Emergent Spacetime in Quantum Lattice Models

Many quantum lattice models have an emergent relativistic description in their continuum limit. The celebrated example is graphene, whose continuum limit is described by the Dirac equation on a Minkowski spacetime. Not only does the continuum limit provide us with a dictionary of geometric observables to describe the models with, but it also allows one to solve models that were otherwise analytically intractable. In this thesis, we investigate novel features of this relativistic description for a range of quantum lattice models. In particular, we demonstrate how to generate emergent curved spacetimes and identify observables at the lattice level which reveal this emergent behaviour, allowing one to simulate relativistic effects in the laboratory. We first study carbon nanotubes, a system with an edge, which allows us to test the interesting feature of the Dirac equation that it allows for bulk states with support on the edges of the system. We then study Kitaev's honeycomb model which has a continuum limit describing Majorana spinors on a Minkowski spacetime. We show how to generate a non-trivial metric in the continuum limit of this model and how to observe the effects of this metric and its corresponding curvature in the lattice observables, such as Majorana correlators, Majorana zero modes and the spin densities. We also discuss how lattice defects and $\mathbb{Z}_2$ gauge fields at the lattice level can generate chiral gauge fields in the continuum limit and we reveal their adiabatic equivalence. Finally, we discuss a chiral modification of the 1D XY model which makes the model interacting and introduces a non-trivial phase diagram. We see that this generates a black hole metric in the continuum limit, where the inside and outside of the black hole are in different phases. We then demonstrate that by quenching this model we can simulate Hawking radiation.Comment: 145 pages, 32 figures, Ph.D. thesi

AdS/CFT correspondence with a three-dimensional black hole simulator

One of the key applications of AdS/CFT correspondence is the duality it dictates between the entanglement entropy of anti–de Sitter (AdS) black holes and lower-dimensional conformal field theories (CFTs). Here we employ a square lattice of fermions with inhomogeneous tunneling couplings that simulate the effect rotationally symmetric three-dimensional (3D) black holes have on Dirac fields. When applied to 3D Banados-Teitelboim-Zanelli (BTZ) black holes we identify the parametric regime where the theoretically predicted two-dimensional CFT faithfully describes the black hole entanglement entropy. With the help of the universal simulator, we further demonstrate that a large family of 3D black holes exhibit the same ground-state entanglement entropy behavior as the BTZ black hole. The simplicity of our simulator enables direct numerical investigation of a wide variety of 3D black holes and the possibility to experimentally realize it with optical lattice technology

Chiral spin chain interfaces as event horizons

The interface between different quantum phases of matter can give rise to novel physics, such as exotic topological phases or non-unitary conformal field theories. Here we investigate the interface between two spin chains in different chiral phases. Surprisingly, the mean-field theory description of this interacting composite system is given in terms of Dirac fermions in a curved space-time geometry. In particular, the boundary between the two phases represents a black hole horizon. We demonstrate that this representation is faithful both analytically, by employing bosonisation to obtain a Luttinger liquid model, and numerically, by employing Matrix Product State methods. A striking prediction from the black hole equivalence emerges when a quench, at one side of the interface between two opposite chiralities, causes the other side to thermalise with the Hawking temperature for a wide range of parameters and initial conditions.Comment: 14 pages, 6 figure

Exploring interacting chiral spin chains in terms of black hole physics

In this paper we explore the properties of a 1-dimensional spin chain in the presence of chiral interactions, focusing on the system's transition to distinct chiral phases for various values of the chiral coupling. By employing the mean field theory approximation we establish a connection between this chiral system and a Dirac particle in the curved spacetime of a black hole. Surprisingly, the black hole horizon coincides with the interface between distinct chiral phases. We examine the chiral properties of the system for homogeneous couplings and in scenarios involving position dependent couplings that correspond to black hole geometries. To determine the significance of interactions in the chiral chain we employ bosonization techniques and derive the corresponding Luttinger liquid model. Furthermore, we investigate the classical version of the model to understand the impact of the chiral operator on the spins and gain insight into the observed chirality. Our findings shed light on the behavior of the spin chain under the influence of the chiral operator, elucidating the implications of chirality in various contexts, including black hole physics.Comment: 18 pages, 12 figures,. arXiv admin note: text overlap with arXiv:2212.1254

Reviewer Acknowledgements 2019

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The WARPS Survey: VI. Galaxy Cluster and Source Identifications from Phase I

We present in catalog form the optical identifications for objects from the first phase of the Wide Angle ROSAT Pointed Survey (WARPS). WARPS is a serendipitous survey of relatively deep, pointed ROSAT observations for clusters of galaxies. The X-ray source detection algorithm used by WARPS is Voronoi Tessellation and Percolation (VTP), a technique which is equally sensitive to point sources and extended sources of low surface brightness. WARPS-I is based on the central regions of 86 ROSAT PSPC fields, covering an area of 16.2 square degrees. We describe here the X-ray source screening and optical identification process for WARPS-I, which yielded 34 clusters at 0.06<z<0.75. Twenty-two of these clusters form a complete, statistically well defined sample drawn from 75 of these 86 fields, covering an area of 14.1 square degrees, with a flux limit of F (0.5-2.0 keV) = 6.5 \times 10^{-14} erg cm^{-2} s^{-1}}. This sample can be used to study the properties and evolution of the gas, galaxy and dark matter content of clusters, and to constrain cosmological parameters. We compare in detail the identification process and findings of WARPS to those from other recently published X-ray surveys for clusters, including RDCS, SHARC-Bright, SHARC-south and the CfA 160 deg$^2$ survey.Comment: v3 reflects minor updates to tables 2 and

Hepatitis delta genotype 5 is associated with favourable disease outcome and better response to treatment compared to genotype 1

Background & Aims: Coinfection with HDV causes rapid progression to liver cirrhosis and hepatic decompensation in patients with chronic hepatitis B. Factors that are associated with disease progression are poorly understood. In this study we aim to identify risk factors associated with disease progression and better characterise clinical differences and treatment response between HDV genotype 1 and 5. Methods: In this retrospective study, all patients under our care between 2005 and 2016 with HBV/HDV coinfection (HBsAg+, anti-HDV antibodies positive) were analysed. Patients were excluded if follow-up was less than 6 months, if they had HCV and/or HIV coinfection or an acute HDV infection. Demographic data, stage of liver disease, development of liver complications and treatment response were recorded. Results: One-hundred seven patients (mean age 36.0 years, 57% male) were followed for a median period of 4.4 years (range 0.6–28.1 years); 64% were of African origin and 17% were of European origin, with 28% of patients being cirrhotic at first visit; 43% patients had actively replicating HDV virus (anti-HDV-IgG+, anti-HDV-IgM+ or HDV RNA+) and 57% of patients were HDV exposed (anti-HDV-IgG+, HDV RNA-). Patients with actively replicating HDV more often developed liver complications than HDV-exposed patients (p = 0.002), but no differences in baseline characteristics were observed. Patients with HDV genotype 5 less often developed cirrhosis or hepatic decompensation compared to patients with HDV genotype 1. Twenty-four patients were treated with peg-IFN and post-treatment response was significantly better in patients infected with genotype 5 (10% GT1 vs. 64% GT5, p = 0.013). Conclusion: Patients infected with HDV genotype 5 appear to have a better prognosis with fewer episodes of hepatic decompensation and better response to peg-IFN treatment than patients infected with HDV genotype 1. Lay summary: Hepatitis delta is a virus that affects the liver. The virus is known to have different subtypes, called genotypes. With this research we discovered that hepatitis delta virus genotype 1 behaves differently than genotype 5 and causes faster development of liver disease. This is important for education of our patients and to determine how often we need to check our patients