# Isolated Heisenberg magnet as a quantum time crystal

@article{Medenjak2019IsolatedHM, title={Isolated Heisenberg magnet as a quantum time crystal}, author={Marko Medenjak and Berislav Bu{\vc}a and Dieter Jaksch}, journal={Physical Review B}, year={2019} }

Local observables of closed many-body quantum systems are generally believed to quickly equilibrate after a quench, according to the eigenstate thermalization hypothesis. Here, the authors show that the paradigmatic Heisenberg quantum magnet violates this fundamental assumption. They analytically find measurable local correlation functions that show perpetual oscillations, while at the same time all single-particle observables equilibrate. They link their existence to the presence of dynamical…

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## References

SHOWING 1-10 OF 110 REFERENCES

### Periodic thermodynamics of isolated quantum systems.

- PhysicsPhysical review letters
- 2014

It is analytically show that, for a class of integrable systems, the relevant ensemble is constructed by maximizing an appropriately defined entropy subject to constraints, which is explicitly identified.

### Time-Resolved Observation of Thermalization in an Isolated Quantum System.

- PhysicsPhysical review letters
- 2016

This work uses trapped atomic ions forming a hybrid Coulomb crystal and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment and observes the emergence of thermalization.

### Quantum quench in an atomic one-dimensional Ising chain.

- PhysicsPhysical review letters
- 2013

This work reports significant modification of the tunneling rate induced by interactions and shows clear evidence for collective effects in the oscillatory response in an ensemble of tilted one-dimensional atomic Bose-Hubbard chains after a sudden quench.

### Effective thermal dynamics following a quantum quench in a spin chain.

- PhysicsPhysical review letters
- 2009

The nonequilibrium dynamics of the quantum Ising model following an abrupt quench of the transverse field is studied, and it is observed that the dependence of tau(Q)(phi) on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.

### Quantum statistical mechanics in a closed system.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1991

A closed quantum-mechanical system with a large number of degrees of freedom does not necessarily give time averages in agreement with the microcanonical distribution, so by adding a finite but very small perturbation in the form of a random matrix, the results of quantum statistical mechanics are recovered.

### Ballistic Spin Transport in a Periodically Driven Integrable Quantum System.

- PhysicsPhysical review letters
- 2019

An analytic family of quasilocal conservation laws that break the spin-reversal symmetry and compute a lower bound on the spin Drude weight, which is found to be a fractal function of the anisotropy parameter.

### Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

- Physics
- 2014

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically…

### Signatures of integrability in the dynamics of Rydberg-blockaded chains

- PhysicsPhysical Review B
- 2019

A recent experiment on a 51-atom Rydberg-blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This…

### Thermalization after an interaction quench in the Hubbard model.

- PhysicsPhysical review letters
- 2009

This work uses nonequilibrium dynamical mean-field theory to study the time evolution of the fermionic Hubbard model after an interaction quench and indicates a dynamical phase transition which should be observable in experiments on trapped fermionics atoms.

### Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model.

- PhysicsPhysical review letters
- 2010

The off-equilibrium dynamics of the infinite-dimensional Bose-Hubbard model after a quantum quench is studied and a dynamical transition separating regimes of small and large quantum quenches starting from the superfluid state is found.