[Paper Review] Quantum Glasses -- a review

Leticia F. Cugliandolo, Mark T. Mueller|arXiv (Cornell University)|Aug 10, 2022

Theoretical and Computational Physics4 citations

TL;DR

This review explores quantum glasses in high-dimensional systems, focusing on equilibrium properties via replica symmetry breaking and mean-field theory. It establishes connections between quantum spin glasses, the Sachdev-Ye-Kitaev (SYK) model, and holographic gravity, revealing universal low-energy dynamics and maximal chaos in SYK systems, with key results including a linear specific heat and saturated Lyapunov exponent.

ABSTRACT

We review recent research on quantum glasses, with a focus on their equilibrium dynamics and the interplay between glassiness and localization phenomena. Interesting relations with the SYK model are discussed.

Motivation & Objective

• To understand the equilibrium phase structure of quantum glasses in high dimensions, particularly those stabilized by quenched disorder and free-energy landscape ruggedness.
• To clarify the distinction between quantum glassiness and many-body localization (MBL), emphasizing different mechanisms of non-ergodicity and stability against baths.
• To establish connections between quantum glass phenomenology and the Sachdev-Ye-Kitaev (SYK) model, especially regarding time-reparametrization symmetry and chaotic dynamics.
• To explore the role of replica symmetry breaking in describing glassy order and collective modes in disordered quantum systems.
• To identify open questions in quantum glass transitions, glass-localization interplay, and deeper links between SYK physics and glass theory.

Proposed method

• Uses the replica method and replica symmetry breaking (RSB) to analyze the phase space structure of quantum glasses, particularly in mean-field limits.
• Applies Landau theory and effective potential approaches to classify universality classes of glassy systems and determine their low-energy collective modes.
• Analyzes the SYK model as a fermionic quantum glass analog, using the equation of motion for the two-point function: $ G_0^{-1} = d_ au $, $ ilde{ ho}( au) = J^2 Q^3( au) $, to describe self-energy corrections.
• Examines time-reparametrization invariance in the SYK model, where a Schwarzian action emerges, signaling a nearly AdS₂ geometry and maximal quantum chaos.
• Compares the SYK model to mean-field spin glass models, noting that coupling multiple SYK systems mimics replica coupling in disordered systems.
• Uses tensor model techniques to reproduce the melon-ladder diagram structure of the SYK model without quenched disorder, linking to self-generated disorder in structural glasses.

Experimental results

Research questions

• RQ1 How does quantum glassiness differ fundamentally from many-body localization (MBL) in terms of stability, ergodicity breaking, and response to baths?
• RQ2 What is the role of replica symmetry breaking in characterizing the phase space clusterization and metastable states in quantum glassy systems?
• RQ3 How do the SYK model and its chaotic dynamics, including a saturated Lyapunov exponent, relate to the low-energy physics of quantum glasses?
• RQ4 In what ways does the emergence of time-reparametrization symmetry and a Schwarzian action in the SYK model reflect universal features of quantum glassy systems?
• RQ5 What are the implications of the SYK model’s non-Fermi liquid behavior and linear specific heat for understanding quantum criticality in high-temperature superconductors and heavy fermion systems?

Key findings

• The Sachdev-Ye-Kitaev (SYK) model exhibits a linear specific heat at low temperatures and a saturated Lyapunov exponent $ ilde{ ho} \leq 2\pi T/\hbar $, indicating maximal quantum chaos.
• The SYK model's two-point function satisfies $ G_0^{-1} = d_\tau $, $ \Sigma(\tau) = J^2 Q^3(\tau) $, with a self-energy structure that leads to a nearly AdS₂ geometry and time-reparametrization invariance.
• Replica symmetry breaking in mean-field quantum glasses leads to a large number of metastable states separated by high free-energy barriers, consistent with glassy dynamics.
• Quantum glasses are stable against coupling to a bath due to the ruggedness of the free-energy landscape, unlike MBL which is fragile to local inclusions of weak disorder.
• The SYK model's dynamics are governed by a Schwarzian action arising from reparametrization invariance, a feature also phenomenologically proposed in mean-field glass models.
• The interplay between quantum fluctuations and glassy order leads to a distinct quantum melting pathway, differing from classical thermal melting, particularly in insulating Heisenberg systems with deconfined spinons.