Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session W15: Quantum Entanglement II |
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Sponsoring Units: GQI Chair: Ian Durham, Saint Anselm College Room: Morial Convention Center 207 |
Thursday, March 13, 2008 2:30PM - 2:42PM |
W15.00001: Experimental demonstration of anyonic statistics with multiphoton entanglement Harald Weinfurter, Witlef Wieczorek, Christian Schmid, Nikolai Kiesel, Reinhold Pohlner, Jiannis Pachos Particles in nature are usually distinguished according to their statistics in two categories: bosons and fermions. However, if one considers only two spatial dimensions statistical behaviour ranging from bosonic to fermionic is found. Particles exhibiting such a behaviour are called anyons. Our experimental demonstration of anyonic statistics is based on a particular two-dimensional model: the toric code proposed by Kitaev [1]. There, anyons arise as excitations that are generated by local operations. We show that for this model anyonic behaviour is revealed for as little as four qubits [2]. This enabled us to experimentally demonstrate anyonic statistics in a quantum simulation with four-photon entanglement. \newline [1] A.~Yu.~Kitaev, Ann. Phys. {\bf 303}, 2 (2003). \newline [2] J.~K.~Pachos {\emph{et al.}}, arXiv:0710.0895v2 [quant-ph] (2007). [Preview Abstract] |
Thursday, March 13, 2008 2:42PM - 2:54PM |
W15.00002: Entanglement entropy and other observables of topological phases with finite correlation length Stefanos Papanikolaou, Kumar S. Raman, Eduardo Fradkin We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems with a finite correlation length. Firstly, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground state wave function of a quantum eight-vertex model in its topological phase, and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a non-trivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy. arxiV: 0709.0729 [Preview Abstract] |
Thursday, March 13, 2008 2:54PM - 3:06PM |
W15.00003: Valence-Bond Monte Carlo for Chains of Non-Abelian Quasiparticles Huan Tran, Nick Bonesteel In non-Abelian FQH states, quasiparticles carry quantum numbers (topological charge) which characterize a degenerate Hilbert space. When these quasiparticles are close enough together, the degeneracy of this Hilbert space is lifted and the quasiparticles are said to interact.\footnote{A. Feiguin \textit {et al.}, PRL \textbf{98}, 160409 (2007).} Here we show that the valence-bond Monte Carlo method introduced by Sandvik\footnote{A. W. Sandvik, PRL \textbf{95}, 207203 (2005).} for spin-1/2 systems can be generalized to simulate 1D chains of such interacting non-Abelian quasiparticles. For uniform chains, our Monte Carlo results for the ground state energy agree with known exact values.$^1$ For random chains we confirm numerically that, as expected,\footnote{ N. E. Bonesteel and K. Yang, PRL \textbf{99}, 140405 (2007).} the ground state freezes into a random singlet phase. By suitably generalizing the notion of valence-bond entanglement entropy\footnote{F. Alet, \textit{et al.}, PRL \textbf{99}, 117204 (2007); R. W. Chhajlany \textit{et al.}, PRL \textbf{99}, 167204 (2007).} to the non-Abelian case we also confirm the predicted result$^3$ that in this phase the entropy of a block of length $L$ scales as $S^{\rm VB}_L \simeq \frac{\ln d}{3} \log_2 L$, where $d$ is the quantum dimension of the quasiparticles. Work supported by US DOE. [Preview Abstract] |
Thursday, March 13, 2008 3:06PM - 3:18PM |
W15.00004: Geometry of metal-insulator transitions in one-dimension Noah Bray-Ali, Lorenzo Campos Venuti, Marco Cozzini, Paolo Zanardi We use the geometric approach to quantum critical points to study the metal-insulator transitions driven by chemical potential, $\mu$, or repulsion, $U$, in the one-dimensional Hubbard model. The transition to the band-insulator, as $\mu\rightarrow \mu_c,$ exhibits conventional scaling of the ground-state fidelity metric tensor $G_{\mu,\nu}\equiv{\rm Re}\left [\left \langle \partial_\mu\psi | \partial_\nu\psi\right \rangle - \left \langle \partial_\mu\psi |\psi\right\rangle\left\langle\psi| \partial_\nu\psi\right \rangle \right ]$. For example, the metric diverges as $G_{U,U}\sim 1/n$, where, $n\sim\sqrt{\mu-\mu_c}$, is the band filling. At the Mott transition, the metric behavior depends on the path of approach to the critical point. [Preview Abstract] |
Thursday, March 13, 2008 3:18PM - 3:30PM |
W15.00005: Topological order at finite temperature: protected or not protected? Claudio Castelnovo, Claudio Chamon We investigate the behavior of the entanglement and topological entropy in the two- and three-dimensional toric code at finite temperature. From our results, we infer that quantum topological order is fragile with respect to thermal fluctuations in spite of the presence of a finite energy gap at zero temperature. In two dimensions, all topological order evaporates at any non-vanishing temperature in the thermodynamic limit. On the contrary, in three dimensions not all topological information is lost, although the topologically protected quantum information (qubit) stored in the ground state of the system is immediately degraded to topologically protected classical probabilistic information (pbit) at any infinitesimal temperature, in the thermodynamic limit. All information is eventually lost beyond a finite temperature phase transition. We comment on the implications of our results with respect to braiding operations and topological quantum computing. [Preview Abstract] |
Thursday, March 13, 2008 3:30PM - 3:42PM |
W15.00006: Long distance entanglement mediated by gapped spin chains Aires Ferreira, Joao Lopes dos Santos This talk will describe an analytical approach for the computation of Long Distance Entanglement (LDE) mediated through one-dimensional quantum spin chains recently found in numerical studies \footnote{L. Campos Venuti, C. Degli Esposti Boschi and M. Roncaglia, Phys. Rev. Lett. \textbf{96} 247206 (2006).}. I review the formalism \footnote{A. Ferreira and J. M. B. Lopes dos Santos, \emph{submitted for publication in APS} pre-print: arXiv:0708.0320 (2007).} that allows the computation of LDE for weakly interacting probes with gapped many-body systems and show that, at zero temperature, a DC response function determines the ability of the physical system to develop genuine quantum correlations between the probes. In the second part of the talk, I show that the biquadratic Heisenberg spin-1 chain is able to produce LDE in the thermodynamical limit and that the finite antiferromagnetic Heisenberg chain maximally entangles two spin-1/2 probes very far apart. This is of crucial importance since feasible mechanisms of entanglement extraction from real solid state systems and their ability to transfer entanglement between distant parties are essential ingredients for the implementation of Quantum Information protocols, such as teleportation or superdense coding. [Preview Abstract] |
Thursday, March 13, 2008 3:42PM - 3:54PM |
W15.00007: Entanglement of Impurities in Spin Chains Erik Sorensen, Nicolas Laflorencie, Ming-Shyang Chang, Ian Affleck Entanglement in $J_1-J_2$, $S=1/2$ quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The impurity contribution to the uniform part of the entanglement entropy, $S_{imp}$, is defined and analyzed in detail in both the gapless, $J_2\leq J_2^c $, as well as the dimerized phase, $J_2>J_2^c$, of the model. This quantum impurity model is in the universality class of the single channel Kondo model and we show that in a quite universal way the presence of the impurity in the gapless phase, $J_2\leq J_2^c$, gives rise to a large length scale, $\xi_K$, associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form $S_{imp}(r/\xi_K,r/R)$ for a system of size $R$. At the critical point, $J_2^c$, an analytic approach based on a Fermi liquid picture, valid at distances $r\gg\xi_K$ and energy scales $T\ll T_K$, is developed and analytic results at $T=0$ and $T\neq 0$ are obtained. In the dimerized phase an appealing picture of the entanglement is developed in terms of a {\it thin soliton} (TS) ansatz permitting variational calculations and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. [Preview Abstract] |
Thursday, March 13, 2008 3:54PM - 4:06PM |
W15.00008: Entanglement Entropy of States with Long-Range Magnetic Order Wenxin Ding, Nicholas Bonesteel, Kun Yang We study the bipartite entanglement entropy of spin models whose ground states have perfect ferromagnetic (FM) or antiferromagnetic (AFM) long-range order. For the FM case the entanglement entropy is taken to be one-half the quantum mutual information so as to properly take into account the ground state degeneracy. The calculation of the entropy for this case is then straightforward and agrees with previous work using a different approach. For the AFM case the problem is reduced to that of four coupled spins. This simplification allows us to determine the asymptotic behavior of the entropy analytically with results which agree well with exact numerical calculations. In both the FM and AFM cases we find the entropy grows logarithmically with block size, $N_1$. For example, if we take $N_1 = N/2$, where $N$ is the total number of spins, then in the FM case the entropy, $E$, scales as $E \simeq \frac{1}{2} \ln N_1$, and in the AFM case, $E \simeq \ln N_1$. In both cases the area law is clearly violated. Implications of these results for more general states with long range order are also discussed. [Preview Abstract] |
Thursday, March 13, 2008 4:06PM - 4:18PM |
W15.00009: Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model Stephan Haas, Rong Yu, Hubert Saleur We have applied the numerical strong disordered renormalization group method to the two-dimensional random transverse field Ising model, and studied the scaling behavior of the entanglement entropy. The leading term of the entanglement entropy scales linearly with the block size, following the so called \emph{area law}. However, besides this \emph{area law} contribution, a subleading logarithmic correction at the quantum critical point is resolved. This correction is understood from the point of view of an underlying percolation transition, both at finite and at zero temperature. [Preview Abstract] |
Thursday, March 13, 2008 4:18PM - 4:30PM |
W15.00010: Entanglement Entropy and Complexity in Random Systems Rodriguez-Laguna Javier Entanglement is considered to be the hallmark of quantum physics, and entanglement entropy (EE) is one of its most natural measurements. Its utility as a marker for quantum criticality for random systems is well established. Recently, it has been shown that the scaling of the running-time in some quantum annealing methods is also related to it. In this work we show how the behaviour of this magnitude in some random systems can provide insight about the complexity of the structure of their quantum critical points. Moreover, we provide some hints that point towards a relation between the behaviour of the EE and the complexity class of classical problems. References: J. Rodriguez-Laguna, J. Phys. A: Math. Theor. 40, 12043 (2007), and JSTAT P05008 (2007). [Preview Abstract] |
Thursday, March 13, 2008 4:30PM - 4:42PM |
W15.00011: Entanglement Entropy Scaling in the Disordered Golden Chain Lukasz Fidkowski, Gil Refael, Nick Bonesteel, Kun Yang, Joel Moore For pure critical spin chains, the scaling of the entanglement entropy of a region of size $L$ with its complement is proportional to $\log L$ with the constant of proportionality being the central charge of the associated conformal field theory. Certain strongly disordered spin chains exhibit critical points with similar $\log L$ scaling. Here we study the disordered golden chain (modeled by fibonacci anyons), and show that the usual random singlet critical point achieved with random antiferromagnetic (AFM) couplings is unstable to ferromagnetic (FM) perturbations. We identify the new mixed FM-AFM fixed point and compute its entanglement entropy scaling. [Preview Abstract] |
Thursday, March 13, 2008 4:42PM - 4:54PM |
W15.00012: Quantum Ergodicity and the Dynamical Generation of Entanglement in Kicked Coupled Tops Collin Trail, Vaibhav Madhok, Ivan Deutsch, Shohini Ghose, Leigh Norris, Arjendu Pattanayak We explain how the long-time average dynamically generated entanglement in a Hamiltonian bipartite system is related to the corresponding classical dynamics in the semiclassical limit. Where classical dynamics is chaotic, ergodic mixing leads to the generation of ``random quantum states.'' These states possess the typical entanglement of a state randomly sampled from the appropriate Hilbert space under the unitarily invariant Haar measure. We exemplify these results using a system of coupled kicked-tops in which entanglement and chaos arise from the same physical effect in contrast to previous studies. We present quantitive predictions of the dynamically generated entanglement, which is influenced by the time symmetries of the system and the structure of the Hilbert space, under a variety of different conditions, and show a close fit to numerical simulations. [Preview Abstract] |
Thursday, March 13, 2008 4:54PM - 5:06PM |
W15.00013: Observation of two-particle Aharonov-Bohm interference Izhar Neder, Nissim Ofek, Yunchul Chung, Moty Heiblum, Diana Mahalu, Vladimir Umansky \textit{Nature} \textbf{448}, 333-337 (19 July 2007) We report the first observation of quantum interference between two independent {\&} non-interacting electrons in a unique interferometer proposed by Yurke et. al. [1] {\&} Samuelsson et. al. [2]. The interference fringes were observed only in the joint probability of electrons arrival at two different drains; hence being the quantum analogue to the Hanbury Brown {\&} Twiss (HBT) experiment with classical waves [3]. This, sought after, counter intuitive effect, is a direct result of the quantum exchange statistics of identical quantum particles. Our observation is a signature of orbital entanglement between two independent electrons, even tough they never interacted with each other. [1] B. Yurke {\&} D. Stoler, Phys. Rev. A46, 2229-2234 (1992) [2] P. Samuelsson, E. V. Sukhorukov {\&} M. Buttiker, Phys. Rev. Lett. 92, 02685 (2004). [3] R. Hanbury Brown {\&} R. Q. Twiss, Phil. Mag. 45, 663-682 (1954). [Preview Abstract] |
Thursday, March 13, 2008 5:06PM - 5:18PM |
W15.00014: Few-electron anisotropic quantum dots in low magnetic fields: exact-diagonalization results for excitations, spin configurations, and entanglement Constantine Yannouleas, Uzi Landman Following earlier studies\footnote{Y. Li, C. Yannouleas, and U. Landman, arXiv:0710.4325v1 [Phys. Rev. B (2007), in press]; C. Yannouleas and U. Landman, Rep. Prog. Phys. {\bf 70}, 2067 (2007)} for $N=2-3$ electrons, exact-diagonalization calculations for $N=4-6$ electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, will be presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the magnetic field and of quantum-dot anisotropy. Analysis of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules (WMs). For strong anisotropy, the WMs acquire a linear geometry, and the wave functions with a total spin projection $S_z=(N-2)/2$ are similar to the strongly entangled $W$ states. For intermediate anisotropy, the WMs exhibit a more complex structure. The degree of entanglement can be quantified through the use of the von Neumann entropy. [Preview Abstract] |
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