Weak Measurement
The usual projective measurements of quantum mechanics have the sometimes inconvenient property that performing a single measurement on a system collapses the wavefunction and destroys all information about the initial state. We are interested in generalized measurements, in particular weak measurements which can avoid this instantaneous collapse via a tradeoff of extracting less information from the system in each measurement. Recently we have numerically demonstrated a weak measurement scheme which can obtain the full spectrum of a spin chain with only local measurements on a single site.
Many-body Chaos
Understanding quantum chaos in strongly interacting many-body systems has become a central pursuit across condensed matter physics, quantum information, and holography. Delving into this fascinating realm, we explore the intricate dynamics of such systems through the lens of thermalization, out-of-time-ordered correlators (OTOCs), spectral form factor (SFF), and level spacing statistics. A key insight is that chaos manifests differently across various time regimes, admitting distinct yet complementary diagnostics. One of the most striking examples of a maximally chaotic system is the Sachdev-Ye-Kitaev (SYK) model of Majorana fermions, whose spectral properties closely mirror those of random matrix theory (RMT), making it a cornerstone for exploring connections between quantum thermalization, holographic duality, and black hole physics. In this work, we build upon this perspective by systematically studying the nature of chaos in a modified SYK-like system—specifically, the complex SYK model with finite mean—across early, intermediate, and late-time dynamics, unraveling how its chaotic properties manifest across different time scales and how the introduction of a finite mean influences its behavior. We achieve this by leveraging three major diagnostics: out-of-time-ordered correlators (OTOCs), the spectral form factor (SFF), and level-spacing statistics.
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.