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  • Open Access

Rigorous Lower Bound on Dynamical Exponents in Gapless Frustration-Free Systems

Rintaro Masaoka1, Tomohiro Soejima (副島智大)2, and Haruki Watanabe1,*

  • *Contact author: hwatanabe@g.ecc.u-tokyo.ac.jp
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Phys. Rev. X 15, 041050 – Published 16 December, 2025

DOI: https://doi.org/10.1103/d4c4-5p2r

Abstract

This work rigorously establishes a universal lower bound z≥2 for the dynamical exponent in frustration-free quantum many-body systems whose ground states exhibit power-law decaying correlations. The derivation relies on the Gosset-Huang inequality, providing a unified framework applicable across various lattice structures and spatial dimensions, independent of specific boundary conditions. Remarkably, our result can be applied to prove bounds for dynamics of classical stochastic processes. Specifically, we utilize a well-established mapping from the time evolution of local Markov processes with detailed balance to that of frustration-free quantum Hamiltonians, known as Rokhsar-Kivelson Hamiltonians. This proves z≥2 for such Markov processes, which is an improvement over existing bounds. Beyond these applications, the quantum analysis of the z≥2 bound is further broadened to include systems exhibiting hidden correlations, which may not be evident from purely local operators.

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Popular Summary

A key challenge in the study of frustration-free (FF) quantum systems is understanding how the FF condition itself influences their universal properties, particularly at quantum critical points. We rigorously prove a universal lower bound for the dynamical exponent in FF systems whose ground-state correlations decay no faster than a power law. Our result, based on the Gosset-Huang inequality universally applies across arbitrary lattices and dimensions, demonstrating that these systems cannot host emergent Lorentz invariance. Furthermore, through a mapping to classical stochastic processes, this bound provides a rigorous bound for the dynamical exponent of local Markov chain Monte Carlo algorithms like Gibbs sampling and Metropolis-Hastings. The findings strongly constrain the low-energy physics of FF systems and the properties of well-known computational methods.

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Phys. Rev. X 15, 041050– Published 16 December, 2025
  • Received 16 July 2024
  • Revised 22 July 2025
  • Accepted 2 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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