Towards next-generation methods to optimize two-dimensional tensor networks: Algorithmic differentiation and applications to quantum magnets

Infinite Projected entangled-pair state (iPEPS) is a two-dimensional tensor network (TN) ansatz targeting the ground states of lattice models directly in the thermodynamic limit. It is the most successful among the true two-dimensional TN methods, challenging the more common density matrix renormalization group computations conducted on a finite-width cylinders. iPEPS, being a variational method does not suffer from the infamous sign problem, and hence could be readily applied to both fermionic problems off the half-filling and frustrated spin system. Using the imaginary-time optimization, the so called Full Update, led to the celebrated results of iPEPS such as the analysis of stripes in doped t-J and Hubbard models or the insight into the magnetization plateaus in Shastry-Sutherland model. However, the physics of the continuous phase transitions from the symmetry-broken Neel phase into the valence-bond solids or spin-liquids in frustrated magnets is still eluding iPEPS. The main difficulty lies in the optimization, since Full Update is just not precise enough. In the pursuit of the best variational iPEPS states, the gradient methods were put forward in 2016 by Corboz and Vanderstraeten. However, due to their complex nature, they have not been widely adopted especially for iPEPS ansatze with larger unit cells. We will introduce an alternative approach first applied in the context of iPEPS by Liao et al., based on the well established method of Algorithmic differentiation (AD) which allows us to evaluate gradients for iPEPS in a robust and conceptually simple way. Finally, we will present the results of our investigation into the physics of frustrated magnets putting AD to work

Host-Parasite Interactions Within Food Webs

Parasitism is one of the most common life history strategies employed in nature, yet the effects of parasites are often thought to be minimal, and the vast majority of studies fail to consider parasites and their effects on host organisms. This is likely a problem, as the magnitude of parasite-mediated effects on their hosts can be quite large. Additionally, the effects of parasites are known to extend beyond the host to affect other species interactions. I used a series of approaches to gain a more integral understanding of host-parasite interactions by studying (1) the effects of parasites on biotic interactions that hosts engage in, (2) how biotic interactions such as predation and competition can affect host immune defense, and (3) how abiotic and biotic factors within the local environment affecting the host can further mediate parasitism dynamics. Specifically, in Chapter 1 I conducted a phylogenetically informed meta-analysis of the effects of parasites on species interactions (i.e., predation, competition, mutualism, and reproduction). I found that despite a strong overall negative effect on species interactions, the effects of parasites surprisingly ranged from being strongly beneficial to strongly deleterious on host species interactions. In Chapter 2 I used larval damselflies and their dominant fish predator to test how cascading effects of predators on host competitive interactions and resource acquisition affected a critical component of damselfly immune function, the phenoloxidase (PO) cascade. I found that neither direct density-mediated effects, indirect, trait-mediated effects, nor combined effects of predators via natural selection affected total PO activity. Instead, PO levels increased with resource availability, implying resource limitation. Finally, in Chapter 3 I used two field experiments and a detailed observational study to investigate how host, abiotic, and biotic factors within the local environment affected the relationships between damselfly (Enallagma spp.) hosts and their water mite (Arrenururs spp.) ectoparasites. I found that parasitism was species-specific and did not vary with host density or host condition (i.e., immune function). Instead, parasitism was largely predicted by abiotic factors (i.e., pH). Collectively, my results indicate that parasites are key players in the complex web of species interactions that compose food webs. Furthermore, host-parasite interactions are mediated by many of the same ecological factors as other species interactions, which has implications for parasitism dynamics within ecological communities. Future studies of food webs must incorporate parasites into their experimental and theoretical designs, and future studies of host-parasite interactions must expand beyond the focal relationship and consider the ecology of both the host and parasite

Developing a framework to evaluate the existence of a complexity threshold

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering; and, (M.B.A.)--Massachusetts Institute of Technology, Sloan School of Management; in conjunction with the Leaders for Manufacturing Program at MIT, 2006.Includes bibliographical references (leaves 49-51).An automotive manufacturer facing decreasing average product volumes as a result of market fragmentation while simultaneously reducing its manufacturing plant footprint must adapt to the difficult challenge of increased product mix within its manufacturing system. The increase in complexity resulting from greater product mix is considered to be a significant driver in increasing plant investment cost and reducing plant operating effectiveness. Thus, the ability to fully understand and more effectively balance the complexity trade-offs associated with different product-to-manufacturing plant allocation scenarios is critically important, as the manufacturer formulates its strategy and analyzes the associated costs and benefits. The ultimate question to be addressed is whether there exists a "complexity threshold" in terms of the maximum number of differentiated body styles (unique vehicle models) to be produced inside a single assembly plant. This thesis analyzes the challenge of manufacturing system and plant complexity by first developing a competitive benchmark study of body-style complexity at the major North American OEMs' plants. Then, manufacturing and operations data is analyzed for evidence of a "complexity threshold" in one manufacturer's operations.(cont.) Finally, a linear-program based optimization model is developed to enable a Manufacturing Planning group to better understand the company's tolerance for plant complexity by quantifying manufacturing costs associated with various product-to-manufacturing plant allocation scenarios. This tool enables the planner to simultaneously consider thousands of different possible combinations of which products to produce in which plants, by analyzing manufacturing investment and per-vehicle operating cost estimates for each combination. The ability to impose constraints on the maximum number of body styles produced at any one plant yields insight on the value of pursuing a higher-mix (in terms of body styles) manufacturing strategy in particular plants, or across the entire plant footprint.by Matthew J. Hasik.M.B.A.S.M

I\u27d Rather Be Forgotten Than Dishonored : An Oral and Life History Project with a Vietnam Veteran

More than 2.7 million Americans served in the military during the Vietnam era and roughly 40,000 of them as helicopter pilots in Vietnam, yet scholars are still trying to understand the Vietnam experience. There is little doubt that the war played an influential role in the lives of that generation. Yet, many Vietnam veterans refrained from talking about their service, making it difficult to study and understand their experiences within the existing historical narrative. Using the life history of Warrant Officer James Scott, Hayley Hasik argues that Vietnam veterans—particularly helicopter pilots—are an underrepresented group that, through oral history, can provide an alternative narrative to enhance our understanding of the war and its aftereffects. Gathering primary sources and understanding how the individual fits—as an individual—into the larger historical narrative provides Vietnam veterans with a “voice” and helps give validity and meaning to the abstract

Improved summations of nn-point correlation functions of projected entangled-pair states

Numerical treatment of two dimensional strongly-correlated systems is both extremely challenging and of fundamental importance. Infinite projected entangled-pair states (PEPS), a class of tensor networks, have demonstrated cutting-edge performance for ground state calculations, working directly in the thermodynamic limit. Furthermore, in recent years the application of PEPS has been extended to also low-lying excited states, using an ansatz that targets quasiparticle states above the ground state with high accuracy. A major technical challenge for those simulations is the accurate evaluation of summations of two- and three-point correlation functions with reasonable computational cost. In this work, we show how a reformulation of $n$-point functions in the context of PEPS leads to extra contributions to the results that prove to play an important role. Benchmarks for the frustrated $J_1-J_2$ Heisenberg model illustrate the improved precision, efficiency and stability of the simulations compared to previous approaches. Leveraging automatic differentiation to generate the most tedious and error-prone parts of the computation, the straightforward implementation presented here is a step towards broader adoption of the PEPS excitation ansatz in future applications.Comment: 12 pages, 5 figure