Many-body localization in the interpolating Aubry-André-Fibonacci model

Antonio Štrkalj,Igor V Gornyi,Elmer V H Doggen,Oded Zilberberg

doi:10.1103/physrevresearch.3.033257

Antonio Štrkalj, Igor V Gornyi + Show 2 more

Open Access

https://doi.org/10.1103/physrevresearch.3.033257

Copy DOI

Abstract

We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbour coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-Andr\'e and the Fibonacci models. We find that stronger many-body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation. As a result, the position of the many-body localization transition depends on the interaction strength for an intermediate degree of deformation of the quasiperiodic modulation. Moreover, in the region of parameter space where the single-particle spectrum contains both localized and extended states, many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger interactions enhance ergodicity. We map the model's localization phase diagram using the decay of the quenched spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground for testing many-body localization under tunable potentials.

Highlights

The study of material properties most commonly begins by assuming a periodic crystalline structure within which extended Bloch waves manifest and form dispersive bands [1]
The physics of quantum many-body interacting systems can be strongly altered by the presence of disorder, which can drive them from an ergodic to a many-body localized (MBL) phase [5,6,7,8,9,10,11,12]
Our results provide a first glimpse into the complex many-body physics found in the i-interpolating Aubry-André-Fibonacci model [31] (IAAF) model, opening the path for additional studies in this tunable setting

Summary

Introduction

The study of material properties most commonly begins by assuming a periodic crystalline structure within which extended Bloch waves manifest and form dispersive bands [1]. The physics of quantum many-body interacting systems can be strongly altered by the presence of disorder, which can drive them from an ergodic to a many-body localized (MBL) phase [5,6,7,8,9,10,11,12]. The latter is interesting due to the fact that a closed MBL system does not thermalize at any time scale and remains robust to small perturbations, such as changing the interaction strength, the strength of disorder, and/or the temperature.

Results

Discussion

Conclusion