[Paper Review] Many-Body Localization in Translational Invariant Diamond Ladders with Flat Bands

Mirko Daumann, Robin Steinigeweg+1 more|arXiv (Cornell University)|Sep 21, 2020

Theoretical and Computational Physics4 citations

TL;DR

This paper demonstrates that many-body localization (MBL) can emerge in a clean, translationally invariant diamond ladder system with flat bands, even without quenched disorder. Using numerical simulations, the authors show that the flat band's degenerate, compact localized states drive MBL, evidenced by violation of the eigenstate thermalization hypothesis (ETH), extensive localization across the energy spectrum, and non-thermal dynamics in observables like entanglement entropy and participation ratio.

ABSTRACT

The presence of flat bands is a source of localization in lattice systems. While flat bands are often unstable with respect to interactions between the particles, they can persist in certain cases. We consider a diamond ladder with transverse hopping that possesses such stable flat bands and show that many-body localization appears in the presence of interactions without quenched disorder. We numerically demonstrate that the eigenstate thermalization hypothesis is violated. We show that the influence of degenerate flat band states spreads across the full energy spectrum and grows extensively in the thermodynamic limit. Furthermore, we verify localization in terms of time evolution of some local observable, revival probability, participation ratio and entanglement entropy.

Motivation & Objective

• To investigate whether many-body localization (MBL) can occur in a clean, translationally invariant system without quenched disorder.
• To explore the role of flat bands (FBs) as a source of localization in interacting fermionic systems.
• To determine if the degeneracy and localization properties of flat band states persist under interactions and lead to MBL.
• To verify MBL through multiple dynamical and spectral diagnostics, including ETH violation, entanglement entropy, and revival probability.
• To examine the scaling behavior of localization indicators in the thermodynamic limit.

Proposed method

• Numerical exact diagonalization for small systems (N=8,10,12) and typicality-based methods for larger systems to compute energy-resolved observables.
• Use of an energy filter (U') to probe the eigenstate thermalization hypothesis (ETH) across the entire energy spectrum, with a Gaussian window of fixed width σ.
• Analysis of local observable time evolution to assess memory retention and localization.
• Calculation of the revival probability and participation ratio to quantify localization in time evolution.
• Computation of entanglement entropy (EE) over time to distinguish between area law (MBL) and volume law (thermal) scaling.
• Systematic comparison of different interaction strengths (V=0,1,100) and hopping parameters (t3=0, 1/4) to probe the transition from single-particle to many-body localization.

Experimental results

Research questions

• RQ1 Can many-body localization occur in a clean, translationally invariant system without quenched disorder?
• RQ2 To what extent do flat band states influence the entire energy spectrum and drive MBL in the presence of interactions?
• RQ3 Does the eigenstate thermalization hypothesis (ETH) break down in this system, indicating MBL?
• RQ4 How do dynamical quantities like revival probability, participation ratio, and entanglement entropy scale with system size in the presence of flat bands?
• RQ5 What is the scaling behavior of entanglement entropy—area law or volume law—and how does it depend on interaction strength and band dispersion?

Key findings

• The eigenstate thermalization hypothesis (ETH) is violated across the entire energy spectrum, with the violation most pronounced in the flat band region, indicating MBL.
• The fraction of states influenced by flat band degeneracy grows extensively with system size, even in the presence of interactions.
• Time evolution of local observables shows persistent memory of initial conditions, with revival probability and participation ratio scaling consistently with localization.
• Entanglement entropy exhibits slow logarithmic growth in the MBL regime (V=1), consistent with localized dynamics, while it shows volume law scaling when the flat band is perturbed (t3=1/4).
• For strong interactions (V=100), the entanglement entropy approaches an area law, indicating suppression of thermalization and localization.
• Finite-size scaling of revival probability and participation ratio supports the existence of MBL in the thermodynamic limit, even without disorder.