Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session S24: Quantum ManyBody Systems and Methods I 
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Sponsoring Units: DCOMP Chair: Chris Marianetti, Columbia University Room: 203AB 
Thursday, March 5, 2015 8:00AM  8:12AM 
S24.00001: ABSTRACT WITHDRAWN 
Thursday, March 5, 2015 8:12AM  8:24AM 
S24.00002: Entanglement spectrum and covalent bonding David Yang, Norm Tubman We present an approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix, using a generalization of the \textsc{Swap} operator. We apply this method to several diatomic molecules and describe how the spatial entanglement spectrum encodes a covalent bond that includes all the manybody correlations. Of particular focus is the C$_2$ molecule, which has been subject to recent controversy. Our results suggest that entanglementbased methods can lead to more realistic analysis of covalent bonds than possible before. [Preview Abstract] 
Thursday, March 5, 2015 8:24AM  8:36AM 
S24.00003: Power law violation of the area law in quantum spin chains Ramis Movassagh, Peter Shor The subvolume scaling of the entanglement entropy with the system's size, n, has been a subject of vigorous study in the last decade. The area law provably holds for gapped one dimensional systems and it was believed to be violated by at most a factor of log(n) in physically reasonable models such as critical systems. We first describe and then generalize our earlier spin1 model [PRL 109, 207202 (2012)] to all integer spins chains, whereby we introduce a class of exactly solvable models that are physical yet violate the area law by a power law [arXiv:1408.1657 quantph]. The proposed Hamiltonian is local and translationally invariant in the bulk. We prove that it is frustration free and has a unique ground state. Moreover, we prove that the energy gap scales as $n^{c}$, where using the theory of Brownian excursions, we prove $c\ge 2$. This rules out the possibility of these models being described by a conformal field theory. We analytically show that the Schmidt rank grows exponentially with $n$ and that the halfchain entanglement entropy to the leading order scales as $\sqrt{n}$. Lastly, we introduce an external field which allows us to remove the boundary terms yet retain the desired properties of the model. [Preview Abstract] 
Thursday, March 5, 2015 8:36AM  8:48AM 
S24.00004: Quantum criticality in ``easyplane'' SU($N$) spin model Jonathan Demidio, Ribhu K. Kaul We investigate a two dimensional quantum spin model with ``easyplane'' SU($N$) anisotropy which describes an $N1$ component superfluid of hardcore bosons. This model exhibits a transition from a magnetically ordered state, corresponding to superfluid order of the bosons, to a nonmagnetic state with broken lattice translation symmetry (a valence bond solid). It has been shown previously that the fully SU($N$) symmetric version of this model exhibits a continuous phase transition consistent with the scenario of deconfined quantum criticality. Using quantum Monte Carlo techniques we study the critical properties in the ``easyplane'' case. [Preview Abstract] 
Thursday, March 5, 2015 8:48AM  9:00AM 
S24.00005: Matrixproduct Ansatz for Fermions in a 1D Continuum S.S. Chung, K. Sun, C.J. Bolech We present a novel implementation of a matrixproduct ansatz for fermions in a 1D continuum, which correctly predicts the ground state properties of a homogeneous interacting spin1/2 system. This includes the signatures of a partially polarized regime, in agreement with a large amount of theoretical work which has guided, and/or has been inspired by, recent coldatom experiments. [Preview Abstract] 
Thursday, March 5, 2015 9:00AM  9:12AM 
S24.00006: Determination of Luttinger parameters for c=2 theories Olabode Sule, Hitesh Changlani, Shinsei Ryu We consider critical SU(3) symmetric spin chains with additional interactions relevant to the physics of the Haldane spin chain. We provide evidence for the mapping of these spin chains to free boson theories with topological terms and central charge c = 2[1]. Our approach is based on nonabelian bosonization[2] together with numerical confirmation using exact diagonalization and the density matrix renormalization group algorithm. Our results generalize what is known for the spin1/2 XXZ model[3]. Using these results we calculate all four parameters that describe the physics of two coupled Luttinger liquids as a function of the parameters of the lattice model. [1] O. Sule, H.J. Changlani, S. Ryu (in preparation) [2] C. Itoi, M.H. Kato, Phys. Rev. B 55, 8295, 1997 [3] S. Furukawa, V. Pasquier, J. Shiraishi, Phys. Rev. Lett. 102, 170602 (2009) [Preview Abstract] 
Thursday, March 5, 2015 9:12AM  9:24AM 
S24.00007: Momentumspace Entanglement Spectrum of Bosons and Fermions with Interactions Rex Lundgren, Jonathan Blair, Martin Greiter, Andreas Laeuchli, Gregory Fiete, Ronny Thomale We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both partitions, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling reveals that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in [Thomale et al., Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may in fact support the numerical study of the physical transitions in the momentum space density matrix renormalization group. Accepted by Physical Review Letters (arXiv:1404.7545) This work was supported by an National Science Foundation Graduate Research Fellowship [Preview Abstract] 
Thursday, March 5, 2015 9:24AM  9:36AM 
S24.00008: Failure of the GGE for integrable models with bound states Natan Andrei, Garry Goldstein In this work we study the applicability of the local GGE to integrable one dimensional systems with bound states. We find that the GGE, when defined using only local conserved quantities, fails to describe the long time dynamics for most initial states including eigenstates. We present our calculations by studying the attractive LiebLiniger gas and the XXZ magnet, though similar results may be obtained for other models. [Preview Abstract] 
Thursday, March 5, 2015 9:36AM  9:48AM 
S24.00009: Steadystate phases of the nonequilibrium RabiHubbard Model Hakan Tureci, Chaitanya Joshi, Mykola Bordyuh, Rosario Fazio, Jonathan Keeling, Marco Schiro We study the realization of a tunable RabiHubbard Model with a coupled cavity array containing Ramanpumped 4level qubits. This effective model is found to display a phase diagram that features a normal phase (vanishing polarization and photon coherence) and a finitefrequency ordered phase. The ordered phase may either display a ``ferroelectric'' order where the photon coherence is uniform through the array, or one with an alternating phase that we refer to as ``antiferroelectric.'' [Preview Abstract] 
Thursday, March 5, 2015 9:48AM  10:00AM 
S24.00010: Local density fluctuation approach to Fermionic lattice models Zhengqian Cheng, Chris Marianetti We formulate an effective action as a function of selected Hubbard operators which reproduces the local density fluctuations of a given lattice model. The relevant Hubbard operators emerge via mapping the lattice Hamiltonian to a composite system with auxiliary holes and gauge bosons which mediate the intercell hopping. After a mean field approximation of the gauge bosons, we get an effective local model which reproduces the expectation value of the relevant Hubbard operators. We apply our method to the one band Hubbard model in one and infinite dimensions, demonstrating good agreement between our computed static observables and the exact solutions. While our approach does not address frequency dependent observables, it has a negligible computational cost as compared to dynamical mean field theory and could be highly applicable in the context of real materials. [Preview Abstract] 
(Author Not Attending)

S24.00011: Densitymatrix renormalization group study of triangular and square Hubbard models Takami Tohyama, Shigetoshi Sota, Tomonori Shirakawa, Seiji Yunoki We perform largescale densitymatrix renormalization group calculations for twodimensional Hubbard models with a triangular lattice and a square lattice. In the triangular Hubbard model, we determined a boundary between metal and insulator and a boundary between spinliquid and antiferromagnetic phases. The presence of spinliquid phase is confirmed by spinspin correlation function. In the square Hubbard model, we introduce a secondneighbor hopping interaction and calculate the dynamical spin correlation function to clarify the doping dependence of magnon excitations. We find a shift of a peak position toward higher energy in the electrondoped side, being consistent with recent resonantinelastic xray scattering. [Preview Abstract] 
Thursday, March 5, 2015 10:12AM  10:24AM 
S24.00012: Manybody localization edge in the randomfield Heisenberg chain David J. Luitz, Nicolas Laflorencie, Fabien Alet We present a large scale exact diagonalization study of the one dimensional spin 1/2 Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to L=22 spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energyresolved interpretation of the many body localization transition including the existence of a manybody mobility edge. The ergodic phase is well characterized by Gaussian orthogonal ensemble statistics, volumelaw entanglement, and a full delocalization in the Hilbert space. Conversely, the localized (nonergodic) regime displays Poisson statistics, arealaw entanglement and signs of multifractality in the Hilbert space where a true localization never occurs. We perform finite size scaling to extract the critical edge and exponent of the localization length divergence. [Preview Abstract] 
Thursday, March 5, 2015 10:24AM  10:36AM 
S24.00013: Chiral spin density wave order on frustrated honeycomb and bilayer triangular lattice Hubbard model at halffilling Kun Jiang, Yi Zhang, Sen Zhou, Ziqiang Wang We study the ground state properties of the Hubbard model on the honeycomb lattice with nearestneighbor $t_1$ and second nearestneighbor hopping $t_2$, which is isomorphic to the bilayer triangular lattice. We show that, at halffilling, chiral spindensity wave ($\chi$SDW) order emerges due to onsite Coulomb interaction $U$ in a wide range of $t_2/t_1$ where both the twosublattice antiferromagnetic order for small $t_2/t_1$ and the decoupled threesublattice 120$^\circ$ magnetic order are strongly frustrated. For fixed $t_2/t_1$, we find that increasing $U$ leads to a continuous transition from a $\chi$SDW semimetal with anomalous Hall effect to a topological chiral Chern insulator exhibiting quantum anomalous Hall effect, which undergoes a first order transition into a $\chi$SDW insulator with zero total Chern number but anomalous AC Hall effect. We obtain the rich phase diagram and discuss the novel magnetic and topological properties. [Preview Abstract] 
Thursday, March 5, 2015 10:36AM  10:48AM 
S24.00014: Summing parquet diagrams via the functional renormalization group: xray problem revisited Peter Kopietz, Anand Sharma, Philipp Lange, Casper Drukier We present a simple and efficient method for summing socalled parquet diagrams of fermionic manybody systems with competing instabilities using the functional renormalization group. Our method is based on partial bosonization of the interaction using multichannel HubbardStratonovich transformations. A straightforward truncation of the resulting renormalization group flow retaining only the frequencyindependent parts of the twopoint and threepoint functions amounts to solving coupled BetheSalpeter equations for the effective interaction to leading logarithmic order. We apply our method to the xray problem and derive the singular frequency dependence of the xray response function and the particleparticle susceptibility. Our method can be applied to various other problems involving strong fluctuations in more than one scattering channel. [Preview Abstract] 
Thursday, March 5, 2015 10:48AM  11:00AM 
S24.00015: Evaluation of highorder moments and cumulants in quantum spin systems Colin West, Artur SaezGarcia, TzuChieh Wei We present a numerical scheme for efficiently extracting the higherorder moments and cumulants of various operators on spin systems represented as tensor product states, for both finite and infinite systems. These quantities can be useful in the evaluation of phase transitions. Of particular interest is the application of this method to calculate the socalled Binder's Cumulant, which can be used to detect critical points even with small finite numerical calculations. [Preview Abstract] 
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