I am teaching Quantum Mechanics II (PHYS 784) and Thermal Physics (PHYS 307) in spring 2021. Access the course content through Blackboard.
We show that knots tied by the eigenenergy strings provide a complete topological classification of one-dimensional non-Hermitian Hamiltonians with separable bands. An algorithm is devised to construct the corresponding tight-binding NH Hamiltonian for any desired knot, and a scheme is proposed to probe the knot structure via quantum quench.
Phys. Rev. Lett. 126, 010401 (2021).
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). [Editors’ Suggestions]
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 ground state wave functions shed light on two Symmetry Protected Topological (SPT) phases of interacting quantum spins in 1D.
Phys. Rev. Lett. 122, 180401 (2019).
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).
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).
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.