Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session L29: Quantum Entanglement 
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Sponsoring Units: GQI Chair: Lana Sheridan, National University of Singapore Room: C148 
Tuesday, March 22, 2011 2:30PM  2:42PM 
L29.00001: Entanglement entropy between two coupled TomonagaLuttinger liquids Shunsuke Furukawa, Yong Baek Kim We consider a system of two coupled TomonagaLuttinger liquids (TLL) on parallel chains and study the R\'enyi entanglement entropy $S_n$ between the two chains. The limit $n\to1$ corresponds to the von Neumann entanglement entropy. The system is effectively described by twocomponent bosonic field theory with different TLL parameters in the symmetric/antisymmetric channels. We argue that in this system, $S_n$ is a linear function of the length of the chains followed by a universal subleading constant $\gamma_n$ determined by the ratio of the two TLL parameters. We derive the formulae of $\gamma_n$ for integer $n\ge 2$ using (a) groundstate wave functionals of TLLs and (b) conformal boundary states, which lead to the same result. These predictions are checked in a numerical diagonalization analysis of a hardcore bosonic model on a ladder. Although our formulae of $\gamma_n$ are not analytic in the limit $n\to 1$, our numerical result suggests that the subleading constant in the von Neumann entropy is also universal. [Preview Abstract] 
Tuesday, March 22, 2011 2:42PM  2:54PM 
L29.00002: Entanglement from Charge Statistics: Exact Relations for ManyBody Systems Francis Song, Christian Flindt, Stephan Rachel, Israel Klich, Karyn Le Hur We present exact formulas for the entanglement and R\'{e}nyi entropies generated at a quantum point contact (QPC) in terms of the statistics of charge fluctuations, which we illustrate with examples from both equilibrium and nonequilibrium transport. The formulas are also applicable to groundstate entanglement in systems described by noninteracting fermions in any dimension, which in one dimension includes the critical spin1/2 XX and Ising models where conformal field theory predictions for the entanglement and R\'{e}nyi entropies are reproduced from the full counting statistics. These results may play a crucial role in the experimental detection of manybody entanglement in mesoscopic structures and cold atoms in optical lattices. [Preview Abstract] 
Tuesday, March 22, 2011 2:54PM  3:06PM 
L29.00003: Quantum Monte Carlo Calculation of the Topological Entanglement Entropy in a Kagome Spin Liquid Roger Melko, Sergei Isakov, Ann Kallin, Matthew Hastings We develop a quantum Monte Carlo procedure to compute the Renyi entanglement entropy of interacting quantum manybody systems at nonzero temperature. We illustrate the method by calculating the topological entanglement entropy in a featureless Mott Insulating phase of a BoseHubbard model on the kagome lattice. The topological entanglement entropy displays a characteristic finitetemperature crossover behavior discussed previously in the context of the toric code. At zerotemperature it becomes the log of the quantum dimension of the topological order, confirming the existence of a Z2 spin liquid phase in the groundstate of this model. [Preview Abstract] 
Tuesday, March 22, 2011 3:06PM  3:18PM 
L29.00004: Entanglement entropy and boundary operators in quantum impurity systems Erik Eriksson, Henrik Johannesson Entanglement in quantum impurity systems can be studied analytically using boundary conformal field theory (BCFT). In particular, the effect from an impurity on the entanglement entropy of a surrounding region is governed by the boundary operator content of the model. We present general results for the corrections to scaling of the R{\'e}nyi entanglement entropies when perturbing the BCFT with boundary operators [arXiv:1011.0448]. These results are then used to predict the asymptotic largeblock behavior of the impurity contribution to the entanglement entropy in various Kondo systems. [Preview Abstract] 
Tuesday, March 22, 2011 3:18PM  3:30PM 
L29.00005: Global quantum correlations in the spin1 bilinearbiquadratic chain Roman Orus, TzuChieh Wei We investigate global properties of the ground state of the spin1 bilinearbiquadratic quantum spin chain in the thermodynamic limit, focusing on the geometric entanglement and fidelity diagram. The two quantities are computed via iTEBD and they appear to be capable of detecting the various wellknown phase transitions in the system, including a KosterlitzThouless one. The two quantities also behave distinctively at other points in the phase diagram. In particular, this is the case for the fidelity diagram at $\theta \approx 1.34 \pi$ (around a possible transition to a spin nematic phase), and also for the geometric entanglement at the integrable gapped point $\theta = 3 \pi /2$, where we conjecture an infinite entanglement length in the system. [Preview Abstract] 
Tuesday, March 22, 2011 3:30PM  3:42PM 
L29.00006: Definitions of entanglement entropy of spin systems in the valencebond basis YuCheng Lin, Anders Sandvik The valencebond structure of spin1/2 Heisenberg antiferromagnets is closely related to quantum entanglement. We investigate definitions of entanglement entropy based on individual valence bonds connecting two subsystems, as well as shared loops of the transposition graph (overlap) of two valencebond states [1]. We reformulate a previously used definition based on valance bonds in the wave function as a true ground state expectation value, and find that its scaling for the Heisenberg chain agrees with an exact result. The loopbased entanglement entropy of the twodimensional Heisenberg model is shown to satisfy the area law (with an additive logarithmic correction), unlike singlebond definitions (which exhibit multiplicative logarithmic corrections). \\[4pt] [1] Y.C. Lin and A.W. Sandvik, arXiv:1005.0821. [Preview Abstract] 

L29.00007: ABSTRACT WITHDRAWN 
Tuesday, March 22, 2011 3:54PM  4:06PM 
L29.00008: General relation between energy spectrum and entanglement spectrum Xiaoliang Qi, Hosho Katsura, Andreas Ludwig We demonstrate that the bipartite density matrix, arising from a spatial bipartitioning of a gapped topological state which possesses gapless edge modes in the form of a conformal field theory (CFT ) (when terminated against a topologically trivial state/vacuum), such as e.g. a general quantum Hall state, is the density matrix of a the chiral edge state CFT at a finite temperature. We obtain this result by applying a physical instantaneous cut of the gapped system, and by viewing the cutting process as a sudden ``quantum quench'' into a CFT, using the tools of boundary conformal field theory. In particular, we obtain a general relation between the Hamiltonian spectrum of gapless theories and the entanglement spectrum of the gapped theory obtained from coupling two gapless theories. [Preview Abstract] 
Tuesday, March 22, 2011 4:06PM  4:18PM 
L29.00009: The entanglement spectrum of perturbed ChernSimons theories Thomas Jackson, Israel Klich Topological field theories  theories insensitive to the metric of the space they live on  have been shown to be applicable to a remarkable variety of condensed matter systems. A natural and important question is how perturbations relevant for real systems (interactions, etc.) deform these topological structures. In this work, we consider perturbations of ChernSimons theory by a small YangMills term, which breaks topological symmetry by introducing local bulk degrees of freedom in the form of massive gluons. We consider the behavior of the entanglement spectrum (the eigenvalues of the reduced density matrix) of this theory under this perturbation. We argue that the act of taking the partial trace may be viewed as adding a chemical potential gradient for the gluons near the boundary of the space, with a length scale determined by the gluon mass  or, colloquially, a ``hot edge.'' [Preview Abstract] 
Tuesday, March 22, 2011 4:18PM  4:30PM 
L29.00010: Entanglement, Dissipation and the Casimir effect Israel Klich The role of dissipation in the Casimir force between metals or dielectric has a been discussed in many works and is an important part of the Casimir theory, where puzzles about the finite temperature corrections to the effect are still being worked out. Here, we study the contribution of dissipation in creating distance dependent entanglement between materials, and on the meaning of the corresponding entropy. [Preview Abstract] 
Tuesday, March 22, 2011 4:30PM  4:42PM 
L29.00011: Entanglement Entropy Scaling of 2D Critical Wave Functions Michael Zaletel, Jens Bardarson, Joel Moore While CFT calculations have revealed a variety of universal predictions for the entanglement spectrum of critical 1+1D field theories, much less is known about higherdimensional systems. CFT methods can be extended to a class of 2+1D theories characterized by a $z = 2$ critical point, the socalled RokhsarKivelson wave functions. The entanglement entropy of RKtype critical wave functions contains a universal logarithmic contribution $\gamma \log( L )$ for some geometries arising from a trace anomaly in the corresponding CFT. We first reexamine the free boson, where the existence of orderunity contributions that depend on the boson compactification radius has been discussed in several recent papers (Hsu et al., St\'ephan et al., Oshikawa). We find analytically and numerically that the logarithmic contribution exists with the coefficient predicted by Fradkin and Moore and is independent of the compactification. However, it appears that their conjecture that general CFTs show the same dependence of $\gamma$ on central charge as the free boson is incorrect. We present arguments and numerical evidence for this conclusion in $c = 1/2$ and $c=1$ lattice models. [Preview Abstract] 
Tuesday, March 22, 2011 4:42PM  4:54PM 
L29.00012: Entanglement spectra of Hofstadter and related models Zhoushen Huang, Daniel Arovas We compute the bipartite entanglement spectra for the Hofstadter model on various twodimensional lattices. The behavior of the entanglement eigenstates in the vicinity of a partition boundary is investigated in detail. We also investigate the formation of entanglement edge states as one tunes through a topological phase transition in Haldane's honeycomb lattice model and other related systems. [Preview Abstract] 
Tuesday, March 22, 2011 4:54PM  5:06PM 
L29.00013: Entanglement Spectrum In Condensed Matter B. Andrei Bernevig I will review the information that entanglement spectra give for a wide range of systems in condensed matter physics, such as fractional quantum hall effect, quantum spin chains, topological insulators, and disordered systems. (the results are based on a series of works performed in collaboration with N. Regnault, R. Thomale, A. Chandran, A Sterdyniak, M. Hermanns, Z. Papic, T.L. Hughes, E. Prodan, D.P. Arovas) [Preview Abstract] 
Tuesday, March 22, 2011 5:06PM  5:18PM 
L29.00014: Simultaneous generation of multiple quadripartite continuousvariable cluster states in the optical frequency comb of a single optical parametric oscillator Matthew Pysher, Yoshichika Miwa, Reihaneh Shahrokhshahi, Russell Bloomer, Olivier Pfister We report the experimental generation of multiple, fourmode, continuousvariable cluster states from a single optical parametric oscillator (OPO) operating below threshold. We use a PPKTP crystal phasematching two concurrent nonlinear interactions to entangle the optical frequency comb formed by the OPO cavity. Four independent entanglement witnesses (a.k.a. infinitesimal operators of stabilizers, or ``nullifiers'') display squeezing in each cluster state, and we utilize the large phasematching bandwidth of the nonlinear interactions to display the simultaneous creation of several such cluster states using only a single pump frequency. A slightly more sophisticated version of this experimental method, using a crystal with three nonlinear interactions and 15 pump frequencies, has theoretically shown the ability to produce arbitrarily large squaregrid cluster states suitable for universal oneway quantum computing. [Preview Abstract] 
Tuesday, March 22, 2011 5:18PM  5:30PM 
L29.00015: Multipartite entanglement in the optical frequency comb of a depletedpump optical parametric oscillator Reihaneh Shahrokhshahi, Olivier Pfister The optical frequency comb (OFC) of a single optical parametric oscillator (OPO) has been shown to be a very interesting candidate for scaling the size of quantum entangled states. In sophisticated OPOs below threshold, squaregrid cluster states of very large size can in principle be generated. Here, we study a very simple OPO well above threshold, in the linearized fluctuation approximation, and investigate the effect of pump depletion on multiple, simultaneously resonant, signalmode pairs. We find that the depleted quantum pump mediates quantum correlations between the signal fields. These correlations lead in turn to inseparability of these fields, as evidenced by the wellknown van LookFurusawa entanglement criteria. Due to its simplicity and its scalability, this fully inseparable multipartite entangled state could used as a resource in quantum information protocols. [Preview Abstract] 
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