# 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…

## 36 Citations

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## References

SHOWING 1-10 OF 73 REFERENCES

### Evolution of entanglement entropy in one-dimensional systems

- Physics
- 2005

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

- Physics
- 2013

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

- Physics
- 2014

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

- Physics
- 2009

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

- Physics
- 2006

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.

- PhysicsPhysical review letters
- 2010

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

- Physics
- 2012

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

- Physics
- 2010

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

- Physics
- 2011

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…

### Nonlocal order in gapless systems: entanglement spectrum in spin chains.

- PhysicsPhysical review letters
- 2010

We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high "entanglement energy" levels, from a…