# 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…

## 268 Citations

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## References

SHOWING 1-10 OF 43 REFERENCES

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

- PhysicsPhysical review letters
- 2011

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

- PhysicsNature
- 2008

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

- Physics
- 2010

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.

- PhysicsPhysical 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.

### Localization of interacting fermions at high temperature

- Physics
- 2007

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

- Physics
- 2010

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

- Physics
- 2005

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

- PhysicsScience
- 2012

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.

- PhysicsPhysical review letters
- 2006

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.