My research interests lie at the intersection of quantum mechanics, condensed matter physics, and statistical mechanics. Particularly I am interested in thermalization and its violation in isolated quantum many-body systems. Currently, I am working on quantum many-body scars (QMBS) which is a new mechanism to evade thermalization.
QMBS
A generic isolated quantum system is expected to be ergodic, i.e., under the unitary dynamics of its Hamiltonian, any initial state would eventually evolve into a featureless thermal state. This loss of information on the initial state’s configuration presents a barrier to protecting quantum information. As a result, it is crucial to search for non-ergodic systems that resist thermalization. The Eigenstate Thermalization Hypothesis (ETH) regulates the characteristics of ergodic quantum systems and describes how far-from-equilibrium initial states evolve in time to reach a final state that is described by a thermal ensemble. ETH suggests all the eigenstates of ergodic systems are thermal and thus any initial state evolves into a thermal state at long times. Two well-known exceptions to the ETH paradigm are integrable and many-body localized systems. In integrable systems, the presence of an extensive number of conserved quantities prevents an initial state from fully exploring all the allowed configurations in the Hilbert space. In MBL systems, the presence of interactions and strong disorder leads to an emergent integrability that prevents thermalization. These two ergodicity-breaking mechanisms are of the strong form in that every eigenstate exhibits features of an athermal state. Recently, experimental findings in an ultracold Rydberg atom chain revealed a new mechanism for weak ergodicity-breaking. When the Rydberg atoms are initialized in a particular state, the so-called Néel state, they do not thermalize and instead display long-lived coherent oscillations. On the other hand, certain other initial states do exhibit thermal behavior. The oscillations are due to the presence of anomalous states that have sub-extensive entanglement entropy in the otherwise thermal bulk spectrum. These special states obey the area-law of EE rather than the volume-law of EE as anticipated by ETH and have substantial overlap with the Néel state which results in the observed coherent revivals. This phenomenon is dubbed quantum many-body scars (QMBS). These scar states are vanishingly rare and typically their number grows only algebraically with system size while the Hilbert space dimension grows exponentially with system size. As a result, these scars only lead to a weak or incomplete breach of ETH.