Entanglement versus chaos in disordered spin chains

Santos, Lea F.; Rigolin, Gustavo; Escobar, C.

doi:10.1103/physreva.69.042304

Cited by 107 publications

(93 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this respect, our analysis shares some motivation with earlier studies of entanglement across a transition to nonintegrability in a class of one-dimensional Harper Hamiltonians by Lakshminarayan et al [24], and spin-1/2 lattice systems by Santos et al [25], and Mejia-Monasterio et al [26] where, however, primary emphasis to pairwise and bipartite entanglement is given. Only recently has genuine multipartite entanglement started to be addressed, notably in the one-dimensional Ising model with a tilted magnetic field [21,27].…”

Section: Introductionmentioning

confidence: 50%

Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

et al. 2008

View full text Add to dashboard Cite

We investigate disordered one-and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of relative delocalization is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and generalized entanglement are investigated in a wide parameter regime by using a family of spin-and fermion-purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.

show abstract

Section: Introductionmentioning

confidence: 50%

Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

et al. 2008

View full text Add to dashboard Cite

show abstract

“…For an even number of spins, there is a "cross-over value", λ GGM c , of λ = J/h, before which the quenched averaged GGM in the disordered system is larger than the GGM in the ordered system. Therefore, there are distinct regimes where introduction of disorder enhances the amount of genuine multiparty entanglement present in the quantum system [64,65]. The existence of entanglement in a quantum system, consisting of several subsystems, indicates the thermodynamic signature of high global order in the whole system while the local order in the subsystems is low [66].…”

Section: Order-from-disorder In Genuine Multipartite Entanglement mentioning

confidence: 99%

Disorder overtakes order in information concentration over quantum networks

et al. 2011

View full text Add to dashboard Cite

We consider different classes of quenched disordered quantum XY spin chains, including quantum XY spin glass and quantum XY model with a random transverse field, and investigate the behavior of genuine multiparty entanglement in the ground states of these models. We find that there are distinct ranges of the disorder parameter that gives rise to a higher genuine multiparty entanglement than in the corresponding systems without disorder -an order-from-disorder in genuine multiparty entanglement. Moreover, we show that such a disorder-induced advantage in the genuine multiparty entanglement is useful -it is almost certainly accompanied by a order-from-disorder for a multiport quantum dense coding capacity with the same ground state used as a multiport quantum network.

show abstract

“…In some studies of entanglement measures, quantum chaos is generated by extrinsic disorder [8]; in others, with a clean but chaotic Hamiltonian [9,10]. The question of whether chaos aids or hinders entanglement generation relevant to quantum-information applications has not yet yielded a clear answer [10].…”

mentioning

confidence: 99%

Entanglement and Dynamics of Spin Chains in Periodically Pulsed Magnetic Fields: Accelerator Modes

2006

View full text Add to dashboard Cite

We study the dynamics of a single excitation in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field. We show that, for experimentally reasonable parameters, a pair of counterpropagating coherent states is ejected from the center of the chain. We find an illuminating correspondence with the quantum time evolution of the well-known paradigm of quantum chaos, the quantum kicked rotor. From this we can analyze the entanglement production and interpret the ejected coherent states as a manifestation of the so-called ''accelerator modes'' of a classically chaotic system. There is considerable interest in the fidelity of quantum state transmission and entanglement measures in spin chains because of their relevance to quantum-information applications. In [1] state transmission in a Heisenberg chain was investigated. In [2] it was shown that such a chain, in the presence of an external, static, parabolic magnetic field, can give perfect transmission of coherent spin states of appropriate width. Obtaining coherent states of specified widths represents a technical challenge though.Here, we investigate the dynamics of a Heisenberg spinchain subjected to short, time-periodic pulses from an external parabolic magnetic field. We find that this provides an effective technique for generating well-defined coherent states, starting from a single excitation at the center of the spin chain. The key to the analysis is that we note, for the first time, a close correspondence between the time evolution of a Heisenberg chain and that of the well-known quantum kicked rotor (QKR) [3,4] in its quantumresonance regime [5]. Our additional parabolic external field extends the correspondence between the Heisenberg spin chain to the nonresonant QKR. Both the nonresonant and resonant QKR have been well investigated experimentally with cold atoms in optical lattices [5,6].There is also much current interest in the interface between quantum chaos and quantum information [7]. In some studies of entanglement measures, quantum chaos is generated by extrinsic disorder [8]; in others, with a clean but chaotic Hamiltonian [9,10]. The question of whether chaos aids or hinders entanglement generation relevant to quantum-information applications has not yet yielded a clear answer [10]. In [11] it was shown that a class of kicked Ising-type chains have quantum behavior related to those of one-body ''image'' systems with a well-defined classical limit, which can be chaotic or integrable.However, to our knowledge, the correspondence between the dynamics of the QKR, a leading paradigm of quantum chaos and the Heisenberg chain, a system of such key interest in quantum-information, has not been noted or exploited previously. We show it means that with the pulsed parabolic field, we can employ certain ''textbook'' [12] expressions found for the QKR and the standard map to describe the entanglement properties. It means also that we see not only generic forms of quantum chaotic behavior in the spin chain, ...

show abstract

Entanglement versus chaos in disordered spin chains

Cited by 107 publications

References 32 publications

Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

Disorder overtakes order in information concentration over quantum networks

Entanglement and Dynamics of Spin Chains in Periodically Pulsed Magnetic Fields: Accelerator Modes

Contact Info

Product

Resources

About