Research

I am a theorist interested in quantum many-body physics. This includes matter (mostly man-made in labs) that consists of many strongly interacting quantum units, for example, atoms, electrons, spins, or qubits. These individual quantum units can nowadays be prepared, manipulated, and probed with unprecedented precision. This gives hope that by coupling these units together in a controlled manner, from bottom up, we may fully exploit the quantum mechanical weirdness to achieve “technology disruptions” in materials, computing and information, sensing etc.

The trouble is that even if we know the individual quantum unit perfectly well, it remains a formidable challenge to comprehend or predict the emergent, collective behaviors of strongly interacting quantum units. Superfluids, superconductors, antiferromagnets, and charge density waves are a few well known examples of condensed quantum phases of matter. It is believed that other, new phases of matter exist outside the established theoretical framework based on symmetry breaking, order parameters and phase transitions. Two such examples are the Laughlin states of fractional quantum Hall state and spin liquids. These highly entangled many-body states do not have conventional order, yet they are distinct from the ordinary insulator or paramagnet. How to characterize and classify these enigmatic phases of quantum matter is still an open problem. Maybe what we have witnessed is only the tip of the iceberg.

Related to the lack of a complete conceptual framework is the impotence of numerical techniques to solve strongly interacting quantum systems (at least in certain parameter regimes). Traditional approaches, for example diagrammatic perturbation theory and quantum Monte Carlo, may become unreliable. And a brute force attack is hopeless, because the complexity of the task grows exponentially with the number of quantum units. For example, solving 40 interacting spins involves 2**40, roughly one trillion, states. Quantum many-body physics is haunted by this curse of exponentially large Hilbert space. This fundamental challenge forces physicists to invent new schemes to represent the many-body wavefunctions and navigate the huge Hilbert space.

Motivated by these challenges, my research group has been building new many-body algorithms and applying them to solve open problems in quantum condensed matter physics. Our recent work focused mostly on ultracold quantum gases of atoms and molecules where the Hamiltonian is well controlled (in comparison, solid materials can be much more complex, involving charge, spin, orbital and lattice degrees of freedom). For interacting Ferm gases and quantum spin models, we pursue massive parallelization of functional renormalization group (FRG) to increase the momentum and frequency resolution. FRG treats all competing orders in interacting quantum systems on equal footing, making it possible to reliably predict the phase diagram. For quantum spin models, we are using two complimentary ansatz based on tensor-network and neural-network representation of the many-body wavefunction respectively. The main goal here is to find the ground state and extract the order (or the lack thereof) from an unbiased variational approach.

In parallel, I am also fascinated by the topological properties of quantum dynamics, for example the time evolution following a quantum quench (a sudden change in the Hamiltonian) and periodically driven quantum systems (also known as Floquet systems). Even in the simple case of noninteracting lattice models, surprisingly rich phenomena occur, leading to topological objects such as space-time magnetic monopoles, Hopf links, and figure-8 knots (see research update for more details).