Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Y27: Quantum Many-Body Systems III |
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Sponsoring Units: DCOMP Chair: Zach Pozun, University of Pittsburgh Room: 501 |
Friday, March 7, 2014 8:00AM - 8:12AM |
Y27.00001: Full-counting statistics and phase transition in an open quantum system of non-interacting electrons Mariya Medvedyeva, Stefan Kehrein We develop a method for calculating the full-counting statistics for a non-interacting fermionic system coupled to memory-less reservoirs. The evolution of the system is described by the Lindblad equation. We introduce the counting field in the Lindblad equation which yields the generating function and allows us to obtain all cumulants of the charge transport. In a uniform system the cumulants of order k are independent of the system size for systems longer than k+1 sites. The counting statistics from the Lindblad approach does not take into account the interference in the reservoirs which gives a decreased value of noise in comparison to the Green function approach which describes phase coherent leads. The two methods yield the same value for the current, which is due to current conservation. The Fano factors are different (and linearly related) and allow us to distinguish between memory-less and phase coherent reservoirs. We also consider the influence of dissipation along the chain allowing for both tunneling into and out of the chain along its length. Infinitesimally small dissipation along the chain induces a quantum phase transition which manifests itself as a discontinuity in transport properties and entropy. [Preview Abstract] |
Friday, March 7, 2014 8:12AM - 8:24AM |
Y27.00002: Quantum Monte Carlo studies of Shannon-Renyi entropies and participation spectra in interacting spin systems David J. Luitz, Fabien Alet, Nicolas Laflorencie Shannon-Renyi entropies are measures of the participation of basis states in a wave function. Previous work for one dimensional systems showed that they exhibit a subleading scaling behavior with system size that contains universal information, such as e.g. the Luttinger Liquid parameter. Here, we introduce quantum Monte Carlo schemes to calculate these quantities and the related participation spectra for unfrustrated quantum many body systems in any dimension and apply them to interacting spin systems. Our results demonstrate the universality of subleading scaling terms for different kinds of phase transitions with a spontaneous breaking of discrete or continuous symmetries and at quantum critical points. Aditionally, we also discuss the signature of quantum phase transitions in the participation spectra of subsystems. [Preview Abstract] |
Friday, March 7, 2014 8:24AM - 8:36AM |
Y27.00003: An ab initio many-body approach to understanding magnetism in the unconventional superconductor, FeSe Brian Busemeyer, Lucas Wagner We report on the progress of many-body ab initio fixed-node diffusion Monte Carlo (FM-DMC) calculations performed on the unconventional superconductor FeSe. The exact nature of the pairing mechanism in unconventional superconductors is still controversial; however, the fact that these materials demonstrate antiferromagnetism near the conditions necessary for superconductivity suggests some combination of lattice and magnetic interactions may be responsible. FN-DMC has been shown to obtain high accuracy on a number of strongly correlated materials, and so is particularly well-suited to study the correlations that give rise to superconductivity. We perform FN-DMC calculations on FeSe to determine the energetic orderings of the low-lying magnetic states, and investigate the dominant correlations between the single particle states. FeSe also demonstrates a pressure dependent transition temperatures, hence, we also investigate the pressure dependence of the energy and dominant correlations in the various magnetic states. We expect our results will shed light on the nature of magnetism in the iron-based superconductors, and possibly its relationship with superconductivity. [Preview Abstract] |
Friday, March 7, 2014 8:36AM - 8:48AM |
Y27.00004: Quantum Monte Carlo Studies of Zinc-Porphyrin and Molybdenum dimer Adem Halil Kulahlioglu, Lubos Mitas We present fixed-node diffusion Monte Carlo (FN-DMC) studies focused on the calculation of vertical excitation energy in Q band corresponding to the excitation between the singlet ground-state ($1^{1}A_{g}$) and the lowest-lying singlet excited state ($1^{1}E_{u}$) of Zinc-Porphyrin (ZnP) molecule and the binding energy of the ground-state Molybdenum dimer (Mo$_2$). In the ZnP study, several trial wave functions for the excited state such as CIS, TDDFT and others were tested. We have obtained a very good agreement both with experiments and with high accuracy basis set correlated wave function calculations. The calculations show that the studied excitation is not well described by single-reference trial wave functions. In the Mo$_2$ study, the bias introduced by the fixed-node approximation with single-reference trial function is significant so we attempt to reduce it by means of the selected Configuration Interaction (selected-CI) technique. The single-particle orbitals that appear to lead to the lowest fixed-node error were generated by the hybrid version of the TPSS meta-GGA (TPSSh) functional. In this way, we have obtained significant improvements over the results from the single-reference trial function. [Preview Abstract] |
Friday, March 7, 2014 8:48AM - 9:00AM |
Y27.00005: Simulations of quantum spin decoherence and spin diffusion using coherent-state representation Viatcheslav Dobrovitski Understanding non-equilibrium spin dynamics and spin diffusion in open quantum systems is of fundamental importance. It is also essential e.g. for NMR characterization of materials based on the spin diffusion between different $^{13}$C sites. However, exact numerical modeling of large 3-D spin systems with arbitrary-range couplings is exponentially difficult, and approximate methods for such systems are actively sought. We consider the approach based on the coherent-state P-representation for the density matrix of the many-spin system [1], as applied to spin decoherence and spin diffusion in the presence of the spin bath. We consider both model spin systems (such as the central spin problem), and realistic NMR experiments (spin diffusion in graphite bilayers and in organic molecular crystals). The approximate modeling results are compared with the exact simulations performed on the systems of 20-25 spins. We determine the features of the system which justify the use of the P-representation modeling, and demonstrate that this approach is applicable to a wide range of situations important for quantum information processing and NMR experiments.\\ \lbrack 1\rbrack K. Al-Hassanieh et al., Phys. Rev. Lett. 97, 037204 (2006); V. V. Dobrovitski et al., Phys. Rev. Lett. 102, 23760 (2009) [Preview Abstract] |
Friday, March 7, 2014 9:00AM - 9:12AM |
Y27.00006: Matrix product states for anyonic systems and efficient simulation of dynamics Sukhbinder Singh, Robert Pfeifer, Guifre Vidal, Gavin Brennen Anyons are exotic quasiparticles that exhibit non-trivial exchange statistics and arise as low lying excitations of topological phases of matter. Many-body systems of anyons offer a realm of new physics to explore that depends on their topological properties. The formalism of Matrix Product States [1] (MPS) has led to significant advances in the study of quantum many-body systems with local degrees of freedom such as spins or bosons. The MPS also forms the basis of the highly successful ``time-evolving block decimation'' [2] (TEBD) algorithm, which can be used to efficiently simulate dynamics of 1D systems. I will describe how to extend the MPS formalism and the TEBD algorithm to study lattice systems of anyons, which carry non-local degrees of freedom. I will also present supporting simulation results for chains of interacting anyons, including results for an anyonic Hubbard-type model [3] that give insight into the transport properties of anyons. \\[4pt] [1] S. Ostlund {\&} S. Rommer, PRL 75, 3537 (1995)\\[0pt] [2] G. Vidal, PRL 91, 147902 (2003)\\[0pt] [3] L. Lehman, V. Zatloukal, et al. PRL 106, 230404 (2011) [Preview Abstract] |
Friday, March 7, 2014 9:12AM - 9:24AM |
Y27.00007: SU(3) classical representation of quantum dynamics of interacting spins Shainen Davidson The Wigner-Weyl representation of quantum mechanics allows quantum operators to be represented as functions over phase space variables. In this representation, the Wigner function plays the role of a phase space probability distribution, although it can be negative due to quantum mechanics. The Truncated Wigner Approximation (TWA) is a semi-classical approach, where the dynamics are approximated using the classical dynamics of phase space variables averaged over the Wigner function. We can use this formalism to study spin dynamics as well; however, if there are any terms not linear in spin operators, the dynamics are not exact. In the case of spin one systems, we can linearize a single spin Hamiltonian by recasting it in terms of $SU(3)$ operators, where now we have eight operators instead of the usual three. Thus with TWA we can study the quantum dynamics of arbitrary spin one systems using eight ``classical'' spin variables per site, and the local TWA will be exact. I will discuss implications of this approach to interacting spin one systems and to the Bose-Hubbard model. [Preview Abstract] |
Friday, March 7, 2014 9:24AM - 9:36AM |
Y27.00008: Eigenvalue degeneracy relations for a fully connected isotropic spin network Mark Coffey, Grant Allen We present and indicate the proofs of identities for the eigenvalue degeneracy of a fully connected spin network with isotropic spin coupling. Such a network has application to quantum information processing, especially for solid-state implementations, and in fact the qubit case with anisotropic coupling has been recently realized. One set of proofs and other relations for the case of qubits is given in the context of hypergeometric summation. We then generalize to arbitrary spin, using combinatorial arguments. [Preview Abstract] |
Friday, March 7, 2014 9:36AM - 9:48AM |
Y27.00009: ABSTRACT WITHDRAWN |
Friday, March 7, 2014 9:48AM - 10:00AM |
Y27.00010: Spectral gaps of AKLT Hamiltonians using Tensor Network methods Artur Garcia-Saez, Valentin Murg, Tzu-Chieh Wei Using exact diagonalization and tensor network techniques we compute the gap for the AKLT Hamiltonian in 1D and 2D spatial dimensions. Tensor Network methods are used to extract physical properties directly in the thermodynamic limit, and we support these results using finite-size scalings from exact diagonalization. Studying the AKLT Hamiltonian perturbed by an external field, we show how to obtain an accurate value of the gap of the original AKLT Hamiltonian from the field value at which the ground state verifies $e_0<0$, which is a quantum critical point. With the Tensor Network Renormalization Group methods we provide direct evidence of a finite gap in the thermodynamic limit for the AKLT models in the 1D chain and 2D hexagonal and square lattices. This method can be applied generally to Hamiltonians with rotational symmetry, and we also show results beyond the AKLT model. [Preview Abstract] |
Friday, March 7, 2014 10:00AM - 10:12AM |
Y27.00011: Matrix product state formulation of frequency-space dynamics at finite temperatures Salvatore R. Manmana, Alexander C. Tiegel, Andreas Honecker We consider finite temperature properties of dynamical spectral functions of $S=1/2$ XXZ chains with Dzyaloshinskii-Moriya (DM) interactions in magnetic fields and analyze the effect of these symmetry breaking interactions on the nature of the spectral functions by comparing to results obtained for systems without DM interactions. This is achieved by extending matrix product state approaches working at finite temperatures to compute dynamical spectral functions in the frequency domain. We provide proof of principle results for the computation of experimentally relevant quantities like line shapes in neutron or light-scattering experiments. Based on our results, we provide an outlook for further improvements and developments of finite temperature approaches to dynamical spectral functions. [Preview Abstract] |
Friday, March 7, 2014 10:12AM - 10:24AM |
Y27.00012: Nonequilibrium dynamical mean-field study of the nonthermal fixed point in the Hubbard model Naoto Tsuji, Martin Eckstein, Philipp Werner A fundamental question of whether and how an isolated quantum many-body system thermalizes has been posed and attracted broad interest since its ideal realization using cold atomic gases. In particular, it has been indicated by various theoretical studies that the system does not immediately thermalize but often shows ``prethermalization'' as a quasi-stationary state, where local observables quickly arrive at the thermal values while the full momentum distribution stays nonthermal for long time. Here we study the thermalization process for the fermionic Hubbard model in the presence of the antiferromagnetic long-range order [1][2]. Time evolution is obtained by the nonequilibrium dynamical mean-field theory. Due to classical fluctuations, prethermalization is prevented, and the transient dynamics is governed by a nonthermal fixed point, which we discuss belongs to a universality class distinct from the conventional Ginzburg-Landau theory. [1] N. Tsuji, M. Eckstein, P. Werner, Phys. Rev. Lett. 110, 136404 (2013). [2] N. Tsuji, P. Werner, Phys. Rev. B 88, 165115 (2013). [Preview Abstract] |
Friday, March 7, 2014 10:24AM - 10:36AM |
Y27.00013: Unexpected z-direction Ising antiferromagnetic order in a frustrated spin-1/2 J 1-J 2 XY model on the honeycomb lattice Zhenyue Zhu, David Huse, Steven White Using the density matrix renormalization group (DMRG) on wide cylinders, we study the phase diagram of the spin-1/2 XY model on the honeycomb lattice, with first-neighbor ($J_1 = 1$) and frustrating second-neighbor ($J_2>0$) interactions. For the intermediate frustration regime $0.22 < J_2 < 0.36$, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any $S_zS_z$ interactions in the Hamiltonian. Surrounding this phase as a function of $J_2$ are antiferromagnetic phases with the moments pointing in the $x-y$ plane for small $J_2$ and a close competition between an $x-y$ plane magnetic collinear phase and a dimer phase for large values of $J_2$. We do not find any spin liquid phases in this model. [Preview Abstract] |
Friday, March 7, 2014 10:36AM - 10:48AM |
Y27.00014: Photo-induced topological phase transitions in the Hubbard model on honeycomb lattice Takahiro Mikami, Naoto Tsuji, Hideo Aoki ``Floquet topological states'' as first proposed by Oka and Aoki [1] are attracting much attention, where Dirac electrons in circularly polarized ac-fields undergo a nonequilibrium transition to topological stationery states with a photo-induced Hall effect in zero magnetic field. Such a transition has indeed been observed recently by a detection of the Floquet band structure on the surface of a topological insulator [2]. In equilibrium, on the other hand, electron correlation has been suggested to produce rich phases on honeycomb lattice. Hence it should be interesting to study what effects the electron correlation can exert on the photo-induced topological transitions. This has motivated us to study of the Hubbard model on honeycomb lattice in circularly polarized ac-fields. For this we have implemented the Floquet DMFT method[3]. We have indeed obtained a novel phase diagram, where most notably (i) there is a lobe structure between the topological and Mott phases and also (ii) a topological-topological transition with a change in the Chern number. \\[4pt] [1] T. Oka and H. Aoki, Phys. Rev. B 79, 081406(R) (2009)\\[0pt] [2] Y. H. Wang, et al., Science 342, 453 (2013)\\[0pt] [3] N. Tsuji, et al., Phys. Rev. Lett. 103, 047403 (2009) [Preview Abstract] |
Friday, March 7, 2014 10:48AM - 11:00AM |
Y27.00015: Classification of spin liquids in materials with strong spin-orbit coupling Johannes Reuther, Shu-Ping Lee, Jason Alicea The investigation of spin liquids is a fascinating field in condensed matter physics that is increasingly motivated by experiments. Exhaustive classifications of spin liquids have been carried out in several systems, particularly when full SU(2) spin-rotation symmetry is present. Systematic studies that explore strongly spin-orbit-coupled magnetic compounds (for which there are many experimental examples) are, however, relatively scarce. We report on a classification of $Z_2$ spin liquids on the square lattice when SU(2) spin symmetry is maximally lifted. Using projective symmetry group methods, we find that, surprisingly, the lifting of spin symmetry yields vastly more spin liquid states compared to SU(2)-invariant systems. Many of these spin liquids possess gapless edge states protected by lattice symmetries and, hence, constitute magnetic analogues of topological crystalline superconductors. [Preview Abstract] |
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