Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session W45: Quantum Manybody Systems and Computational Physics |
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Sponsoring Units: DCOMP Chair: Ettore Vitali, California State University, Fresno Room: 706 |
Friday, March 6, 2020 8:00AM - 8:12AM |
W45.00001: Isometric Tensor Network Representation of String-Net Liquids Tomohiro Soejima, Karthik Siva, Nick Bultinck, Shubhayu Chatterjee, Frank Pollmann, Michael Zaletel Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical computations, it remained unclear which phases admit an isoTNS representation. In this work, we show that two-dimensional string-net liquids, which represent a wide variety of topological phases including discrete gauge theories, admit an exact isoTNS representation. We further show that the isometric form can be preserved after applying a finite depth local quantum circuit. Taken together, these results show that long-range entanglement by itself is not an obstruction to isoTNS representation and suggest that all two-dimensional gapped phases with gappable edges admit an isoTNS representation. |
Friday, March 6, 2020 8:12AM - 8:24AM |
W45.00002: Dynamical phases of interacting Andre-Aubry-Harper model Yong-Chan Yoo, Junhyun Lee, Brian Swingle The dynamics of non-integrable quantum many-body systems have received extensive attention for both theoretical and practical purposes. One important issue we address in this talk is the phase transition between thermal and many-body-localized states and the dynamical properties of their possible intermediate states. We calculate the non-equilibrium steady states (NESS) of the boundary-driven strongly interacting Andre-Aubry-Harper model by employing the time-evolving block decimation on matrix product density operators. The spin and energy transport properties of the system are obtained from the NESS, which reveals a rich phase diagram while tuning the quasiperiodic potential strength. We uncover an exotic dynamical phase following the thermal phase where the spin transport becomes sub-diffusive while the butterfly velocity remains non-zero, and also investigate the entanglement properties of each phase. |
Friday, March 6, 2020 8:24AM - 8:36AM |
W45.00003: Topological signatures of Multipartite Entanglement Fabio Lingua, Wei Wang, Liana Shpani, Barbara Capogrosso-Sansone We present a proposal to relate topological structure of worldline configurations to multipartite entanglement. Configurations result from the path-integral formulation of the density matrix in the limit of zero temperature. We consider hard-core bosons for which configurations, i.e. collections of particle paths, can be seen as geometric braids with a certain topological structure. We propose that properties of worldline configurations may realize a more comprehensive deciphering of multipartite entanglement. |
Friday, March 6, 2020 8:36AM - 8:48AM |
W45.00004: Dynamical properties of correlated many-body systems from Quantum Monte Carlo simulations Ettore Vitali, Patrick Kelly, Annette Lopez, Kaelyn Dauer I will discuss recent advances in the ab-initio study of correlated many-body quantum systems, and in particular the possibility to compute dynamical correlation functions from first principles using Quantum Monte Carlo techniques. Using the Hubbard model as an example, I will address the calculation of the spectral function, that can be experimentally measured in spectroscopy experiments, and the density structure factors, that can be measured in scattering experiments. The purpose is to allow us to directly compare the predictions of Quantum Monte Carlo techniques with experiments. I will present results for cold atomic Fermi systems in the BEC-BCS crossover in two and three dimensions and for cold atoms on optical lattices. I will also discuss results and perspectives for repulsive models, in connection with high-temperature superconductivity. |
Friday, March 6, 2020 8:48AM - 9:00AM |
W45.00005: Padé resummation of the linked cluster expansion of the many-particle path-integral. Anish Bhardwaj, Efstratios Manousakis We have developed a quantum cluster expansion, analogous to the well-known Mayer cluster expansion for the classical partition function and the pair distribution function, and a quantum version of the virial expansion by starting from the many-body path-integral. We first derive the diagrammatic series expansion for the pair distribution function and show that the expansion is linked. This expansion can also be thought of as a power series expansion in the particle density. To resum the series, we use a Padé approximation scheme in momentum space, which is constrained to yield the calculated order by order expansion terms and the classical limit correctly. We have tested the approach on a Lennard-Jones and a hard-sphere system and our results agree very well with those obtained from the path-integral Monte Carlo. Our method has immediate application to the case of short-range hard-core potential where the established analytical and semi-analytical tools of many-body perturbation theory and quantum statistical mechanics cannot be applied in a straightforward manner. |
Friday, March 6, 2020 9:00AM - 9:12AM |
W45.00006: An approach to discovering the low-energy space for effective quantum models of realistic systems. Brian Busemeyer, Joao N. B. Rodrigues, Shivesh Pathak, Lucas K. Wagner Low-energy effective models can be powerful tools for understanding realistic systems, but in many cases it is difficult to quantify the accuracy of those models for a specific system. Density matrix downfolding (DMD) [1] is one approach to determining accurate effective models from first-principles many-body calculations, but requires a sample of low-energy wave functions with varying properties. We present a new method, constrained variational Monte Carlo, which targets low-energy wave functions while varying other properties, such as the average double-occupation of orbitals. We tested the approach on the hydrogen molecule at stretched and compressed bond lengths, and use it to explore how the low-energy space changes with bond length. For example, when the bond is stretched the low-energy space shifts such that interactions become necessary to accurately describe it. Models fitted to the generated states were solved and reproduced the exact low-energy spectrum of the first-principles Hamiltonian. The method provides a systematic many-body approach to exploring the low-energy space of realistic systems. [1] Changlani et al., J. Chem. Phys., 143, 10, 102814, (2015). |
Friday, March 6, 2020 9:12AM - 9:24AM |
W45.00007: Variational-Correlations Approach to Quantum Many-body Problems Arbel Haim, Gil Refael We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin 1/2 Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed. |
Friday, March 6, 2020 9:24AM - 9:36AM |
W45.00008: Emergence of diffusive dynamics in an efficiently-solvable quantum lattice model Jie Zou, Xiaopeng Li Thermalization is a common phenomenon in nature, having a characteristic feature of irreversibility due to entropy increase. However, quantum mechanics, the principle for the microscopic world, is reversible. In past few decades, much effort has been devoted to this field in order to reconcile this conflict, and the eigenstate thermalization hypothesis has been proposed as one way to formulate quantum thermalization. In this talk, I will present our recent work on a one-dimension spinless hardcore fermion model with a variable range of interactions. We solve this problem by mapping it into a free fermion case, and we calculate its time evolution with an efficient Monte Carlo sampling algorithm. We observe that although our model is integrable in energy level spacing, the physical observables show certain thermalization behaviors. Furthermore, with increasing temperature, our system shows a crossover from ballistic to diffusive. It is worth mentioning that in our study we can reach a number of lattice sites of hundreds to thousands, much larger than typical numerical studies on quantum dynamics, which allows us to exclude finite-size artifacts. |
Friday, March 6, 2020 9:36AM - 9:48AM |
W45.00009: Off-shell effective energy theory: a unified treatment of the Hubbard model from d=1 to d= ∞ Zhengqian Cheng, Chris Marianetti Here we propose an exact formalism, off-shell effective energy theory (OET), which provides a thermodynamic description of a generic quantum Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix ansatz, and we renormalize the CPE using a standard expansion of the ground state energy. We present dual realizations of OET based on a partitioning of the kinetic and potential energy, denoted as K and X, respectively. We showcase the OET for the one band Hubbard model in d=1, 2, and ∞ , showing favorable agreement with exact or state-of-the-art results over all parameter space; and a negligible computational cost. Physically, K describes the Fermi liquid, while X gives an analogous description of both the Luttinger liquid and the Mott insulator. Our approach should find broad applicability in lattice model Hamiltonians, in addition to real materials systems. |
Friday, March 6, 2020 9:48AM - 10:00AM |
W45.00010: The Superfluid Pairing Gap for an Ultracold Atomic Unitary Fermi Gas Annette Lopez, Ettore Vitali, Patrick Kelly We address the problem of computing the superfluid pairing gap of a fermionic cold gas from first principles. Cold atomic Fermi systems are unique laboratories to explore many-body systems, due to the unprecedented experimental control that can be currently achieved. The ability to provide robust theoretical predictions for cold atoms can have a significant impact in condensed matter physics, nuclear physics, and nuclear astrophysics. In particular, cold gases can shed light into some of the most mysterious physical systems in the universe, like the interiors of neutron stars. In this work we use unbiased Quantum Monte Carlo techniques interfaced with state of art analytic continuation technique to compute the spectral function of a unitary Fermi gas and the superfluid gap. |
Friday, March 6, 2020 10:00AM - 10:12AM |
W45.00011: Normalizing Cluster Wavefunctions in the Interstitial Region Within the Muffin-tin Approximation Daniel Gebremedhin, Charles Albert Weatherford, Brian Wilson In multiple-scattering methods, overlap integrals of cluster wavefunctions for |
Friday, March 6, 2020 10:12AM - 10:24AM |
W45.00012: Temperature scaling in Monte Carlo nonequilibrium relaxation Yoshihiko Nonomura, Yusuke Tomita The nonequilibrium relaxation (NER) method is an alternative approach to overcome the critical slowing down in Monte Carlo simulations. In local-update algorithms, NER is based on the power-law critical relaxation derived from the dynamical finite-size scaling (DFSS) theory, and off-critical scaling behaviors are also derived from the same formalism. In cluster-update algorithms, critical nonequilibrium relaxation is described by the stretched-exponential formula [1-4], which can be derived phenomenologically [5]. In the present talk, we show that off-critical scaling behaviors in cluster-update algorithms can be formulated by generalizing the nonequilibrium-to-equilibrium scaling [1,3-5]. By taking the magnetic susceptibility as an example, from the early-time critical relaxation, χ(t)∼exp(ctσ), and the equilibrium behavior near the critical point Tc, χ(T)∼(T-Tc)-γ, we have χ(t,T)∼(T-Tc)-γfsc[ctσ+log(T-Tc)γ] with a scaling function fsc(x). This scaling is confirmed numerically, and the one derived similarly in local-update algorithms holds better than that from DFSS. |
Friday, March 6, 2020 10:24AM - 10:36AM |
W45.00013: A statistical mechanics definition of the hydration shell of a membrane in an open system Molecular Dynamics Simulation. John Whittaker, Luigi Delle Site Defining and quantifying the solvation shell of a biological macromolecule poses a major challenge, and even with state of the art equipment and methods, the question of the extent of hydration can vary depending on the quantity of interest, emphasizing the need for an unambiguous definition. The adaptive resolution simulation (AdResS) technique offers the unique ability to estimate the extent of the hydration shell around a biomolecule through the use of an open boundary atomistic system embedded within a thermodynamic reservoir of non-interacting, structureless particles. Here, we apply the latest AdResS scheme to the study of a pure DPPC membrane solvated in liquid water and determine that the mandatory solvation shell of a DPPC membrane extends to ~1.5 nm away from the DPPC phosphate headgroups, well beyond distances predicted from radial distribution functions. |
Friday, March 6, 2020 10:36AM - 10:48AM |
W45.00014: Topologically induced pre-scrambling and dynamical detection of topological phase transitions at infinite temperature Ceren Dag, Luming Duan, Kai Sun Out-of-time-order correlators (OTOCs) measured at infinite temperature are well-established tools to study quantum chaos in quantum many-body systems as well as information properties of black holes. Here we report that infinite-temperature OTOCs could also directly probe quantum phase transitions at zero temperature in contrast to common intuition. We reveal the mechanism that allows OTOC to prioritize the low energy effects over strong thermal fluctuations at infinite temperature and find that the mechanism is driven by topological degeneracy and hence is highly universal and robust, as long as the underlying system can be formulated in 1D Majorana basis. Using the Majorana representation, we analytically and numerically show that the infinite-temperature OTOCs detect the presence of Majorana zero modes at the ends of the chain that is associated with 1D Z2 topological order. Such sensitivity to zero modes introduces a new time-scale to the dynamics of non-integrable systems where the information scrambling temporarily freezes, suggesting a restricted scrambling for the topologically-protected quantum information. We dub the phenomenon as topologically induced pre-scrambling. |
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