Holographic entanglement renormalisation for fermionic quantum matter: geometrical and topological aspects

On performing a sequence of renormalisation group (RG) transformations on a system of two-dimensional non-interacting Dirac fermions placed on a torus, we demonstrate the emergence of an additional spatial dimension arising out of the scaling of multipartite entanglement. The renormalisation of entanglement under this flow exhibits a hierarchy across scales as well as number of parties. Geometric measures defined in this emergent space, such as distances and curvature, can be related to the RG beta function of the coupling $g$ responsible for the spectral gap. This establishes a holographic connection between the spatial geometry of the emergent space in the bulk and the entanglement properties of the quantum theory lying on its boundary. Depending on the anomalous dimension of the coupling $g$, three classes of spaces (bounded, unbounded and flat) are generated from the RG. We show that changing from one class to another involves a topological transition. By minimising the central charge of the conformal field theory describing the noninteracting electrons under the RG flow, the RG transformations are shown to satisfy the $c-$theorem of Zamolodchikov. This is shown to possess a dual within the emergent geometric space, in the form of a convergence parameter that is minimised at large distances. In the presence of an Aharonov-Bohm flux, the entanglement gains a geometry-independent piece which is shown to be topological, sensitive to changes in boundary conditions, and can be related to the Luttinger volume of the system of electrons. In the presence of a strong transverse magnetic field, the system becomes insulating and Luttinger's theorem does not hold. We show instead that the entanglement contains a term that can be related to the Chern numbers of the quantum Hall states. This yields a relation between the topological invariants of the metallic and the quantum Hall systems.Comment: 41 pages, 16 figure

Caregiver Burden and Resilience in Family Members of Alcohol Dependent Patients: Observations from Eastern India

Background: Caregiver burden for alcohol dependent patients refers to the physical, emotional, financial, and social challenges faced by individuals who provide care and support to someone struggling with alcohol dependence. Caregivers often experience high levels of stress, anxiety, and emotional distress when dealing with a loved one\u27s alcohol dependence. The present study tried to analyse the caregiver burden and resilience among family members of alcohol dependent individuals in eastern India. Methods: A cross-sectional observational study patients attending general outpatient clinics who had positive alcohol consumption history and were being accompanied by their caregivers to the facility. Patient and caregiver’s demographics were noted followed by caregiver’s burden and resilience indices using Burden Scale for Family Caregiving (BSFC) and Brief Resilience Scale (BRS). Responses were analysed statistically. Results: 35.9% patients severely alcohol dependent. Composite caregiver burden score showed 50.6% caregivers were moderately burdened, followed by 37.6% caregivers who were found to be severely burdened. Most caregivers showed low resilience. Severity of alcohol dependence was positively correlated with patient’s age, while caregiver’s burden was found to have significant positive correlation with both patient and caregiver’s age, and severity of alcohol dependence. Resilience was negatively correlated with patient as well as caregiver’s age and severity of alcohol dependence (p=0.000). Female caregivers reported lower resilience as compared to male caregivers (p=0.003). Conclusion: Caregiving is a challenging responsibility. It is important for caregivers to recognize the impact of alcohol dependence on their lives and to seek support, both for themselves and for the person with addiction