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Many-body localisation in non-fractured systems

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posted on 2022-12-09, 15:03 authored by Christian Duffin

Many-body localisation (MBL) in closed quantum systems can often be understood in terms of the fracturing of the Fock space graph, where some Fock states are disconnected from the rest. The inability of some configurations to evolve into others results in broken ergodicity, and thus MBL. However, there are examples of systems with non-fractured Fock space graphs that still exhibit broken ergodicity, which can instead be attributed to reduced connectivity between Fock states. This work explores several models that possess this property. The first is the EastREM model, which describes a disordered lattice of spins with locally constrained spin-flipping. Here, MBL is understood to be introduced by the constraint due to some spin flips being forbidden. The GOEastREM is also introduced, which replaces the blocks with random matrices, thus ensuring that the overall block property is maintained, but their internal structure is randomised. Here, we discover that MBL is common between both models, confirming that it can be attributed to the block property specifically. The investigation is then extended to the case of periodic driving, in order to see whether this recovers ergodicity in both models. What we find is that the MBL eigenstates are mostly unchanged, independent of parameters used. The next model introduced is the GOE chain, which simplifies the block property by making them all equally sized. This model is studied using exact diagonalisation techniques, a flow equation method, and further analytically via the forward-scattering approximation. From our numerical work we determine that the system is Anderson localised by the blocks, regardless of parameters. This is contradicted by the forward-scattering approximation (FSA), which suggests that a phase transition exists at finite hopping amplitude. We attribute this to the failure of the FSA to take into account backward propagations, which negates self-interference due to Bragg reflections. Finally, we investigate Stark many-body localisation, found in interacting systems with a tilted potential term. Under periodic driving, we determine a resonance condition by which the localising effect of the potential is broken.

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

Loughborough University

Rights holder

© Christian Duffin

Publication date

2022

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of the degree of Doctor of Philosophy of Loughborough University.

Language

  • en

Supervisor(s)

Achilleas Lazarides

Qualification name

  • PhD

Qualification level

  • Doctoral

This submission includes a signed certificate in addition to the thesis file(s)

  • I have submitted a signed certificate

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