Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session S20: Quantum Many-Body Systems and Methods I |
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Sponsoring Units: DCOMP Chair: Brian Moritz, SLAC Room: 319 |
Thursday, March 17, 2016 11:15AM - 11:27AM |
S20.00001: Tensor Network Algorithms for Braiding Anyons Babatunde Ayeni, Sukhwinder Singh, Robert Pfeifer, Gavin Brennen Anyons are point-like (quasi)particles which exist only in two-dimensional systems and have exchange statistics that are neither bosonic nor fermionic. These particles were first proposed as a mere theoretical curiosity, but it was later shown that they arise in topological states of matter and that certain species of non-Abelian anyons can be used for low error quantum computation. Despite the importance of anyons, fundamentally and technologically, comparatively little is understood about their many body behaviour especially when the non local effects of braiding are taken into account. This largely due to the lack of efficient numerical methods to study them. In order to circumvent this problem, and to broaden our understanding of the physics of anyons, the authors have developed several numerical methods based on tensor network algorithms including: anyonic Matrix Product States (MPS), anyonic Time Evolving Block Decimation (TEBD), anyonic Density Matrix Renormalization Group (DMRG), and Anyonic U(1) MPS. These can be used to simulate static interacting and itinerant braiding anyons on a finite or infinite lattice. We have used our methods to study the phase diagrams of some species, such as Abelian Z3 anyons and non-Abelian Fibonacci and Ising. [Preview Abstract] |
Thursday, March 17, 2016 11:27AM - 11:39AM |
S20.00002: A Tensor Network Framework for Topological Order in Higher Dimensions Burak Sahinoglu, Michael Walter, Dominic Williamson We present a general scheme for constructing topological lattice models in any space dimension using tensor networks. Our approach relies on finding "simplex tensors" that satisfy a finite set of tensor equations. Given any such tensor, we construct a discrete topological quantum field theory (TQFT) and local commuting projector Hamiltonians on any lattice. The ground space degeneracy of these models is a topological invariant that can be computed via the TQFT, and the ground states are locally indistinguishable when the ground space is nondegenerate on the sphere. Any ground state can be realized by a tensor network obtained by contracting simplex tensors. Our models are exact renormalization fixed points, covering a broad range of models in the literature. Lastly, we identify symmetries on the virtual level of the tensor networks of our models that generalize the topological invariance properties beyond fixed point models. This framework combined with recent tensor network techniques is convenient for studying excitations, their statistics, phase transitions, and ultimately for classification of gapped phases of many-body theories in 3+1 and higher dimensions. [Preview Abstract] |
Thursday, March 17, 2016 11:39AM - 11:51AM |
S20.00003: Some tensor-network diagnostics for a class of 2D SPT states with internal symmetry Abhishodh Prakash, Tzu-Chieh Wei We demonstrate some diagnostic techniques to characterize certain 2D tensor network states with internal symmetries that are classified by the third group cohomology of the symmetry group. We use the discussions of Else et al. [Phys. Rev. B 90, 235137 (2014)] to extract data that determines the phase of matter from the tensors that make up a specific class of wave functions. This is possible because the symmetry transformation at the `physical' level, which is of product form, translates to a symmetry in the `virtual' level which may no longer be of product form. An appropriate analysis of the virtual-space symmetry helps us obtain the topological information (the 3-cocycle twist) that places the wave function in the classification scheme. This reproduces the results of Chen et al. [Phys. Rev. B 87,155114 (2013)] without using projection operators in merging two 'Matrix Product Operators' of the symmetry representation of two group actions. [Preview Abstract] |
Thursday, March 17, 2016 11:51AM - 12:03PM |
S20.00004: Weak-coupling instabilities of SU(N) fermions on the Bernal-stacked honeycomb bilayer in presence of on-site Hubbard Interactions Sumiran Pujari, Thomas C. Lang, Ribhu K. Kaul Bernal-stacked bilayer graphene hosts an interesting 'non-relativistic' semi-metallic dispersion different from monolayer graphene. At this quadratic band touching, short-range interactions are marginal and hence cause instabilities to a variety of ground states. In this work we consider the instabilities of even $N$ species of fermions on the Bernal bilayer with an $SU(N)$-symmetric contact interaction. For $SU(2)$ fermions with an on-site Hubbard interaction the ground state has been found to be to a magnetic Néel state for all strengths of the interaction. In contrast, the leading weak coupling instability for $N>2$ is a non-magnetic ground state, which is gapped and odd under time reversal. On the other hand, at strong coupling we expect Néel or VBS ground states of the effective self-conjugate $SU(N)$ spin models. Motivated by this observation, we investigate the phase diagram for even $N>2$ using determinantal quantum Monte Carlo computations. [Preview Abstract] |
Thursday, March 17, 2016 12:03PM - 12:15PM |
S20.00005: A many-body interpretation of Majorana bound states, and conditions for their localisation Thomas O'Brien, Anthony Wright We derive a condition for the existence of completely or exponentially localised Majorana bound states (with the potential for non-Abelian statistics) in a generic many-body system. We discuss the relationship between the existence of these operators and the protection of the ground state degeneracy from local perturbations. We use our methods to study the exponential decay of the Majorana bound states in the non-interacting Kitaev chain, finding complete agreement between our many-body calculation and single-particle results. We then apply these results to various interacting systems which have previous evidence for Majorana bound states. [Preview Abstract] |
Thursday, March 17, 2016 12:15PM - 12:27PM |
S20.00006: Hybrid-Space Density Matrix Renormalization Group Study of the Two-Dimensional Hubbard Model Georg Ehlers, Reinhard M. Noack We investigate the ground state of the two-dimensional Hubbard model on a cylinder geometry at intermediate coupling and weak doping. We study properties such as the behavior of the ground-state energy, pair-field correlations, and the appearance of stripes. We find striped ground states generically, with the width of the stripes depending on the filling, the boundary conditions, and the circumference of the cylinder. Furthermore, we analyse the interplay between the different stripe configurations and the decay of the pairing correlations. Our analysis is based on a hybrid-space density matrix renormalization group (DMRG) approach, which uses a momentum-space representation in the transverse and a real-space representation in the longitudinal direction. Exploiting the transverse momentum quantum number makes significant speedup and memory savings compared to the real-space DMRG possible. In particular, we obtain computational costs that are independent of the cylinder width for fixed size of the truncated Hilbert space. [Preview Abstract] |
Thursday, March 17, 2016 12:27PM - 12:39PM |
S20.00007: Improving the efficiency of the Finite Temperature Density Matrix Renormalization Group method Alberto Nocera, Gonzalo Alvarez I review the basics of the finite temperature DMRG method, and then show how its efficiency can be improved by working on reduced Hilbert spaces and by using canonical approaches. My talk explains the applicability of the ancilla DMRG method beyond spins systems to t-J and Hubbard models, and addresses the computation of static and dynamical observables at finite temperature. Finally, I discuss the features of and roadmap for our DMRG$++$ codebase. [Preview Abstract] |
Thursday, March 17, 2016 12:39PM - 12:51PM |
S20.00008: Geometric stability of the many-body localized phase in two and higher dimensions Anushya Chandran, Arijeet Pal, Chris Laumann, Antonello Scardicchio Isolated disordered quantum systems need not equilibrate and be described by statistical mechanics; this is the phenomenon of many-body localization (MBL). In higher dimensions, the existence of MBL is a delicate question due to the possibility of inclusions of lower dimensional "thermal" regions. In this talk, I will argue that MBL is stable in higher dimensions by analyzing the geometry of a MBL insulator coupled to a thermal edge and develop a phenomenology of such systems. [Preview Abstract] |
Thursday, March 17, 2016 12:51PM - 1:03PM |
S20.00009: Many-body localization characterized from a one-particle perspective Soumya Bera, Henning Schomerus, Fabian Heidrich-Meisner, Jens Bardarson We show that the one-particle density matrix can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The eigenstates of density matrix are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the eigenvalues reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and found that it is independent of system size in the localized phase. [Preview Abstract] |
Thursday, March 17, 2016 1:03PM - 1:15PM |
S20.00010: Characterizing gapped phases of a 1D spin chain with on-site and spatial symmetries Colin West, Abhishodh Prakash, Tzu-Chieh Wei We investigate the phase diagram of a spin-1 chain whose Hamiltonian is invariant under translation, lattice inversion and a global $A_4$ symmetry in the spin degrees of freedom. The classification scheme by Chen, Gu, and Wen allows us to enumerate all possible phases under the given symmetry. Then, we determine which of these phases actually occur in the two-parameter Hamiltonian. Using numerical methods proposed by Pollmann and Turner (2012) we determine the characteristic projective parameters for the Symmetry Protected Topological (SPT) phases. In addition, we present a method for determining the projective commutation parameter in these phases. The resulting phase diagram is rich and contains at least nine different SPT phases. [Preview Abstract] |
Thursday, March 17, 2016 1:15PM - 1:27PM |
S20.00011: Continuous Matrix Product States for Spin-1/2 Fermions with Mass- and Spin-Imbalance Sangwoo S. Chung, C. J. Bolech Recently, we have proposed a continuous matrix product states (cMPS) ansatz that can approximate ground states of interacting spin-1/2 fermions with spin-imbalance in 1D. We now extend that effort to describe a more general system, having both spin- and mass-imbalance. With mass-imbalance, there is no exact solution for the Gaudin-Yang Hamiltonian, and this is one of the first applications of the fermionic cMPS on non-integrable systems. [Preview Abstract] |
Thursday, March 17, 2016 1:27PM - 1:39PM |
S20.00012: Controlled quantum transport in a disordered one-dimensional lattice Sahel Ashhab We investigate the effect of disorder on the transfer of quantum states across a one-dimensional lattice with varying levels of control resources. We find that the application of properly designed control signals, even when applied only to the two ends of the lattice, allows perfect state transfer up to disorder strengths that would not allow a generic quantum state to propagate the length of the lattice. At sufficiently large disorder strengths, however, the local control signals fail to send the quantum state from one end of the system to the other end. Our results shed light on the interplay between disorder and controlled transport in one-dimensional systems. [Preview Abstract] |
Thursday, March 17, 2016 1:39PM - 1:51PM |
S20.00013: Inhomogeneous CDMFT and nonmagnetic impurities in graphene M. Charlebois, D. S\'en\'echal, A.-M. Gagnon, A.-M.S. Tremblay In cluster dynamical mean-field theory (CDMFT), we usually apply the self-consistency condition on an infinite super-lattice of identical clusters. However, in some problems a large unit cell is required, for instance in the presence of a periodically repeated impurity. Since the impurity solver (exact diagonalization) can only treat small clusters, we break the unit cell into multiple small clusters that can be solved individually. This new technique is called inhomogeneous CDMFT (1) and is analogous to inhomogeneous DMFT (2). In this presentation, we will explain both the CDMFT and inhomogeneous CDMFT self-consistency loops within a unified, simple picture. We then apply this technique to a nonmagnetic impurity in graphene and study the emerging magnetism. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory studies. \\ (1) Charlebois, M. et al., Phys. Rev. B 91, 035132 (2015). \\ (2) Snoek, M. et al., New J. Phys. 10, 093008 (2008). [Preview Abstract] |
Thursday, March 17, 2016 1:51PM - 2:03PM |
S20.00014: Spin selective localization transition in disordered interacting system in two dimensions: A quantum Monte-Carlo study Shashi Kunwar, Prabuddha Chakraborty, Rajesh Narayanan The phenomenon of Anderson localization wherein non-interacting electrons are localized by quenched impurities is a subject matter that has been extremely well studied. However, localization transition under the combined influence of interaction and quenched disorder is less well understood. In this context we study the localization transition in a two-dimensional Hubbard model under the influence of a spin-selective disorder i.e, disorder which is operational on just one of the spin-species. The model is analyzed by laying recourse to a Quantum Monte Carlo based scheme. Using this approach we show the possibility of a metal-insulator transition. However, we will show that this metal-insulator transition is extremely sensitive to the filling-fraction inherent in the system. Our results will be encapsulated in a phase diagram. [Preview Abstract] |
Thursday, March 17, 2016 2:03PM - 2:15PM |
S20.00015: Real space study of current flow through nanoscopic Kondo lattices John Van Dyke, Dirk Morr We study current flow through a nanoscopic Kondo lattice in real space and with finite applied voltage. We show how the presence of a defect, such as an f-electron vacancy, modifies the current flow in its vicinity, depending on lead geometry and coupling to phonons. Finally, we report a self-consistent calculation of the change in the hybridization between the conduction and f-electrons caused by the applied bias. [Preview Abstract] |
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