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“Of course, the most rewarding part is the ‘Aha’ moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.”

— Maryam Mirzakhani (1977-2017).

Research Updates:

Topological invariant for quantum quench

We introduce the concept of loop unitary and show its homotopy invariant characterizes the dynamical topology of the quench dynamics of band insulators. Phys. Rev. Lett. 124, 160402 (2020).

Higher-order topological phases from driving

How to dynamically generate higher-order topological phases with zero- and π-corner modes? We illustrate a scheme by two examples: the Floquet quadrupole and octupole insulators. A pair of Z_2 invariants are introduced to fully characterize these Floquet phases.
Phys. Rev. Lett. 124, 057001 (2020).

Exact solution of a quantum spin model

Exact ground state wave functions shed light on two Symmetry Protected Topological (SPT) phases of quantum spins. Phys. Rev. Lett. 122, 180401 (2019).

Topological circuits of inductors and capacitors

Loops, stars, and ladder with a twist. Build your own topological circuits and witness the bulk-boundary correspondence, connections, monopoles and 2nd Chern number.  Annals of Physics 399, 289 (2018).

Functional renormalization group

We solve the dipolar Heisenberg model on triangular lattice using pseudo-fermion functional renormalization group. The 120-degree order is found melted completely and give way to a wide region of quantum paramagnetic phase with no magnetic long range order. Phys. Rev. Lett. 120, 187202 (2018).

Tensor network

We solve the dipolar Heisenberg model on square lattice using tensor network algorithms. Its phase diagram contains the Neel, stripe, spiral, and a quantum paramagnetic phase. Is it a spin liquid? Phys. Rev. Lett. 119, 050401 (2017).

Our research is being supported by Air Force Office of Scientific Research and National Science Foundation. Previously, it was also sponsored by National Institute of Standards and Technology (Department of Commerce), and Office of Naval Research.