Resonant energy scales and local observables in the many-body localised
phase
- URL: http://arxiv.org/abs/2202.10482v2
- Date: Wed, 15 Jun 2022 17:16:56 GMT
- Title: Resonant energy scales and local observables in the many-body localised
phase
- Authors: Samuel J. Garratt and Sthitadhi Roy
- Abstract summary: We formulate a theory for resonances in the many-body localised phase of disordered quantum spin chains in terms of local observables.
Key result is to show that there are universal correlations between the matrix elements of local observables and the many-body level spectrum.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We formulate a theory for resonances in the many-body localised (MBL) phase
of disordered quantum spin chains in terms of local observables. A key result
is to show that there are universal correlations between the matrix elements of
local observables and the many-body level spectrum. This reveals how the matrix
elements encode the energy scales associated with resonance, thereby allowing
us to show that these energies are power-law distributed. Using these results
we calculate analytically the distributions of local polarisations and of
eigenstate fidelity susceptibilities. The first of these quantities
characterises the proximity of MBL systems to noninteracting ones, while the
second highlights their extreme sensitivity to local perturbations. Our
theoretical approach is to consider the effect of varying a local field, which
induces a parametric dynamics of spectral properties. We corroborate our
results numerically using exact diagonalisation in finite systems.
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