Quenched vs Annealed: Glassiness from SK to SYK

作     者：Baldwin, C.L. Swingle, B. 

作者机构：National Institute of Standards and Technology GaithersburgMD20899 United States Joint Quantum Institute University of Maryland College ParkMD20742 United States Condensed Matter Theory Center University of Maryland College ParkMD20742 United States Maryland Center for Fundamental Physics University of Maryland College ParkMD20742 United States Joint Institute for Quantum Information and Computer Science University of Maryland College ParkMD20742 United States Department of Physics University of Maryland College ParkMD20742 United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2019年

核心收录：

主　　题：Annealing 

摘      要：We show that any SYK-like model with finite-body interactions among local degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space;and second, a replica treatment of two prominent examples which exhibit phase transitions from an annealed phase to a non-annealedphase as a function of temperature. We further show that this effect appears only at O(N)’th order in a 1/N expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the non-bosonic nature of the particles in SYK is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography. Copyright © 2019, The Authors. All rights reserved.