Characterization of Phase Transitions in a Lipkin-Meshkov-Glick Quantum Brain Model

TL;DR

This paper investigates how biologically inspired synaptic feedback influences phase transitions in a quantum brain model based on the Lipkin-Meshkov-Glick framework, revealing feedback-induced phase diagram deformations and criticality tuning.

Contribution

It introduces a feedback mechanism into the quantum brain model, demonstrating its significant impact on phase structure and critical boundaries, and provides both phase-space and dynamical analyses.

Findings

Feedback expands the paramagnetic phase at the expense of ferromagnetic phases.

Longitudinal field enhances feedback effects on phase boundaries.

Dynamical mean-field analysis accurately reproduces quantum evolution.

Abstract

In this work we analyze the emergence of phase transitions in a quantum brain model inspired by the Lipkin-Meshkov-Glick framework, where biologically motivated synaptic feedback modulates the collective interaction in a nonlinear and state-dependent manner. We demonstrate that incorporating this retroactive mechanism substantially reshapes the phase structure, yielding an expansion of the paramagnetic phase at the expense of the ferromagnetic phases relative to the feedback-free scenario. This effect is markedly enhanced in the presence of a longitudinal field, as the feedback couples directly to the longitudinal magnetization, leading to an appreciable displacement of the critical boundaries. We characterize the ensuing transitions from a phase-space perspective by means of the ground-state Husimi distribution and the Wehrl entropy, which provide a robust diagnosis of qualitative changes in localization and enable a quantitative assessment of feedback-induced deformations of the phase diagram. Additionally, we perform an explicit dynamical analysis based on mean-field equations for the collective-spin orientation self-consistently coupled to the synaptic dynamics, which reproduces with high fidelity the quantum time evolution of collective observables for the protocols considered. Overall, these findings substantiate the suitability of this quantum brain model as a controlled theoretical framework for elucidating how synaptic plasticity mechanisms can parametrically tune and reshape collective criticality.