Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session J24: Quantum Many-Body Systems and Methods I |
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Sponsoring Units: DCOMP Chair: Cyrus Umrigar, Cornell University Room: 326 |
Tuesday, March 19, 2013 2:30PM - 2:42PM |
J24.00001: Density dependence of fixed-node errors in quantum Monte Carlo: spin-polarized systems and triplet correlations Adem Kulahlioglu, Kevin Rasch, Shuming Hu, Lubos Mitas We present an analysis focused on the fixed-node bias of trial wave functions for fully spin-polarized atomic systems. We benchmark the case of three electrons in the lowest state for a given symmetry which exhibits near-degeneracy effects similar to the in Be-like systems. The trial wave functions examined have been constructed at the HF level and at the pairing level in the form of a pfaffian. We find very significant fixed-node errors at the HF level, of the order of tens of percent. On the other hand, we observe that the pfaffian wave function correlated in the triplet pair channel enables us to get essentially exact results. We demonstrate that the key reason behind the large fixed-node erorr of the HF wavefunction is its artificial nodal domain topology. In addition, the fixed-node error is studied as a function of electron density by varying the atomic charge Z. We find that it scales linearly with Z what is very similar to our previous study on Be-like systems with similar dependence on density but pairing in the singlet channel. [Preview Abstract] |
Tuesday, March 19, 2013 2:42PM - 2:54PM |
J24.00002: Fixed-node errors in electronic structure quantum Monte Carlo: interplay of density and node nonlinearities Lubos Mitas, Kevin Rasch, Shuming Hu We analyze valence electronic structure quantum Monte Carlo (QMC) calculations of first- and second-row atom systems. It turns out that there are significant differences (twofold or more) between the valence fixed-node errors of the first- vs second-row atom systems for single-configuration trial wave functions. The differences are illustrated on a set of atoms, molecules and Si and C solids that are valence isoelectronic, have similar correlation energies, bond patterns, geometries, same ground states and symmetries. Our analysis shows that the root cause of these differences is the increase of electron density combined with the degree of the node nonlinearity. The findings have implications for QMC fixed-node biases in systems with many elements including transition metals and others, which fall under the same electronic structure pattern. The finding has implications for both for accuracy of fixed-node energies, efficiency in elimination of the fixed-node bias and also for pseudopotential construction for very heavy elements. It has potential implications also for other correlated wave function approaches. [Preview Abstract] |
Tuesday, March 19, 2013 2:54PM - 3:06PM |
J24.00003: Diffusion quantum Monte Carlo for atomic spin-orbit interactions Minyi Zhu, Shi Guo, Lubos Mitas We present a generalization of the quantum Monte Carlo methods (QMC) for dealing with the spin-orbit (SO) effects in heavy atom systems. For heavy elements, the spin-orbit interaction plays an important role in electronic structure calculation and becomes comparable to the exchange, correlations and other effects. We implement relativistic lj-dependent effective core potentials for valence-only calculations. Due to the spin-dependent Hamiltonian, the antisymmetric trial wave functions are constructed from two-component spinors in jj-coupling so that the states are labeled by its total angular momentum J. A new spin representation is proposed which is based on summation over all possible spin states without generating large fluctutations and the fixed-phase approximation is used to avoid the sign problem. Our approach is different from the recent idea based on rotating (sampling) the spinors according to the action of the spin-orbit operator. We demonstrate the approach on heavy atom and small molecular systems in both variational and diffusion Monte Carlo methods and we calculate both ground and excited states. The results show very good agreement with independent methods and experimental results within the accuracy of the used effective core potentials. [Preview Abstract] |
Tuesday, March 19, 2013 3:06PM - 3:18PM |
J24.00004: Wavefunction Monte Carlo for Transport in Open Quantum Systems James Gubernatis The wave function Monte Carlo method is a technique for solving the stochastic differential equation associated with the master equation (Lindblad equation) for transport in an open quantum system. For an anisotropic, spin 1/2, XXZ Heisenberg chain in an external magnetic field, whose ends interact with heat baths, we compute the heat transport through the chain as a function of chain length, temperature difference at the ends, and the anisotropy of the chain's exchange interaction from both a wavefunction Monte Carlo simulation and a deterministic solution of the master equation for the open system's density matrix. Having both solutions creates benchmarks for the more fundamental objective of studying the consequence of replacing a piecewise deterministic step, which is typically part of the wavefunction Monte Carlo method, with a stochastic step. This replacement affords the potential of simulating longer chain lengths. [Preview Abstract] |
Tuesday, March 19, 2013 3:18PM - 3:30PM |
J24.00005: Prospects for efficient QMC defect calculations: the energy density applied to Ge self-interstitials Jaron Krogel, Jeongnim Kim, David Ceperley Defect formation energies require expensive energy difference calculations between defective and bulk systems over a range of system sizes. At the point of convergence, subregions added to represent larger systems no longer contribute to the formation energy and therefore display similar local energetics. A recent formulation of the energy density for QMC is capable of identifying separate energetic contributions from each atom, enabling the identification of the bulk-like regions in a defect system that only add noise to the final result. The potential efficiency gains of this approach are explored in a realistic defect system, the germanium self-interstitial. Calculations involving up to 217 atoms at fixed volume show that the extent of the strain energy field depends strongly on the interstitial site. Bulk-like regions are largest for the hexagonal interstitial increasing the efficiency by a factor of 2-3. In contrast, the split structure interstitial has few bulk-like atoms and shows no speedup. Possible approaches to further improve the efficiency will be discussed. [Preview Abstract] |
Tuesday, March 19, 2013 3:30PM - 3:42PM |
J24.00006: Analytic time evolution, random phase approximation, and Green functions for matrix product states Jesse M. Kinder, Claire C. Ralph, Garnet Kin-Lic Chan Drawing on similarities in Hartree-Fock theory and the theory of matrix product states (MPS), we explore extensions to time evolution, response theory, and Green functions. We derive analytic equations of motion for MPS from the least action principle, which describe optimal evolution in the small time-step limit. We further show how linearized equations of motion yield a MPS random phase approximation, from which one obtains response functions and excitations. Finally, we describe site-based Green functions associated with MPS. Using the fluctuation-dissipation theorem, we analyze the correlations introduced by the random phase approximation relative to the ground state wave function. [Preview Abstract] |
Tuesday, March 19, 2013 3:42PM - 3:54PM |
J24.00007: Application of Multi-Orbital DMFT to the Dynamic Hubbard Model Christopher Polachic, Frank Marsiglio Using multi-orbital dynamical mean field theory we explore the relationship between site parameters, band filling and electron-hole asymmetry arising through the electronic dynamic Hubbard model. We evaluate the emergence of hole pairing which has previously been observed through exact diagonalization and two-site DMFT studies. [Preview Abstract] |
Tuesday, March 19, 2013 3:54PM - 4:06PM |
J24.00008: Thermo-Electric Transport Out-of-Equilibrium Prasenjit Dutt, Karyn Le Hur The manipulation of mesoscopic systems to engineer quantum circuits has become a crucial tool to test and explore novel phenomena which arise due to quantum coherence effects. Electronic transport through these systems under the combined influence of voltage biases and thermal gradients poses several open questions, the understanding of which has an immense scope for future applications. We provide an effective equilibrium description of the steady state dynamics of quantum impurity models far-from-equilibrium, which generalizes the theory presented in P.Dutt et al. (Annals of Physics, 326, 2963(2011)), to include thermal gradients. We study the interplay of strong voltage biases and large thermal gradients and its effect on the emergent Abrikosov-Suhl resonance. Taking the linear response limit, we compute the various thermo-electric coefficients of the system, such as the Peltier coefficient and thermal conductance, and verify the reciprocity relations of Onsager. [Preview Abstract] |
Tuesday, March 19, 2013 4:06PM - 4:18PM |
J24.00009: Thermalization threshold in models of 1D fermions Subroto Mukerjee, Ranjan Modak, Sriram Ramswamy The question of how isolated quantum systems thermalize is an interesting and open one. In this study we equate thermalization with non-integrability to try to answer this question. In particular, we study the effect of system size on the integrability of 1D systems of interacting fermions on a lattice. We find that for a finite-sized system, a non-zero value of an integrability breaking parameter is required to make an integrable system appear non-integrable. Using exact diagonalization and diagnostics such as energy level statistics and the Drude weight, we find that the threshold value of the integrability breaking parameter scales to zero as a power law with system size. We find the exponent to be the same for different models with its value depending on the random matrix ensemble describing the non-integrable system. We also study a simple analytical model of a non-integrable system with an integrable limit to better understand how a power law emerges. [Preview Abstract] |
Tuesday, March 19, 2013 4:18PM - 4:30PM |
J24.00010: Topological Entanglement Entropy with a Twist Benjamin Brown, Stephen Bartlett, Andrew Doherty, Sean Barrett Topologically ordered phases of matter offer an attractive approach to fault tolerant quantum computation. They give rise to exotic quasi-particle excitations known as anyons. Anyons have a degenerate Hilbert space associated to them, which can be used to encode quantum information over non-local degrees of freedom. Recently, it has been shown that twists, the end points of dislocations in the toric code model, and the quasi-particles available on the toric code have some features analogous to a different anyon model; the Ising anyon model. Characteristics of topologically ordered phases can be assessed by calculating the topological entanglement entropy of regions of the ground state of its Hamiltonian. Further to this, the data of its anyonic excitations can be calculated using the von Neumann entropy. We present analytic results showing that twists have the same topological data as Ising anyons using extensions of known topological entanglement entropy formulas. This extends further the analogy between twists and Ising anyons. [Preview Abstract] |
Tuesday, March 19, 2013 4:30PM - 4:42PM |
J24.00011: Nature of the Spin-Liquid Ground State of the S=1/2 Heisenberg Model on the Kagome Lattice Stefan Depenbrock, Ian McCulloch, Ulrich Schollwoeck We perform a density-matrix renormalization group (DMRG) study of the $S=\frac{1}{2}$ Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep more than 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of $-0.4386(5)$, a spin gap of $0.13(1)$, very short-range decay in spin, dimer and chiral correlation functions and finite topological entanglement $\gamma$ consistent with $\gamma=\textrm{log}_2 2$, ruling out gapless, chiral or non-topological spin liquids. At the same time, DMRG results provide strong evidence for a gapped topological $Z_2$ spin liquid. [Preview Abstract] |
Tuesday, March 19, 2013 4:42PM - 4:54PM |
J24.00012: Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems Hidemaro Suwa We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional {\it XXZ} spin-Peierls system. The criticality is totally consistent with the $J_1-J_2$ model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. [Preview Abstract] |
Tuesday, March 19, 2013 4:54PM - 5:06PM |
J24.00013: A Study of the Uniqueness of the Density for Nonequilibrium Systems Selman Hershfield By the Hohenberg-Kohn theorem the density in equilibrium is a unique functional of the the single particle potential. To gain an understanding of whether this is true in a nonequilibrium system with a current flowing, the density is studied for several noninteracting models. Although noninteracting models are not as realistic as interacting ones, they do have the advantage that they can be solved exactly. For sufficiently high bias or chemical potential difference we find that the density is not a unique functional of the potential for some models in the finite spatial region we study numerically. In other models the density is a unique functional of the potential even for large bias. An algorithm will be presented for finding cases where degeneracies exist and a simple physical picture will be given to understand them. [Preview Abstract] |
Tuesday, March 19, 2013 5:06PM - 5:18PM |
J24.00014: Scaling of the Renyi entropy in 1D critical SU(N) spin chains Jonathan Demidio, Matthew S. Block, Ribhu K. Kaul Using quantum Monte Carlo techniques, we study an SU($N$) antiferromagnet with each spin transforming in the fundamental representation. The spin interaction simply permutes ``colors'' on neighboring sites. This permutation operator is of interest to ultra-cold atomic systems, since at low energies it is the dominant effective interaction of the SU($N$) symmetric Hubbard model with one atom per site. We calculate the entanglement entropy across a partition in the spin chain via the so-called ``replica trick,'' whereby the partition function is simulated on the modified topology of an n-sheeted Riemann surface. In the thermodynamic limit, quantum critical spin chains in 1D are described by 2D conformal field theories (CFTs). Thus, the scaling form of the entanglement entropy provides information about the underlying CFT. In particular we extract the central charge of the CFT, which depends only on the symmetries of the spin model and not its microscopic details. We find that the central charge is given by $c=N-1$, which is in agreement with previous theoretical predictions. We also find agreement in the scaling form of the entanglement entropy, which depends on the number of replicas in the Riemann surface. [Preview Abstract] |
Tuesday, March 19, 2013 5:18PM - 5:30PM |
J24.00015: Measuring Entanglement at a Quantum Critical Point with Numerical Linked Cluster Expansion Ann B. Kallin, Katharine Hyatt, Rajiv R. P. Singh, Roger G. Melko We develop a method to calculate the bipartite entanglement entropy of quantum lattice models in the thermodynamic limit, using a Numerical Linked Cluster Expansion (NLCE) involving only rectangular clusters. The NLCE is based on exact diagonalization of all N x M rectangular clusters at the interface between entangled subsystems A and B. We show that the method can be used to obtain the Renyi entanglement entropy of the two-dimensional transverse field Ising model, for arbitrary real Renyi index. Furthermore, extrapolating these results as a function of the order of the calculation, one can obtain subleading universal pieces of the entanglement entropy at a quantum critical point. These results are compared with series expansions, quantum Monte Carlo simulations and field theories, where available, and they demonstrate the utility of the NLCE in obtaining accurate results for the universal properties of this critical point for von Neumann and non-integer Renyi entropies. [Preview Abstract] |
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