Quantum Entanglement Growth Under Random Unitary Dynamics

@article{Nahum2016QuantumEG,
  title={Quantum Entanglement Growth Under Random Unitary Dynamics},
  author={Adam Nahum and Jonathan Ruhman and Sagar Vijay and Jeongwan Haah},
  journal={arXiv: Statistical Mechanics},
  year={2016}
}
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time--dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the `entanglement tsunami' in Hamiltonian… 

Emergent statistical mechanics of entanglement in random unitary circuits

We map the dynamics of entanglement in random unitary circuits, with finite on-site Hilbert space dimension $q$, to an effective classical statistical mechanics. We demonstrate explicitly the

Entanglement formation in continuous-variable random quantum networks

TLDR
By mapping the ensemble-averaged entanglement dynamics on an arbitrary network to a random-walk process on a graph, this work is able to exactly solve the entangler dynamics.

Markovian entanglement dynamics under locally scrambled quantum evolution

We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a

Coarse-grained dynamics of operator and state entanglement

We give a detailed theory for the leading coarse-grained dynamics of entanglement entropy of states and of operators in generic short-range interacting quantum many-body systems. This includes

Dynamics of entanglement and transport in one-dimensional systems with quenched randomness

Quenched randomness can have a dramatic effect on the dynamics of isolated 1D quantum many-body systems, even for systems that thermalize. This is because transport, entanglement, and operator

Entanglement growth after inhomogenous quenches

We study the growth of entanglement in quantum systems with a conserved quantity exhibiting diffusive transport, focusing on how initial inhomogeneities are imprinted on the entropy. We propose a

Measurement-Induced Phase Transitions in the Dynamics of Entanglement

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate $p$

Entanglement growth in diffusive systems

Entanglement helps in understanding diverse phenomena, going from quantifying complexity to classifying phases of matter. Here we study the influence of conservation laws on entanglement growth.

Dynamics of entanglement and transport in 1 D systems with quenched randomness

Quenched randomness can have a dramatic effect on the dynamics of isolated 1D quantum manybody systems, even for systems that thermalize. This is because transport, entanglement, and operator

Entanglement transitions via space-time rotation of quantum circuits

Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries. Two distinct routes to impede entanglement growth are inducing localization via
...

References

SHOWING 1-10 OF 102 REFERENCES

Entanglement dynamics in quantum many-body systems

We study entanglement growth in quantum many-body systems and propose a method to experimentally measure it. We show that entanglement growth is related to the spreading of local operators. In

Dynamics of entanglement and transport in 1 D systems with quenched randomness

Quenched randomness can have a dramatic effect on the dynamics of isolated 1D quantum manybody systems, even for systems that thermalize. This is because transport, entanglement, and operator

Operator Spreading in Random Unitary Circuits

Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results

The emergence of typical entanglement in two-party random processes

We investigate the entanglement within a system undergoing a random, local process. We find that there is initially a phase of very fast generation and spread of entanglement. At the end of this

Universal slow growth of entanglement in interacting strongly disordered systems.

TLDR
This work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase.

Measuring entanglement entropy in a quantum many-body system

TLDR
Making use of the single-site-resolved control of ultracold bosonic atoms in optical lattices, two identical copies of a many-body state are prepared and interfered to directly measure quantum purity, Rényi entanglement entropy, and mutual information.

Statistical Distribution of Quantum Entanglement for a Random Bipartite State

We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The full probability

Extended slow dynamical regime close to the many-body localization transition

Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at

Evolution of entanglement entropy following a quantum quench : Analytic results for the XY chain in a transverse magnetic field

The non-equilibrium evolution of extended quantum systems is one of the most challenging problems of contemporary research in theoretical physics. The subject is in a renaissance era after the

Entanglement growth during thermalization in holographic systems

We derive in detail several universal features in the time evolution of entanglement entropy and other nonlocal observables in quenched holographic systems. The quenches are such that a spatially
...