Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session B62: Quantum Many Body Systems & Methods I |
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Sponsoring Units: DCOMP Chair: Jack Wells, Nvidia Room: Room 417 |
Monday, March 6, 2023 11:30AM - 11:42AM |
B62.00001: Dynamical properties of the Holstein chain from finite-temperature density matrix renormalization group method Fabian Heidrich-Meisner, Janez Bonca, David Jansen We present density-matrix renormalization group results for spectral |
Monday, March 6, 2023 11:42AM - 11:54AM |
B62.00002: Exact continuum representation of long-range interacting systems Andreas A Buchheit, Torsten Keßler, Peter K Schuhmacher, Benedikt Fauseweh Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of long-range interacting lattices that separates the model into a term describing its continuous analogue, the integral contribution, and a term that fully resolves the microstructure, the lattice contribution. For any system dimension, any lattice, any power-law interaction and for linear, nonlinear, and multi-atomic lattices, we show that the lattice contribution can be described by a differential operator based on the multidimensional generalization of the Riemann zeta function, namely the Epstein zeta function. Our representation provides a broad set of tools for studying the analytical properties of the system and it yields an efficient numerical method for the evaluation of the arising lattice sums. We benchmark its performance by computing forces and energies in relevant physical examples, in which the standard continuum approximation fails: Skyrmions, defects in ion chains, and spin waves in a pyrochlore lattice with dipolar interactions. We demonstrate that our method exhibits the accuracy of exact summation at the numerical cost of an integral approximation. We furthermore extend our method to the study of boundary effects. |
Monday, March 6, 2023 11:54AM - 12:06PM |
B62.00003: Unconventional Superconductivity and Collective Excitations in Long-Range Interacting Systems Benedikt Fauseweh, Andreas A Buchheit, Torsten Keßler, Peter K Schuhmacher Long-range interactions are ubiquitous in nature across all scales. They are the driver behind the emergence of complex structures, from the quarks that form the atomic nucleus over the microscopic formation of solids and molecules based on atoms and ions to galaxy patterns spanning billions of light years. Modeling and predicting the emergent dynamics of many-body systems that are subject to such long-range interactions is a problem for numerical approaches, as the computational effort scales directly with the number of particles involved, making calculations for macroscopic systems intractable. |
Monday, March 6, 2023 12:06PM - 12:18PM |
B62.00004: A journey to the edge of Krylov space Ruth Shir, Eliezer Z Rabinovici, Julian Sonner, Adrian Sánchez-Garrido, José Barbón, Ritam Sinha Quantum complexity is now at the forefront of many areas of physics, including high energy physics, condensed matter physics and quantum information. In this talk we will introduce and present results for a relatively new player in the quantum complexity field, indeed a whole new notion of quantum complexity: Krylov complexity. Its definition is organic, it shows interesting properties at short, long and very-long time scales, and it can distinguish integrable from chaotic systems. We will present the so far leading numerical results for Krylov complexity in many-body strongly interacting systems, in particular the maximally chaotic Sachdev-Ye-Kitaev model and the integrable XXZ spin chain, pushing computational limits to the edge of Krylov space. |
Monday, March 6, 2023 12:18PM - 12:30PM |
B62.00005: Quantum Trajectory Method for Particles with Spin 1/2 Richard Lombardini, Bill Poirier Time propagation of non-relativistic spin-free quantum systems can be modeled with ensembles of real-valued interacting trajectories obeying a Newton-like equation, instead of the traditional formalism involving wavefunctions obeying the time-dependent Schrödinger equation. The new approach has been fully developed by Poirier [Chemical Physics, 370, 4-14 (2010)] and successfully applied to molecular dynamics simulations accurately capturing nuclear quantum effects. We present an extension of this work to address non-relativistic spin 1/2 systems traditionally modeled by spinor wavefunctions obeying the Pauli equation. Under this new formalism, we will show that the dynamical model for a free-particle system with translational motion restricted to one-dimension and spin in three-dimensions turns into a set of three coupled PDEs. Quantum force and quantum spin force terms appear in these equations, which both also arise in the Bohmian hydrodynamic formulation of quantum mechanics. Novel numerical techniques [L. Dupuy, F. Talotta, F. Agostini, D. Lauvergnat, B. Poirier, and Y. Scribano, Journal of Chemical Theory and Computation (accepted)] are introduced in the propagation showing stable dynamics. |
Monday, March 6, 2023 12:30PM - 12:42PM |
B62.00006: Tracing the Successes and Failures of the HF-GKBA in Non-equilibrium Systems Cian C Reeves The Kadanoff-Baym equations (KBE) are a formally exact set of equations (provided that the exact self-energy is known) for the propagation of non-equilibrium Green's functions (NEGF). However, KBE suffers from poor numerical scaling with the system size and the simulation time. Practical calculations thus often resort to the approximate Hartree-Fock generalized Kadanoff-Baym ansatz (HF-GKBA). However, comparison of HF-GKBA with exact or KBE results shows good agreement only for relatively short times, but such direct comparison has been limited to a limited set of problems: simple two band models with onsite interactions. I will show that the highly restricted models are partly to blame for the poor performance of HF-GKBA. We study several classes of non-equilibrium systems with long-range interactions and various forms of non-equilibrium state preparation. Further, we will demonstrate under which conditions the non-equilibrium dynamics is amenable to efficient numerical approximations that can further reduce the computational cost. This work outlines the reliability of HF-GKBA for studying realistic non-equilibrium systems fully from first-principles. |
Monday, March 6, 2023 12:42PM - 12:54PM |
B62.00007: Finite Temperature Phase Diagram of the Fully Frustrated Transverse Field Ising Model Gabe Schumm, Kai-Hsin Wu Using quantum Monte Carlo simulations, we study the fully frustrated transverse field Ising model on the square lattice. This model is defined with ferromagnetic bonds on all rows, but on every other column, with anti-ferromagnetic bonds in their place. This construction makes it impossible satisfy all bonds in an elementary plaquette, providing a rich ground-state degeneracy of the classical model. The addition of a transverse field (Γ) lifts the degeneracy, and the system exhibits “order-by-disorder,” up to a critical value Γc, as studied in previous works. We confirm the location and universality class of this quantum phase transition, and further explore the nature of this system at finite T. To do so, we consider two order parameters; based on spins and dimers, with the latter defined on the dual lattice. We find different (but simply related) scaling exponents for these order parameters, and both exhibit a robust, emergent U(1) symmetry that persists deep into the ordered phase up to very large system sizes. While it is numerically challenging to beat this length scale, we show that the 4-fold degenerate, columnar dimer ordering does indeed stabilize by annealing through the critical temperature. We also find that along the finite temperature phase boundary, the value of the critical exponent ν varies continuously, from ν=1 in the limit Γ → Γc to ν =∞ in the limit Γ → 0, in analogy to the 2D, four-state classical clock model, which, however, does not exhibit any emergent U(1) symmetry. While the reason behind the emergent symmetry together with varying exponent is unknown, we suggest possible explanations for this behavior. |
Monday, March 6, 2023 12:54PM - 1:06PM |
B62.00008: Spin and charge excitations across the phase diagram of the 2D Hubbard model. James LeBlanc Leveraging the power of algorithmic Matsubara integration (AMI) we can generate pseudo-analytic results for virtually any diagrammatic expansion. We generate the longitudinal spin and charge susceptibilities for the 2D Hubbard model and employ our AMI toolset to obtain expressions that are explicit functions of chemical potential, temperature, interaction strength and frequency (both real and Matsubara). |
Monday, March 6, 2023 1:06PM - 1:18PM |
B62.00009: Pairing Susceptibility in the 2D Hubbard model Rayan Farid, Maxence Grandadam, James LeBlanc We compute the diagrammatic expansion of particle-particle pairing susceptibility for a Hubbard interaction on a 2D square lattice. We implement Algorithmic Matsubara Integration (AMI) to generate symbolic analytical expressions which can be evaluated without finite system approximations. We compute only vertex diagrams in the perturbative series that directly relate to pairing and probe the full external momenta dependence of the pairing susceptibility. We perform real-space Fourier transformation and study the interplay of competing symmetries (dx2-y2, dxy, and p wave) in the weak coupling limit of the model. The symmetry projected pairing is further parameterized over a large phase space of temperature, chemical potential, and second nearest hopping and the relevant physics are discussed. |
Monday, March 6, 2023 1:18PM - 1:30PM |
B62.00010: A general nonlinear Hall current in time-reversal breaking insulators Daniel Kaplan, Tobias Holder, Binghai Yan It is well known that the quantum anomalous Hall effect (QAHE) can only arise in insulators with nontrivial topology. Here, we show that at nonlinear order, currents emerge in a time reversal breaking insulator even when their Chern number is zero. Three mechanisms can be identified which create such a Hall response: an interband quasi-particle velocity, a wavepacket center shift, and a renormalization of the Berry curvature. We show that in strained twisted bilayer graphene the new nonlinear contribution is comparable with measured deviations of the QAHE from perfect quantization. Our results establish a fundamental difference between anomalous Hall currents in periodic systems as compared to 2DEGs, and might have implications for the use of the QAHE as a resistance standard. |
Monday, March 6, 2023 1:30PM - 1:42PM |
B62.00011: Estimating the reflected entropy from random matrices Zhuan Li, Roger Mong The reflected entropy SR(ρAB) of a density matrix ρAB is a useful tool to estimate the bounds for the entropy of purification. Because of this, it further determines the size of a tensor network we need to represent the purification of the state ρAB. When the dimension of the Hilbert space is large, calculating the entropy of purification of ρAB becomes impractical. So we approximate the entropy of purification with the average reflected entropy<SR(ρAB)>, where ρ is a random density matrix. But random matrices obey the volume law rather than the area law, we cannot directly apply this approximation to a physics model. To overcome this problem, we introduce the double restriction TrA(ρ) = ρB and TrB(ρ) = ρA to the random density matrix ρ, and calculate<SR(ρAB)>for a given mutual information. We then compare our results with the actual reflected entropies on small random systems and spin chain models, e.g., the 1-dimensional Ising model and XXZ model. |
Monday, March 6, 2023 1:42PM - 1:54PM |
B62.00012: Correlation consistent effective core potentials for late 3d transition metals adapted for plane wave calculations Benjamin E Kincaid, Lubos Mitas, Haihan Zhou, Guangming Wang We construct a new modification of correlation consistent effective potentials (ccECPs) for the late 3d elements Cr-Zn with Ne-core that are adapted for efficiency and low energy cutoffs in plane wave calculations. The decrease in accuracy is rather minor such that the constructions are in the same overall accuracy class as the original ccECPs. The resulting new constructions work with |
Monday, March 6, 2023 1:54PM - 2:06PM |
B62.00013: Evaluating quantum expectation values with the off-diagonal series expansion Lev Y Barash, Uday Singla, Itay Hen We introduce a stochastic technique for evaluating the expectation values of evolved (pure) quantum states under a given Hamiltonian, based on the off-diagonal series expansion. We test our method by calculating the expectation values of operators on a state evolving under the influence of a transverse-field Ising Hamiltonian. |
Monday, March 6, 2023 2:06PM - 2:18PM |
B62.00014: Planckian scaling of the optical conductivity in the 2D Hubbard model Maxence Grandadam, James LeBlanc The optical conductivity of systems with strong interactions is one of the most studied quantities experimentally, yet its computation from microscopic models remains challenging. In the context of linear response theory and of the Kubo formula for conductivity, this difficulty is embedded in the momentum and energy dependence of the electron self-energy and of the vertex corrections. In this work, we present a study of the optical conductivity using Algorithmic Matsubara Integration which allows for the evaluation of diagrammatic series up to a fixed order directly on the real frequency axis without relying on analytic continuation tools. |
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