d 12 wave Superconductivity and antiferromagnetism in strongly correlated systems by a new variational approach

In Chapter 1, we introduce the physics of the HTSC, starting with an historical overview of the problem and describing some experimental results that characterize these materials. Subsequently, we introduce the t 12J model, which allows a microscopic description of the HTSC and we introduce the Resonating Valence Bond (RVB) wave function. In Chapter 2, we will describe the numerical techniques used for obtaining the results of our thesis. We start from the Lanczos method, that enable us to obtain exact results for small cluster size and then we enter in the topic of the quantum Monte Carlo technique. We describe the variational Monte Carlo method, the optimization algorithm and we will introduce the Green\u2019s function Monte Carlo and fixed-node approximation, that improve the variational results. In Chapter 3, we will introduce our new variational wave function which generalizes the RVB state we show our results on the charge fluctuations (phase separation problem) for the two-dimensional t 12J model. The main results of this chapter has been published in Physical Review B [7]. In Chapter 4, we will study the magnetic and superconducting properties of the two-dimensional t 12J and t 12t\u2032 12J model, trying to understand the role of the next-nearest-neighbor hopping term on the magnetic and superconducting phases. We will show a phase diagram of the magnetic and superconducting correlations, which qualitatively reproduce the actual phase diagram of HTSC and gives some indication on the origin of the electronic pairing. The main results of this chapter were submitted to Physical Review B [8]

Finite compressibility in the low-doping region of the two-dimensional t−Jt{-}J model

We revisit the important issue of charge fluctuations in the two-dimensional $t{-}J$ model by using an improved variational method based on a wave function that contains both the antiferromagnetic and the d-wave superconducting order parameters. In particular, we generalize the wave function introduced some time ago by J.P. Bouchaud, A. Georges, and C. Lhuillier [J. de Physique {\bf 49}, 553 (1988)] by considering also a {\it long-range} spin-spin Jastrow factor, in order to correctly reproduce the small-$q$ behavior of the spin fluctuations. We mainly focus our attention on the physically relevant region $J/t \sim 0.4$ and find that, contrary to previous variational ansatz, this state is stable against phase separation for small hole doping. Moreover, by performing projection Monte Carlo methods based on the so-called fixed-node approach, we obtain a clear evidence that the $t{-}J$ model does not phase separate for $J/t \lesssim 0.7$ and that the compressibility remains finite close to the antiferromagnetic insulating state.Comment: 10 page

Magnetism and superconductivity in the t−t′−Jt{-}t^\prime{-}J model

We present a systematic study of the phase diagram of the $t{-}t^\prime{-}J$ model by using the Green's function Monte Carlo (GFMC) technique, implemented within the fixed-node (FN) approximation and a wave function that contains both antiferromagnetic and d-wave pairing. This enables us to study the interplay between these two kinds of order and compare the GFMC results with the ones obtained by the simple variational approach. By using a generalization of the forward-walking technique, we are able to calculate true FN ground-state expectation values of the pair-pair correlation functions. In the case of $t^\prime=0$, there is a large region with a coexistence of superconductivity and antiferromagnetism, that survives up to $\delta_c \sim 0.10$ for $J/t=0.2$ and $\delta_c \sim 0.13$ for $J/t=0.4$. The presence of a finite $t^\prime/t<0$ induces a strong suppression of both magnetic (with $\delta_c \lesssim 0.03$, for $J/t=0.2$ and $t^\prime/t=-0.2$) and pairing correlations. In particular, the latter ones are depressed both in the low-doping regime and around $\delta \sim 0.25$, where strong size effects are present.Comment: 10 pages, 9 figure

How can LCA include prospective elements to assess emerging technologies and system transitions? The 76th LCA Discussion Forum on Life Cycle Assessment, 19 November 2020

This paper summarizes the 76th LCA Discussion Forum end its main findings. Main issues when addressing emerging technologies\ua0identified were: the lack of primary data, the need for (shared) future background scenarios and (guidlines for) a common methodology. The following\ua0recommendations have been derived by the organizers: 1) Specific foreground inventories are always tailor-made, but consistency can be improved through\ua0lists of mandatory considerations.\ua02) Continue sharing (future) technology data and proxy processes, that can be readily replicated to new studies and assist in developing inventories.\ua03) Streamline and unify the process of including scenarios for background systems. New approaches may provide first important solutions to efficiently\ua0include consistent future scenarios in prospective LCA