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arXiv:0708.3682 · Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics

Entanglement in disordered systems at criticality

Imre Varga, Jose Antonio Mendez-Bermudez

Published Feb 6, 2008• 7 citations
arXivHTMLPDF

Abstract

Abstract Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight‐binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system are calculated in a one‐electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssc.200777589

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Abstract Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum computation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight‐binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system are calculated in a one‐electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract We focus on tight‐binding Hamiltonians on a regular one‐dimensional lattice with non‐random long‐range inter‐site coupling Jmn = J/|m−n|μ and random uncorrelated site energies. Within the model the localization‐delocalization transition occurs at one of the energy band edges provided 1 < μ < 3/2. Using the model we demonstrate that the ratio of the first two momenta of the participation number distribution for the critical states is a size invariant parameter at some value of the disorder magnitude Δc. We claim that the invariance manifests the transition. We find that Δc ≠ 0 at 1 < μ < 3/2, suggesting that the system undergoes the localization‐delocalization transition with respect to disorder magnitude. At μ ≥ 3/2, all states are localized. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random (‘pure’) quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.
The entanglement entropy is related to quantum phase transitions. It behaves differently when a quantum system is in a phase with a finite correlation length (such as an insulator phase), compared to a system in a critical phase in which the correlation length is infinite such as a metallic phase. The entanglement entropy of disordered systems does not depend only on the length of the relevant segment and the size of the system but also on the specific realization of disorder. Thus, the entanglement entropy of a disordered system exhibits mesoscopic fluctuations. Here we shall show numerical results that exhibit a crossover in the distribution of the entanglement entropy from a normal distribution at the weak localization regime to a log-normal distribution at the strong localization regime.
Abstract We study the entanglement creation between two flux qubits interacting with electromagnetic field modes. No direct interaction between the qubits exists. Entanglement is reached using the entanglement swapping method by an interference measurement performed on photons. We discuss the influence of off‐resonance and multi‐photon initial states on the qubit–qubit entanglement. The presented scheme is able to drive an initially separable state of two qubits into an highly entangled state suitable for quantum information processing (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of entanglement in spin chain systems, both near and at a quantum critical point. Our results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories. We explore some of the implications of this connection.
Abstract We study the relaxation of a non‐equilibrium carrier distribution under the influence of the electron‐electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part including the disorder and a two‐particle part accounting for the Coulomb interaction. We apply the equation‐of‐motion approach for the density matrix, which provides a fully microscopic description of the relaxation. Our results show that the nonequilibrium distribution in this closed and internally interacting system relaxes exponentially fast during the initial dynamics. This fast relaxation can be described by a phenomenological damping rate. The total single particle energy decreases in the redistribution process, keeping the total energy of the system fixed. It turns out that the relaxation rate decreases with increasing disorder. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)