204 research outputs found
Integrals of motion in the Many-Body localized phase
We construct a complete set of quasi-local integrals of motion for the
many-body localized phase of interacting fermions in a disordered potential.
The integrals of motion can be chosen to have binary spectrum , thus
constituting exact quasiparticle occupation number operators for the Fermi
insulator. We map the problem onto a non-Hermitian hopping problem on a lattice
in operator space. We show how the integrals of motion can be built, under
certain approximations, as a convergent series in the interaction strength. An
estimate of its radius of convergence is given, which also provides an estimate
for the many-body localization-delocalization transition. Finally, we discuss
how the properties of the operator expansion for the integrals of motion imply
the presence or absence of a finite temperature transition.Comment: 65 pages, 12 figures. Corrected typos, added reference
Many-body localization beyond eigenstates in all dimensions
Isolated quantum systems with quenched randomness exhibit many-body
localization (MBL), wherein they do not reach local thermal equilibrium even
when highly excited above their ground states. It is widely believed that
individual eigenstates capture this breakdown of thermalization at finite size.
We show that this belief is false in general and that a MBL system can exhibit
the eigenstate properties of a thermalizing system. We propose that localized
approximately conserved operators (l-bits) underlie localization in such
systems. In dimensions , we further argue that the existing MBL
phenomenology is unstable to boundary effects and gives way to l-bits.
Physical consequences of l-bits include the possibility of an eigenstate
phase transition within the MBL phase unrelated to the dynamical transition in
and thermal eigenstates at all parameters in . Near-term experiments
in ultra-cold atomic systems and numerics can probe the dynamics generated by
boundary layers and emergence of l-bits.Comment: 12 pages, 5 figure
Localized systems coupled to small baths: from A to Z
We investigate what happens if an Anderson localized system is coupled to a
small bath, with a discrete spectrum, when the coupling between system and bath
is specially chosen so as to never localize the bath. We find that the effect
of the bath on localization in the system is a non-monotonic function of the
coupling between system and bath. At weak couplings, the bath facilitates
transport by allowing the system to 'borrow' energy from the bath. But above a
certain coupling the bath produces localization, because of an orthogonality
catastrophe, whereby the bath 'dresses' the system and hence suppresses the
hopping matrix element. We call this last regime the regime of
"Zeno-localization", since the physics of this regime is akin to the quantum
Zeno effect, where frequent measurements of the position of a particle impede
its motion. We confirm our results by numerical exact diagonalization
The Casimir Energy for a Hyperboloid Facing a Plate in the Optical Approximation
We study the Casimir energy of a massless scalar field that obeys Dirichlet
boundary conditions on a hyperboloid facing a plate. We use the optical
approximation including the first six reflections and compare the results with
the predictions of the proximity force approximation and the semi-classical
method. We also consider finite size effects by contrasting the infinite with a
finite plate. We find sizable and qualitative differences between the new
optical method and the more traditional approaches.Comment: v2: 14 pages, 11 eps figures; typo in eq. (21) removed, clarification
added, fig. 10 improved; version published in Phys. Rev.
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