Macroscopic suppression of supersonic quantum transport

TL;DR

The paper addresses the problem of macroscopic transport in strongly interacting quantum lattice gases, where conventional Lieb-Robinson bounds give only $O(1)$ leakage that does not scale with the total particle number $N$. It introduces a novel geometric exponential tilting method to prove a universal MASSMAT principle, bounding the transport probability of a macroscopic $(\beta-\alpha)N$-particle cluster by $\exp(-aN((\beta-\alpha)d_{XY}-v|t|))$, thereby establishing a dynamical large deviation principle with an $N$-dependent light cone. The main contributions include a rigorous MASSMAT bound for Hamiltonians of the form $H=H_0+V$ with short-range hopping, valid for both bosons and fermions and extensible to time-dependent settings, along with a clarifying framework that sharpens previous macroscopic transport bounds. The results imply an emergent strict causality for macroscopic transport, with potential experimental realization in ultracold lattice gases and implications for quantum hydrodynamics and thermalization analyses.

Abstract

We consider a broad class of strongly interacting quantum lattice gases, including the Fermi-Hubbard and Bose-Hubbard models. We focus on macroscopic particle clusters of size $θN$, with $θ\in(0,1)$ and $N$ the total particle number, and we study the quantum probability that such a cluster is transported across a distance $r$ within time $t$. Conventional effective light cone arguments yield a bound of the form $\exp(v t-r)$. We report a substantially stronger bound $\exp(θN(vt-r))$, which provides exponential suppression that scales with system size. Our result establishes a universal dynamical large deviation principle: macroscopic suppression of supersonic macroscopic transport (MASSMAT).

Figures (4)

• Figure 1: Our main result establishes the green light cone $\sim v t$, with $v$ given by \ref{['SR']}, outside of which the exponential decay rate becomes $\propto N$, i.e., extensive. Since $v$ is larger than the quantity $\kappa$ in \ref{['eq:oldkappa']} that bounded the speed of macroscopic clusters in prior work faupin2022maximallemm2023information, there is a separation of the new macroscopic MASSMAT light cone and the usual $\mathcal{O}(1)$ light cone (yellow region). Note that we establish the MASSMAT light cone for short-ranged hopping terms, whereas hamazaki2022speedfaupin2022maximallemm2023informationvan2023topologicalvan2024optimalli2025macroscopic considered long-ranged hopping terms as well.
• Figure S1: Schematic diagram for the decomposition \ref{['decomp']}.
• Figure S2: Schematic diagram for $S$ and $\Omega_\pm$.
• Figure S3: The function $f(s)$.

Theorems & Definitions (13)

• Theorem 1: MASSMAT principle
• Lemma 2
• proof
• Lemma 3
• proof
• Definition 4: Second quantization functor
• Proposition 5: Properties of $\mathop{\mathrm{\mathrm{d}\Gamma}}\nolimits$ and $\Gamma$
• Definition 6: Exponential tilting operator
• Lemma 7
• proof