵn,α(k) and ϵ(2)n,α(k).
• The total negativity is recovered from the charge-imbalance-resolved negativity via integration over α, confirming consistency.
• The results suggest a universal structure for symmetry-resolved entanglement in integrable models, extendable beyond free fermions.