Dynamics of the entanglement spectrum in spin chains

@article{Torlai2013DynamicsOT,
  title={Dynamics of the entanglement spectrum in spin chains},
  author={Giacomo Torlai and Luca Tagliacozzo and Gabriele De Chiara},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2013},
  volume={2014}
}
We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for… 
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36 Citations
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36 Citations

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References

SHOWING 1-10 OF 73 REFERENCES

Evolution of entanglement entropy in one-dimensional systems

We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length and its complement, starting from a pure state…

Entanglement spectrum and entangled modes of random XX spin chains

We study in this work the ground state entanglement properties of finite XX spin-1/2 chains with random couplings, using Jordan-Wigner transformation. We divide the system into two parts and study…

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a…

Reduced density matrices and entanglement entropy in free lattice models

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a…

Energy and multipartite entanglement in multidimensional and frustrated spin models

We investigate the relation between the entanglement properties of a quantum state and its energy for macroscopic spin models. To this aim, we develop a general method to compute energy bounds for…

Entanglement spectra of quantum Heisenberg ladders.

This work analyzes the entanglement spectrum of gapped two-leg quantum Heisenberg ladders on a periodic ribbon partitioned into two identical periodic chains, stating a direct correspondence between the low-energy entangler spectrum of a partitioned system and the true spectrum of the virtual edges.

Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry

We study the entanglement spectrum of spin-$1/2$ $XXZ$ ladders both analytically and numerically. Our analytical approach is based on perturbation theory starting either from the limit of strong rung…

Entanglement spectrum of a topological phase in one dimension

We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of…

Entanglement spectrum of one-dimensional extended Bose-Hubbard models

The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the blocklike nature of the reduced density matrix in number sectors and the…

Boundary-locality and perturbative structure of entanglement spectra in gapped systems.

Focusing on gapped phases of several one-dimensional systems, it is shown how this spectrum is dominated by contributions from the boundary between the parts, contradicting the view of an "entanglement Hamiltonian" as a bulk entity.
...