Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Q33: Quantum Entanglement II |
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Sponsoring Units: GQI Room: 706 |
Wednesday, March 5, 2014 2:30PM - 2:42PM |
Q33.00001: Universal Renyi mutual information in classical systems: the case of kagome ice Armin Rahmani, Gia-Wei Chern We study the Renyi mutual information of classical systems characterized by a transfer matrix. We first establish a general relationship between the Renyi mutual information of such classical mixtures of configuration states, and the Renyi entropy of a corresponding Rokhsar-Kivelson--type quantum superposition. We then focus on chiral and nonchiral kagome-ice systems, classical spin liquids on the kagome lattice, which respectively have critical and short-range correlations. Through a mapping of the chiral kagome ice to the quantum Liftshitz critical field theory, we predict a universal subleading term in the Renyi mutual information of this classical spin liquid, which can be realized in the pyrochlore spin ice in a magnetic field. We verify our prediction with direct numerical transfer-matrix computations, and further demonstrate that the nonchiral kagome ice (and the corresponding quantum Rokhsar-Kivelson superposition) is a topologically trivial phase. Finally, we argue that the universal term in the mutual information of the chiral kagome ice is fragile against the presence of defects. [Preview Abstract] |
Wednesday, March 5, 2014 2:42PM - 2:54PM |
Q33.00002: Eigenstate Thermalization and the Sign-Structure of Quantum Many-Body Eigenstates Matthew Fisher, Tarun Grover Eigenstate Thermalization Hypothesis (ETH) posits that a generic finite-energy density eigenstate of an ergodic quantum system satisfies the ``volume law'' of entanglement entropy -- the bipartite Renyi entanglement entropies associated with a subregion scale in proportion to the subregion's volume. Here we argue that the volume law for Renyi entropies originates from the intricate ``sign structure'' of the many body eigenstates. Specifically, we show that the amplitude fluctuations in a many body eigenstate carry very little entanglement compared to the fluctuations in the sign of the wavefunction, and it is the latter which are essential for the aforementioned volume law. We present analytical and numerical results that support these conclusions. [Preview Abstract] |
Wednesday, March 5, 2014 2:54PM - 3:06PM |
Q33.00003: Entanglement Temperature and Entanglement Entropy of Excited States Gabriel Wong, Israel Klich, Leopaldo A. Pando Zayas, Diana Vaman We derive a general relation between the ground state entanglement Hamiltonian and the physical stress tensor within the path integral formalism. For spherical entangling surfaces in a CFT, we reproduce the \emph{local} ground state entanglement Hamiltonian derived by Casini, Huerta and Myers. The resulting reduced density matrix can be characterized by a spatially varying ``entanglement temperature.'' Using the entanglement Hamiltonian, we calculate the first order change in the entanglement entropy due to changes in conserved charges of the ground state, and find a local first law-like relation for the entanglement entropy. Our approach provides a field theory derivation and generalization of recent results obtained by holographic techniques. However, we note a discrepancy between our field theoretically derived results for the entanglement entropy of excited states with a non-uniform energy density and current holographic results in the literature. Finally, we give a CFT derivation of a set of constraint equations obeyed by the entanglement entropy of excited states in any dimension. Previously, these equations were derived in the context of holography. [Preview Abstract] |
Wednesday, March 5, 2014 3:06PM - 3:18PM |
Q33.00004: How universal is the entanglement spectrum? Anushya Chandran, Vedika Khemani, Shivaji Sondhi It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the ES and the Renyi entropies can mislead entirely, while for quantum Hall systems the ES has much less universal content than assumed to date. [Preview Abstract] |
Wednesday, March 5, 2014 3:18PM - 3:30PM |
Q33.00005: Entanglement at an O(3) Critical Point with a Numerical Linked-Cluster Expansion Ann B. Kallin, Rajiv Singh, Miles Stoudenmire, A. John Berlinsky, Roger Melko Using the Numerical Linked-Cluster Expansion technique on rectangular clusters, we study the scaling of Renyi entanglement entropies at an O(3) quantum critical point, realized through the spin-1/2 Heisenberg bi-layer. There is a subleading logarithmic contribution to the entanglement due to the presence of a vertex in the entanglement boundary, with a coefficient that is known to be universal. We compute this ``corner coefficient'' and compare our value to that from both a non-interacting field theory, and the Ising fixed point in 2+1 dimensions. The corner coefficient has the potential to distinguish between these and other universality classes, through a variety of numerical calculations of strongly interacting quantum critical points. [Preview Abstract] |
Wednesday, March 5, 2014 3:30PM - 3:42PM |
Q33.00006: Entanglement entropy in mesoscopic conductors Konrad Thomas, Christian Flindt The degree of entanglement in a many-body quantum system can be characterized by the entanglement entropy. We consider the entanglement entropy generated between two electronic reservoirs connected by a quantum point contact (QPC) [1,2]. The entanglement entropy is obtained from the fluctuations of the electric current which we evaluate numerically exact using a tight-binding model of the system [3]. Within our approach we can investigate the influence of time-dependent modulations, including the opening and closing of the QPC [4]. We focus on electronic conductors, but our ideas may also be realized in cold atomic gases. \newline\newline [1] I.~Klich and L.~S.~Levitov, Phys. Rev. Lett. 102, 100502 (2009)\newline [2] H.~F.~Song, C.~Flindt, S.~Rachel, I.~Klich, and K.~Le~Hur, Phys. Rev. B 83, 161408(R) (2011) \& Phys. Rev. B 85, 035409 (2012)\newline [3] K.~Sch\"{o}nhammer, Phys. Rev. B 75, 205329 (2007)\newline [4] K.~H.~Thomas and C.~Flindt, in.~prep. [Preview Abstract] |
Wednesday, March 5, 2014 3:42PM - 3:54PM |
Q33.00007: Entanglement entropy of fermionic quadratic band touching model Xiao Chen, Gil Young Cho, Eduardo Fradkin The entanglement entropy has been proven to be a useful tool to diagnose and characterize strongly correlated systems such as topologically ordered phases and some critical points. Motivated by the successes, we study the entanglement entropy (EE) of a fermionic quadratic band touching model in $(2+1)$ dimension. This is a fermionic ``spinor'' model with a finite DOS at k=0 and infinitesimal instabilities. The calculation on two-point correlation functions shows that a Dirac fermion model and the quadratic band touching model both have the asymptotically identical behavior in the long distance limit. This implies that EE for the quadratic band touching model also has an area law as the Dirac fermion. This is in contradiction with the expectation that dense fermi systems with a finite DOS should exhibit $L\log L$ violations to the area law of entanglement entropy (L is the length of the boundary of the sub-region) by analogy with the Fermi surface. We performed numerical calculations of entanglement entropies on a torus of the lattice models for the quadratic band touching point and the Dirac fermion to confirm this. The numerical calculation shows that EE for both cases satisfy the area law. We further verify this result by the analytic calculation on the torus geometry. [Preview Abstract] |
Wednesday, March 5, 2014 3:54PM - 4:06PM |
Q33.00008: Particle entanglement in continuum many-body systems via quantum Monte Carlo C.M. Herdman, P.-N. Roy, R.G. Melko, A. Del Maestro Entanglement of spatial bipartitions, used to explore lattice models in condensed matter physics, may be insufficient to fully describe itinerant quantum many-body systems in the continuum. We introduce a procedure to measure the R\'{e}nyi entanglement entropies on a particle bipartition, with general applicability to continuum Hamiltonians via Path Integral Monte Carlo methods. Via direct simulations of interacting bosons in one spatial dimension, we confirm a logarithmic scaling of the single-particle entanglement entropy with the number of particles in the system. The coefficient of this logarithmic scaling increases with interaction strength, saturating to unity in the strongly interacting limit. Additionally, we show that the single-particle entanglement entropy is bounded by the condensate fraction, suggesting a practical route towards its measurement in future experiments. [Preview Abstract] |
Wednesday, March 5, 2014 4:06PM - 4:18PM |
Q33.00009: Entanglement scaling in the quantum Heisenberg bilayer model Stefan Wessel, Johannes Helmes We employ quantum Monte Carlo simulations to quantify the bipartite entanglement in the spin-1/2 quantum Heisenberg model on the square lattice bilayer in terms of the second R\'enyi entropy. The dependence on the interlayer coupling of the dominant area law contribution to the entanglement is analyzed, in particular its enhancement across the quantum phase transition. In addition, we study the various sub-leading logarithmic correction terms due to Goldstone excitations and corner contributions, related to the subsystem's geometry. We compare our numerical findings to previous analytical predictions and discuss limitations in extracting universal contributions due to finite size restrictions for numerical studies. [Preview Abstract] |
Wednesday, March 5, 2014 4:18PM - 4:30PM |
Q33.00010: Entanglement properties of the antiferromagnetic-singlet transition in the two dimensional Hubbard model Richard T. Scalettar, Chia-Chen Chang, Rajiv R.P. Singh Entanglement entropy is a manifestation of quantum coherence. In a many body system, it can provide distinct signatures of quantum criticality and topological order. Measurements of entanglement entropy typically require knowledge of the many body wave functions. Due to their non-local nature, it is difficult to evaluate entanglement properties of correlated systems using numerical methods that rely on local operators. Here we present a study of Renyi entanglement entropy (EE) for fermonic bilayer Hubbard model at half-filling using a recently proposed formalism [1] within the determinantal quantum Monte Carlo framework. We obtain temperature dependence of the Renyi EE. At low temperatures, a sharp signal in the EE is observed as the system undergoes the singlet-antiferromagnetism transition. Scaling properties of the Renyi EE resulting from different bipartite divisions of the bilayer are explored. In the non-interacting limit, the results of the simulations are compared with those obtained with the correlation matrix method. \\[4pt] [1] T. Grover, Phys. Rev. Lett. {\bf 111}, 130402 (2013). [Preview Abstract] |
Wednesday, March 5, 2014 4:30PM - 4:42PM |
Q33.00011: Collapsing Schrodinger Cats in the Density Matrix Renormalization Group Hongchen Jiang, Leon Balents In this paper, we propose a modified Density Matrix Renormalization Group (DMRG) algorithm to preferentially select minimum entropy states (minimally entangled states) in finite systems with asymptotic ground state degeneracy. The algorithm adds a ``quench'' process to the conventional DMRG method, which mimics the decoherence of physical systems, and collapses non-locally entangled states such as Schrodinger cats. We show that the method works for representative models with ground state degeneracy arising from either topological order or spontaneous discrete symmetry breaking. In the minimal entropy states thus obtained, properties associated with thermodynamic limit, such as topological entanglement entropy and magnetic order parameters, can be obtained directly and efficiently. [Preview Abstract] |
Wednesday, March 5, 2014 4:42PM - 4:54PM |
Q33.00012: Emergent irreversibility and entanglement spectrum statistics Eduardo Mucciolo, Claudio Chamon, Alioscia Hamma We study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than Hamitonian, and since energy levels are not well defined, the well-established connection between the statistical fluctuations of the energy spectrum and irreversibility cannot be made. We show that the entanglement spectrum provides a more general connection. Irreversibility is marked by a failure of a disentangling algorithm and is preceded by the appearance of Wigner-Dyson statistical fluctuations in the entanglement spectrum. This analysis can be done at the wavefunction level and offers a new route to study quantum chaos and quantum integrability. [Preview Abstract] |
Wednesday, March 5, 2014 4:54PM - 5:06PM |
Q33.00013: Nonsymmetrized Correlations in Mesoscopic Current Measurements Wolfgang Belzig, Adam Bednorz, Christoph Bruder, Bertrand Reulet A long-standing problem in quantum mesoscopic physics is which operator order corresponds to noise expressions like $\langle I(\omega)I(-\omega)\rangle$, where $I(\omega)$ is the measured current at frequency $\omega$. Symmetrized order describes a classical measurement while nonsymmetrized order corresponds to a quantum detector, e.g., one sensitive to either emission or absorption of photons. We show that both order schemes can be embedded in quantum weak-measurement theory taking into account measurements with memory, characterized by a memory function which is independent of a particular experimental detection scheme [A. Bednorz, C. Bruder, B. Reulet, and W. Belzig, Phys. Rev. Lett. \textbf{110}, 250404 (2013)]. We discuss the resulting quasiprobabilities for different detector temperatures and how their negativity can be tested on the level of second-order correlation functions already. Experimentally, this negativity can be related to the squeezing of the many-body state of the transported electrons in an ac-driven tunnel junction. [Preview Abstract] |
Wednesday, March 5, 2014 5:06PM - 5:18PM |
Q33.00014: Four and Five-body non-local correlations in pure and mixed states Santosh Shelly Sharma, Naresh Kumar Sharma In our earlier works [1], quantifiers of four and three-body correlations based on four qubit invariants had been constructed for pure states. The principal construction tools, local unitary invariance and notion of negativity fonts, make it possible to outline the process of selective construction of meaningful invariants that quanify $N$ and $ N-1 $ qubit correlations. It is found that, in general, starting from degree $ k $ invariants relevant to detection and quantifcation of specific type of non-local quantum correlations in $(N-1)$ $(N>2)$ qubit system, one can construct degree $k $ coefficients of an $N$-qubit bilinear form. When $k=2^{N-2}$ ($N>2$), one of the invariants of degree $2^{N-1}$ quantifies N-body non-local correlations The process is recursive. While for few body systems it yields analytical expressions in terms of functions of state coefficients, for larger systems it can be the guiding principle to numerical caculations of invariants. To illustrate the process, an expression for a five qubit correlation quantifier for pure states is constructed. In addition, the extension to specific rank two mixed states through convex-roof extension is investigated. [1] S. Shelly Sharma and N. K. Sharma, Phys. Rev. A 87, 022335 (2013); Phys. Rev. A 82, 052340 (2010). [Preview Abstract] |
Wednesday, March 5, 2014 5:18PM - 5:30PM |
Q33.00015: Rotational Covariance and GHZ Contradictions for three or more particles of any dimension Jay Lawrence Greenberger-Horne-Zeilinger (GHZ) states are characterized by a special symmetry under independent uniaxial rotations of particles. Observables representing particular detector arrangements transform covariantly and exhibit a wealth of GHZ contradictions. Hidden variables cannot reproduce this covariance for any number of particles (N ? 3) of any spin S (or dimension d = 2S + 1). However, finding specific and experimentally verifiable contradictions covering all cases requires increasingly more complex arguments, utilizing more observables, for more difficult cases [1]. We illustrate a new method that utilizes explicit reference to hidden variable failure, which succeeds for the most difficult. The method is applied to the case of three particles of any prime dimension. 1. J. Lawrence, eprint arXiv:1308.3808 [quant/ph]. [Preview Abstract] |
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