**Entanglement**

Entanglement and superposition are fundamental concepts in quantum mechanics and vital for quantum computation. Systems with a large degree of entanglement are valuable resources for quantum information and computation, as they help to cut down the number of qubits required to maintain coherence, which is needed to preserve information. Entanglement can also be used as a proxy for determining topological order, and states which show long range entanglements are potentially useful for implementing fault tolerant quantum computing. One common measure of entanglement is von Neumann entanglement entropy, which we access numerically through techniques such as exact diagonalization or Quantum Monte Carlo simulations. Another measure of entanglement is the amount to which a set of physical properties of the system violate Bell’s inequality

# Quantum Phase Transition

A quantum phase transition (QPT) is a transition between different phases of matter at zero temperature accessed by varying a parameter other than temperature such as magnetic field, pressure, disorder or gating. In a QPT the ground state of the many-body system gets restructured due to quantum fluctuations arising from Heisenberg’s uncertainty principle. Close to the quantum critical point (QCP), the length and time scale of the quantum fluctuations become scale invariant. Quantum fluctuations dominate when the characteristic frequency is larger than the temperature. The divergent correlations at the QPT also lead to many-particle entanglement.

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One of the questions we address in our group is how can we distinguish the non-local correlations arising from interactions from those that arise from pure statistics? We study QPT in various systems, such as the Bose-Hubbard model, Fermi Hubbard model, and the Kitaev honeycomb lattice model.