Universal properties of the entanglement entropy in quantum integrable models

This thesis is a review of the works and ideas I have been developing in my doctoral studies, and it is mainly based on Castro-Alvaredo & Levi [2011]; Castro-Alvaredo et al. [2011]; Levi [2012]; Levi et al. [2013]. The specific aims of these works were to explore the methods developed in Calabrese & Cardy [2004]; Cardy et al. [2008] with the purpose of quantifying entanglement in a quantum field theory, and have a deeper understanding of their predicting power on lattice systems. The first chapter is meant to be a review of quantum entanglement in many-body physics, and the methods we use to establish the link to QFT. In the second chapter, after a small introduction on conformal field theory, we collect the results of Calabrese & Cardy [2004], focusing in particular on the replica trick and the twist field. The third chapter is devoted to adapting these tools to massive QFT, as performed in Cardy et al. [2008]. In particular we focus on the form factor program for the twist field, by means of which we are able to outline the behavior of entanglement entropy in massive theories in a non perturbative way. We expand on the results found in Castro-Alvaredo & Levi [2011], where higher particle form factors were studied for the roaming trajectory model, and the SU(3)2-homogenous sine-Gordon model. We then carry out a numerical study of the Δ-function of the twist field for these two models. In the fourth chapter we focus on the connection between the Δ-function of the twist field and Zamolodchikov c-function, as performed in Castro-Alvaredo et al. [2011]. In addressing this issue we perform a thorough study of the two point function of the twist field and the trace of the stress-energy tensor. This allows us to introduce a class of composite twist fields, which were the main topic of Levi [2012]. In the fifth and last chapter we group the most common methods used to study the entanglement entropy of quantum spin chains. We start with the XY chain analysis, which is performed with a combination of analytical and numerical methods based on free fermion techniques. We then perform a numerical study of the XXZ chain by means of the density matrix renormalization group approach. Eventually we present the results obtained for these two models in Levi et al. [2013]

Universal properties of the entanglement entropy in quantum integrable models

This thesis is a review of the works and ideas I have been developing in my doctoral studies, and it is mainly based on Castro-Alvaredo & Levi [2011]; Castro-Alvaredo et al. [2011]; Levi [2012]; Levi et al. [2013]. The specific aims of these works were to explore the methods developed in Calabrese & Cardy [2004]; Cardy et al. [2008] with the purpose of quantifying entanglement in a quantum field theory, and have a deeper understanding of their predicting power on lattice systems. The first chapter is meant to be a review of quantum entanglement in many-body physics, and the methods we use to establish the link to QFT. In the second chapter, after a small introduction on conformal field theory, we collect the results of Calabrese & Cardy [2004], focusing in particular on the replica trick and the twist field. The third chapter is devoted to adapting these tools to massive QFT, as performed in Cardy et al. [2008]. In particular we focus on the form factor program for the twist field, by means of which we are able to outline the behavior of entanglement entropy in massive theories in a non perturbative way. We expand on the results found in Castro-Alvaredo & Levi [2011], where higher particle form factors were studied for the roaming trajectory model, and the SU(3)2-homogenous sine-Gordon model. We then carry out a numerical study of the Δ-function of the twist field for these two models. In the fourth chapter we focus on the connection between the Δ-function of the twist field and Zamolodchikov c-function, as performed in Castro-Alvaredo et al. [2011]. In addressing this issue we perform a thorough study of the two point function of the twist field and the trace of the stress-energy tensor. This allows us to introduce a class of composite twist fields, which were the main topic of Levi [2012]. In the fifth and last chapter we group the most common methods used to study the entanglement entropy of quantum spin chains. We start with the XY chain analysis, which is performed with a combination of analytical and numerical methods based on free fermion techniques. We then perform a numerical study of the XXZ chain by means of the density matrix renormalization group approach. Eventually we present the results obtained for these two models in Levi et al. [2013].EThOS - Electronic Theses Online ServiceGBUnited Kingdo

An Observational Retrospective Cohort Trial on 4,828 IVF Cycles Evaluating Different Low Prognosis Patients Following the POSEIDON Criteria

Objective: To study the actual controlled ovarian stimulation (COS) management in women with suboptimal response, comparing clinical outcomes to the gonadotropins consume, considering potential role of luteinizing hormone (LH) addition to follicle-stimulating hormone (FSH).Design: Monocentric, observational, retrospective, real-world, clinical trial on fresh intra-cytoplasmic sperm injection (ICSI) cycles retrieving from 1 to 9 oocytes, performed at Humanitas Fertility Center from January 1st, 2012 to December 31st, 2015.Methods: COS protocols provided gonadotropin releasing-hormone (GnRH) agonist long, flare-up, short and antagonist. Both recombinant and urinary FSH were used for COS and LH was added according to the clinical practice. ICSI outcomes considered were: gonadotropins dosages; total, mature, injected and frozen oocytes; cumulative, transferred and frozen embryos; implantation rate; pregnancy, delivery and miscarriage rates. Outcomes were compared according to the gonadotropin regimen used during COS.Results: Our cohort showed 20.8% of low responders, defined as 1-3 oocytes retrieved and 79.2% of "suboptimal" responders, defined as 4-9 oocytes retrieved. According to recent POSEIDON stratification, cycles were divided in group 1 (6.9%), 2 (19.8%), 3 (11.7%), and 4 (61.5%). The cohort was divided in 3 groups, according to the gonadotropin's regimen. Women treated with FSH plus LH showed worst prognostic factors, in terms of age, basal FSH, AMH, and AFC. This difference was evident in suboptimal responders, whereas only AMH and AFC were different among treatment groups in low responders. Although a different result, in terms of oocytes and embryos detected, major ICSI outcomes (i.e., pregnancy and delivery rates) were similar among groups of COS treatment. Outcomes were significantly different among Poseidon groups. Implantation, pregnancy and delivery rates were significantly higher in Poseidon group 1 and progressively declined in other POSEIDON groups, reaching the worst percentage in group 4.Conclusions: In clinical practice, women with worst prognosis factors are generally treated with a combination of LH and FSH. Despite low prognosis women showed a reduced number of oocytes retrieved, the final ICSI outcome, in terms of pregnancy, is similarly among treatment group. This result suggests that the LH addition to FSH during COS could improve the quality of oocytes retrieved, balancing those differences that are evident at baseline

Improved high-resolution GPR imaging and characterization of prehistoric archaeological features by means of attribute analysis

We propose a novel procedure for the analysis and interpretation of Ground-Penetrating Radar (GPR) data from archaeological data and we test the method in challenging conditions at a prehistoric settlement on the Stromboli Island (Italy). The main objective of the proposed procedure is to enhance the GPR capability of identifying and characterizing small-size and geometrically irregular archaeological remains buried beneath rough topographic surface conditions. After the basic GPR processing sequence, including topographic correction using a high-resolution Digital Elevation Model acquired from 3-D Laser Scanner, the procedure encompasses a multi-attribute analysis and iso-attribute surfaces calculation with different volume extraction solutions to emphasize vertical and lateral variations within GPR data cubes. The test was performed in cooperation with the archaeological team to calibrate the results and to provide detailed information about buried targets of potential archaeological interests to plan further excavations. The results gave evidence of localized buried remains and allowed detailed preexcavation planning. The archaeological excavations validated the results obtained from the GPR survey. The research demonstrates that the proposed GPR procedure enhances the ability to identify and characterize archaeological remains with high accuracy even in complex surface and subsurface conditions. Such logistical situation is very common, particularly in prehistoric sites, which are often characterized by discontinuous, small and irregular targets that cannot be identified by standard processing and analysis strategies