Mixed-state phase transitions in spin-Holstein models

TL;DR

This paper investigates mixed-state phase transitions in a 2D spin-Holstein model, revealing that mixed-state diagnostics like von Neumann and Rényi-2 CMI can detect phase transitions missed by pure-state approaches.

Contribution

It introduces the use of mixed-state diagnostics to identify phase transitions in coupled electron-phonon systems, extending the understanding beyond pure-state methods.

Findings

Pure-state approach fails to detect the transition at strong coupling.

Mixed-state measures like von Neumann and Rényi-2 CMI reveal phase transition signatures.

Different diagnostics identify transitions at different coupling strengths.

Abstract

Understanding coupled electron-phonon systems is one of the fundamental issues in strongly correlated systems. In this work, we aim to extend the notion of mixed-state phases to the realm of coupled electron/spinphonon systems. Specifically, we consider a two-dimensional cluster Hamiltonian locally coupled to a set of single bosonic modes with arbitrary coupling strength. First, we adopt a pure-state framework and examine whether a ground state phase transition out of the symmetry-protected topological phase can be captured using the standard polaron unitary transformation. This approach involves restricting the analysis to the low-energy manifold of the phonon degrees of freedom. We find that the pure-state approach fails to detect the anticipated transition to a topologically trivial phase at strong spin-phonon coupling. Next, we turn to a mixed-state picture. Here, we analyze mixed states of the model obtained by tracing out the phonons degrees of freedom. We employ two distinct diagnostics for mixed-state phase transitions: (i) the von Neumann conditional mutual information (CMI) and (ii) the R\'enyi-2 CMI. We argue that both measures detect signatures of mixed-state phase transitions, albeit at different critical spin-phonon coupling strengths, corresponding to subtly distinct notions of the mixed-state phases.