Lizards and Bugambilias

This is a creative-writing thesis, a collection of poetry. The poems are divided into three sections, which share thematic content. In this collection, the poetry explores issues of place, family and identity, all closely tied to the geographic/cultural area of South Texas. The critical introduction explains both the organization of and the influences on the poems

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su$(1|1)$ supersymmetric spin chains with long-range interactions which includes as particular cases the su$(1|1)$ Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su$(1|1)$ permutation operator, and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low energy excitations and the low temperature behavior of the free energy, which coincides with that of a $(1+1)$-dimensional conformal field theory (CFT) with central charge $c=1$ when the chemical potential lies in the critical interval $(0,\mathcal E(\pi))$, $\mathcal E(p)$ being the dispersion relation. We also analyze the von Neumann and R\'enyi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson $(1+1)$-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge $c=1$. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su$(1|1)$ elliptic chain.Comment: 13 pages, 6 figures, typeset in REVTe

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models with su$(m+1)$ spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su$(m+1)$ type. We evaluate in closed form the reduced density matrix of a block of $L$ spins when the whole system is in its ground state, and study the corresponding von Neumann and R\'enyi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as $a\log L$ when $L$ tends to infinity, where the coefficient $a$ is equal to $(m-k)/2$ in the ground state phase with $k$ vanishing su$(m+1)$ magnon densities. In particular, our results show that none of these generalized Lipkin-Meshkov-Glick models are critical, since when $L\to\infty$ their R\'enyi entropy $R_q$ becomes independent of the parameter $q$. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su$(m+1)$ Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when $m-k\ge3$. Finally, in the su$(3)$ case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su$(3)$. This is also true in the su$(m+1)$ case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an $(m+1)$-simplex in $\mathbf R^m$ whose vertices are the weights of the fundamental representation of su$(m+1)$.Comment: Typeset with LaTeX, 32 pages, 3 figures. Final version with corrections and additional reference

Activation of the Epidermal Growth Factor Receptor (EGRF) is Required for CXCL12 Mediated ERK and Akt Signaling during Prostate Myofibroblast Phenoconversion

Benign prostate hyperplasia (BPH), a condition of the prostate common in aging in men, is associated with urinary voiding dysfunction, or Lower Urinary Tract Symptoms (LUTS). Although inflammation and abnormal muscle contraction are known to be key players in the development of LUTS, tissue fibrosis may also be an important and previously unrecognized contributing factor. Tissue fibrosis arises from the differentiation of fibroblasts into myofibroblasts, which produce and secrete collagens and fibronectins that remodel the extracellular matrix (ECM). This differentiation process is usually accomplished by activation of the TGF-β/TGFβRII axis. However, in this study we report that the CXC-type chemokine, CXCL12, and its receptor, CXCR4, which are up-regulated with aging in the prostate, can drive this differentiation process as well. We have observed that CXCL12 can promote myofibroblast phenoconversion in the absence of exogenous TGF-β and can up-regulate the expression of myofibroblast genes (α-SMA, COL1, TGF-β) in primary and immortalized prostate fibroblasts. Recently we discovered that the activated CXCL12/CXCR4 axis signals through the EGFR and through downstream MEK/ERK and Akt pathways during myofibroblast differentiation, but not through Smad proteins. Smad proteins are the primary signaling proteins utilized by the TGFβRII. This suggests that CXCL12/CXCR4-mediated signaling events in prostate myofibroblast phenoconversion may proceed through non-canonical pathways that do not depend on TGF-β/TGFβRII axis activation or Smad signaling. Furthermore, we observed significant reduction in the activation of EGFR and ERK pathways when treating fibroblasts with an EGFR inhibitor as well as a pan-Metalloprotease inhibitor previous to chemokine treatment. Conversely, chemical inhibition of TGF-βRII or Smad3 activation did not prevent CXCL12-mediated EGFR, MEK/ERK activation or myofibroblast phenoconversion. Based on these findings, we hypothesize that EGFR activation by CXCL12/CXCR4 might be required for ERK and Akt activation during myofibroblasts conversion, and may be coupled to the shedding of extracellular ligands of EGFR by extracellular protease