Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session N26: Entanglement in Many-Body Systems |
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Sponsoring Units: GQI Chair: Ari Mizel, LPS Room: 328 |
Wednesday, March 20, 2013 11:15AM - 11:27AM |
N26.00001: Noise of Quantum Channels can Generate Quantum Entanglement from Classical Correlation Laszlo Gyongyosi, Sandor Imre Transmission of quantum entanglement will play a crucial role in future networks and long-distance quantum communications. Quantum Key Distribution, the working mechanism of quantum repeaters and the various quantum communication protocols are all based on quantum entanglement. To share entanglement between distant points, high fidelity quantum channels are needed. In practice, these communication links are noisy, which makes it impossible or extremely difficult and expensive to distribute entanglement. In this work we first show that quantum entanglement can be generated by a fundamentally new idea, exploiting the most natural effect of the communication channels: the noise itself of the link. We prove that the noise transformation of communication links that are not able to transmit quantum entanglement can be used to generate entanglement from classically correlated, unentangled input. We call this new phenomenon the Correlation Conversion property (CC-property) of communication channels. Our results have serious implications and fundamental consequences for the future of quantum communications, and for the development of global-scale quantum communication networks. [Preview Abstract] |
Wednesday, March 20, 2013 11:27AM - 11:39AM |
N26.00002: Measuring Entanglement Entropy of a Generic Many-Body System with a Quantum Switch Dmitry Abanin, Eugene Demler Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the R\'enyi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order.\\[4pt] [1] D. A. Abanin, E. A. Demler, Phys. Rev. Lett. 109, 020504 (2012) [Preview Abstract] |
Wednesday, March 20, 2013 11:39AM - 11:51AM |
N26.00003: Postion-momentum duality in the entanglement spectrum of free fermions Ching Hua Lee, Xiao-Liang Qi The entanglement spectrum (ES) provides a valuable way of studying the topological properties of a system, i.e. those of exotic phases where no usual topological order parameter exists. In this talk, I shall discuss a framework where the partitionings of various spaces, i.e. real, momentum and spin space are treated on equal footing. This relies on an equivalence of the eigenvalue spectra of certain combinations of projection operators. For instance, the ES remains invariant if we mathematically interchange the real-space projector with the occupied band projector. One can go a step further and conclude that exchanging the physical roles of real-space and momentum space projectors lead to two different systems with identical ES. Such reinterpretations allow one to extend well-known results involving real-space cuts in critical systems to those with simultaneous momentum-space cuts. The results for gapped systems are even more interesting, with the real-space ES of a generic band insulator shown to be identical to that of two different layers or spins in a specific fermi liquid state. This framework also allows one to view the Wannier polarization spectrum as the infinite temperature limit of the ES of a certain system originally defined at zero temperature. [Preview Abstract] |
Wednesday, March 20, 2013 11:51AM - 12:03PM |
N26.00004: Characterizing disordered fermion systems using the momentum-space entanglement spectrum Ian Mondragon-Shem, Mayukh Khan, Taylor Hughes We show that momentum-space entanglement can reveal the existence of robust extended states in disordered fermions systems. This approach represents a novel alternative to the more conventional position-space entanglement used in condensed matter settings. We illustrate this proposal by using explicit 1D models with spatially correlated disorder that exhibit phases which avoid complete Anderson localization. The momentum space entanglement spectrum clearly reveals the location of delocalized states in the energy spectrum and can be used as a signature of the phase transition between a delocalized and localized phase. We further discuss possible applications to 2D systems that exhibit topological properties which arise from the existence of robust bulk extended states in their energy spectrum. [Preview Abstract] |
Wednesday, March 20, 2013 12:03PM - 12:15PM |
N26.00005: Geometric entanglement for the toric code, color code and quantum double models Tzu-Chieh Wei, Rom\'an Or\'us, Oliver Buerschaper, Maarten Van den Nest We use the geometric entanglement to characterize ground states in the toric code, color code and quantum double models. We find that the entanglement in all these cases scales with the system size plus a constant term. Such a constant contribution has a topological origin, characterized previously by the entanglement entropy. In particular, the constant term in the color code is twice that in the toric code, a result consistent with a recent study that the color code is equivalent to two copies of the toric code. [Preview Abstract] |
Wednesday, March 20, 2013 12:15PM - 12:27PM |
N26.00006: Log divergence in finite-size quantum Riemann metric Tiago Souza, Michael Kolodubetz, Anatoli Polkovnikov We study the geometric tensor, an object that describes distances between quantum states within a ground state manifold. Traditionally, it has been studied for changes in external parameters, e.g., magnetic field, at fixed system size. Here, instead, we treat the system size as a tunable parameter, and hence analyze the distance between wave functions at different system sizes. For some simple fermion models, we find that the geometric tensor diverges logarithmically with system size in the thermodynamic limit, similar to the entanglement entropy in a CFT. We discuss similar calculations for the XY model, and comment on the relationship to RG. [Preview Abstract] |
Wednesday, March 20, 2013 12:27PM - 12:39PM |
N26.00007: Entanglement Entropy of the composite fermion non-Fermi liquid state at $\nu=1/2$ Junping Shao, Eun-Ah Kim There has been much interest in entanglement entropy as a measure to theoretically probe strongly correlated states that do not involve broken symmetries. In particular, one may hope entanglement entropy can offer quantitative characteristic of Non-Fermi liquids which are otherwise defined based on ``what they are not part of.'' Swingle and Senthil [1] conjectured that the entanglement entropy of non-Fermi liquids will be at most of order $L^{d-1}\log{L}$ for a region of linear size $L$. However, to date, there is no explicit calculation of entanglement entropy for non-Fermi liquids (though there are calculations for spin-liquids with spinon fermi surface). Here we perform a Monte Carlo calculation of the entanglement entropy for the best established example of strongly correlated non-Fermi liquid: gapless state at $\nu=1/2$. We use a composite fermion many body wavefunction in a toroidal geometry and use the swap operator to calculate the second Renyi entropy. We discuss the resulting scaling behavior in the context of the Swingle-Senthil conjecture.\\[4pt] [1] B. Swingle and T. Senthil, arXiv:1112.1069. [Preview Abstract] |
Wednesday, March 20, 2013 12:39PM - 12:51PM |
N26.00008: Renyi Entropy of the Interacting Fermi Liquid Jeremy McMinis, Norm Tubman Entanglement properties, including the Renyi $\alpha$-entropies and scaling laws, are becoming increasingly important in condensed matter physics. In this work we use variational quantum Monte Carlo to compute the Renyi $\alpha$-entropies, their scaling laws, and the relationship between different $\alpha$-entropies for one of the most important phases in condensed matter, the interacting Fermi liquid. Contrary to recent theoretical predictions, we find that interactions increase the prefactor for the $\alpha$-entropy scaling laws for all particle interaction strengths and forms. [Preview Abstract] |
Wednesday, March 20, 2013 12:51PM - 1:03PM |
N26.00009: Multipartition of Spatially Entangled Systems with Sine Square Deformation Isao Maruyama We propose a method to decouple quantum systems without disturbing the Fermi sea, extending the sine-square deformation (SSD)[1,2] toward more general cases. This multipartition operation opens a way to real-time manipulation for separating the gapless Fermi liquid system spatially into several decoupled systems without losing quantum entanglement among them. As a demonstration of entanglement preservation, by solving the time-dependent Scr\"odinger equation numerically, we show that our method works well in entanglement dynamics of non-interacting tight-binding models on a one dimensional zigzag chain and a two dimensional square lattice. [1] A. Gendiar, et. al., Prog. Theo. Phys. 122. 953 (2009) [2] IM, et.al., Phys. Rev. B. 84. 165132 (2011) and references therein [Preview Abstract] |
Wednesday, March 20, 2013 1:03PM - 1:15PM |
N26.00010: Entanglement in fermionic superlattices Raimundo dos Santos, Tiago Mendes-Santos, Thereza Paiva We discuss how entanglement of strongly correlated fermions is influenced by a superlattice structure, by considering a one-dimensional Hubbard superlattice, made up of a repeated pattern of $L_U$ repulsive sites followed by $L_0$ free sites. Lanczos diagonalization of lattices up to 24 sites are used to calculate the von Neumann entropy and the negativity. The breakdown of particle-hole symmetry broadens the maxima of the entropy in the underdoped region, while the entanglement in the overdoped region is crucially influenced by the nature of the magnetic state, with dips at densities corresponding to repulsive layer singlets and to $q=\pi$ (in units of inverse unit cell length, $L_U+L_0$) spin-density waves; at these special densities the system is either a Mott insulator or a `compressible insulator'. We have also found that sites in the repulsive layer (for $L_U\geq2$) are monogamically entangled with each other. [Preview Abstract] |
Wednesday, March 20, 2013 1:15PM - 1:27PM |
N26.00011: Thermal Reduced Density Matrices in Fermion and Spin Ladder Systems Xiao Chen, Eduardo Fradkin A recent numerical study [1] found that the reduced density matrix of a spin 1/2 system on a two-leg ladder is the same as the spectrum of a spin 1/2 chain at a finite temperature determined by the spin gap of the ladder. We investigate this interesting result by considering two-leg ladders of free fermions and spin systems with a gapped ground state using several controlled approximations. We calculate the entanglement entropy for the cut made between the chains. In the fermionic system we find the explicit form of the reduced density matrix for one of the chains and determine the entanglement spectrum explicitly. In the case of the spin system, we consider both the strong coupling limit by using perturbation theory and weak coupling limit by using replica trick method. The calculation shows that, 1) the Von Neumann entropy equals to the thermal entropy of one chain, 2) the R'enyi entropy is equivalent to the free energy of one chain, and 3) the coupling constant (gap) plays the role of effective temperature. This result can be generalized to other coupled critical systems with a bulk gap. This work was supported in part by the NSF grant DMR-1064319 at the University of Illinois [1] D. Poilblanc, Phys. Rev. Lett. {\bf 105}, 077202 (2010) [Preview Abstract] |
Wednesday, March 20, 2013 1:27PM - 1:39PM |
N26.00012: Entanglement measures and the quantum to classical mapping Jesko Sirker A quantum model can be mapped to a classical model in one higher dimension. Here we introduce a finite-temperature correlation measure based on a reduced density matrix $\bar\rho_{\bar A}$ obtained by cutting the classical system along the imaginary time (inverse temperature) axis. We show that the von-Neumann entropy $\bar S_{\rm ent}$ of $\bar\rho_{\bar A}$ shares many properties with the mutual information, yet is based on a simpler geometry and is thus easier to calculate. For one-dimensional quantum systems in the thermodynamic limit we prove that $\bar S_{\rm ent}$ is non-extensive for all temperatures $T$. For the integrable transverse Ising and $XXZ$ models we demonstrate that the entanglement spectra of $\bar\rho_{\bar A}$ in the limit $T\to 0$ are described by free-fermion Hamiltonians and reduce to those of the regular reduced density matrix $\rho_A$---obtained by a spatial instead of an imaginary-time cut---up to degeneracies. [Preview Abstract] |
Wednesday, March 20, 2013 1:39PM - 1:51PM |
N26.00013: Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model Rex Lundgren, Victor Chua, Gregory Fiete We study the quantum entanglement of the spin and orbital degrees of freedom in the one-dimensional Kugel-Khomskii model, which includes both gapless and gapped phases, using analytical techniques and exact diagonalization with up to 16 sites. We compute the entanglement entropy, and the entanglement spectra using a variety of partitions or ``cuts'' of the Hilbert space, including two distinct real-space cuts and a momentum-space cut. Our results show the Kugel-Khomski model possesses a number of new features not previously encountered in studies of the entanglement spectra. Notably, we find robust gaps in the entanglement spectra for both gapped and gapless phases with the orbital partition, and show these are not connected to each other. We observe the counting of the low-lying entanglement eigenvalues shows that the ``virtual edge'' picture which equates the low-energy Hamiltonian of a virtual edge, here one gapless leg of a two-leg ladder, to the ``low-energy'' entanglement Hamiltonian breaks down for this model, even though the equivalence has been shown to hold for similar cut in a large class of closely related models. [Preview Abstract] |
Wednesday, March 20, 2013 1:51PM - 2:03PM |
N26.00014: Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains Andrew James, Robert Konik We study the entanglement entropy and spectra of a coupled array of N one dimensional quantum Ising chains in their continuum limit. Employing a DMRG algorithm specifically adapted to the study of coupled, continuum systems, we are able to study large arrays of chains (up to N=200) both in their gapped phase and in the approach to criticality. Away from criticality the entanglement entropy obeys an area law. Close to criticality the entanglement entropy continues to obey the area law but possesses an additive piece scaling as $c_{eff}\log (N)/6$ with $c_{eff} \approx 1$. We also study the entanglement spectra of the coupled chains. Away from criticality in the disordered phase the low lying portion of the entanglement spectra appears similar to that of a single gapped quantum Ising chain. As the critical point is approached the entanglement gap closes. A finite size scaling analysis shows that the entanglement gap and the energy gap vanish at the same value of interchain coupling. [Preview Abstract] |
Wednesday, March 20, 2013 2:03PM - 2:15PM |
N26.00015: Entanglement spectrum and entangled modes of random XX spin chains Mohammad Pouranvari, Kun Yang We study in this work the ground state entanglement properties of finite XX spin-1/2 chains in with random couplings, using Jordan-Wigner transformation. We divide system into two parts and study reduced density matrixes (RDMs) of its subsystems. Due to the free-fermion nature of the problem, the RDMs take the form of that of a free fermion thermal ensemble. Finding spectrum of the corresponding entanglement Hamiltonian and corresponding eigenvectors, and comparing them with real space renormalization group (RSRG) treatment, we establish the validity of the RSRG approach for entanglement in the limit of strong disorder, but also find its limitations when disorder is weak. In the latter case our work provides a way to visualize the effective spins that form long distance singlet pairs. [Preview Abstract] |
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