Localization-protected quantum order

@article{Huse2013LocalizationprotectedQO,
  title={Localization-protected quantum order},
  author={David A. Huse and Rahul M. Nandkishore and Vadim Oganesyan and Arijeet Pal and S.L.Sondhi},
  journal={Physical Review B},
  year={2013},
  volume={88},
  pages={014206}
}
Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate, even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can order, in that individual many-body eigenstates can break symmetries or display topological order in the infinite-volume limit. Indeed, isolated localized quantum systems can order even at energy densities where the corresponding thermally equilibrated system… 
View PDF on arXiv
268 Citations
Highly Influential Citations
12
Background Citations
73
Methods Citations
6
Results Citations
2

Figures from this paper

268 Citations

Quantum order, entanglement and localization in many-body systems

The interplay of disorder and interactions can have remarkable effects on the physics of quantum systems. A striking example is provided by the long conjectured—and recently confirmed—phenomenon of…

Nonequilibrium quantum order at infinite temperature: Spatiotemporal correlations and their generating functions

Localisation-protected quantum order extends the idea of symmetry breaking and order in ground states to individual eigenstates at arbitrary energy. Examples include many-body localised static and…

Localization and topology protected quantum coherence at the edge of hot matter

This work demonstrates the coherent revival of an edge spin over a time scale that grows exponentially with system size, in sharp contrast to the general expectation that quantum bits strongly coupled with a hot many-body system will rapidly lose coherence.

Many-body localization, thermalization, and entanglement

Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. However, not all systems fall into this category, with many body localization providing a generic…

Entanglement and localization in long-range quadratic Lindbladians

Existence of Anderson localization is considered a manifestation of coherence of classical and quantum waves in disordered systems. Signatures of localization have been observed in condensed matter…

Localization and symmetry breaking in the quantum quasiperiodic Ising glass

Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. In this article, we show that such systems can exhibit dynamically stable…

Many-body localization, symmetry and topology

This work explores how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.

Nonlocal adiabatic response of a localized system to local manipulations

We examine the response of a system localized by disorder to a time-dependent local perturbation that varies smoothly with a characteristic timescale τ. We find that such a perturbation induces a…

Perturbative instability of nonergodic phases in non-Abelian quantum chains

An important challenge in the field of many-body quantum dynamics is to identify non-ergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian…

Digital quantum simulation of Floquet symmetry-protected topological phases

Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals1–8, in…
...

References

SHOWING 1-10 OF 43 REFERENCES

Bringing order through disorder: localization of errors in topological quantum memories.

It is demonstrated that the induced localization of Anderson localization allows the topological quantum memory to regain a finite critical anyon density and the memory to remain stable for arbitrarily long times.

Thermalization and its mechanism for generic isolated quantum systems

It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki.

Many-body localization phase transition

We use exact diagonalization to explore the many-body localization transition in a random-field spin-1/2 chain. We examine the correlations within each many-body eigenstate, looking at all…

Chaos and quantum thermalization.

  • Srednicki
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics.

Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states

Localization of interacting fermions at high temperature

We suggest that if a localized phase at nonzero temperature $Tg0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and…

Area laws for the entanglement entropy - a review

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay…

String-net condensation: A physical mechanism for topological phases

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''…

Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Just as group theory allows us to construct 230 crystal structures in three-dimensional space, group cohomology theory is used to systematically construct different interacting bosonic SPT phases in any dimension and with any symmetry, leading to the discovery of bosonic topological insulators and superconductors.

Topological entanglement entropy.

The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity.