Fate of measurement-induced phase transition in long-range interactions

TL;DR

This paper investigates how long-range interactions affect measurement-induced phase transitions in quantum many-body systems, identifying conditions under which the transition persists or disappears based on interaction decay.

Contribution

It provides a comprehensive analysis of the robustness of measurement-induced phase transitions in long-range interacting systems, establishing specific decay exponent thresholds for their existence.

Findings

MIP occurs for decay exponent $ ext{alpha} > ext{alpha}_c$

MIP is absent for $ ext{alpha} < ext{alpha}_c$

Proposed conditions $ ext{alpha} > d/2+1$ and $ ext{alpha} > d+1$ for observing MIP

Abstract

We consider quantum many-body dynamics under quantum measurements, where the measurement-induced phase transitions (MIPs) occur when changing the frequency of the measurement. In this work, we consider the robustness of the MIP for long-range interaction that decays as $r^{-\alpha}$ with distance $r$. The effects of long-range interactions are classified into two regimes: (i) the MIP is observed $(\alpha > \alpha_c)$, and (ii) the MIP is absent even for arbitrarily strong measurements $(\alpha<\alpha_c)$. Using fermion models, we demonstrate both regimes in integrable and non-integrable cases. We identify the underlying mechanism and propose sufficient conditions to observe the MIP, that is, $\alpha > d/2+1$ for general bilinear systems and $\alpha > d+1$ for general non-integrable systems ($d$: spatial dimension). Numerical calculation indicates that these conditions are optimal.