*Click the menu above to learn more about Phys 784: Quantum Mechanics II in spring 2019*

My research interest is theoretical condensed matter physics, more specifically, many-body problems in quantum gases, quantum materials, as well as quantum devices. Some recent projects are summarized below. My group has openings** **for graduate students (GRA) and undergraduate students (summer research assistant or senior research). Please contact ezhao2 “at” gmu.edu or drop by my office if you are interested.

**Research Updates:**

##### 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).

##### Scramble like a black hole

Is there a condensed matter system that scrambles information/thermalizes as fast as a black hole? Our calculation of a random dipolar spin model suggests that it comes rather close. *arXiv:*1810.03815 (2018).

##### Total anarchy: spins on triangular lattice

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).

##### How to make a Weyl superconductor

Stack s-wave superconductors and spin active materials into a superlattice. Nodes,

Weyl fermions, and Fermi arcs emerge. *Phil. Trans. R. Soc.* A 376, 20150151 (2018). Invited contribution to theme issue “Andreev bound states.”

##### Tensor networks

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).

##### Shaken optical lattice

We develop an analytical theory for interacting fermions on shaken square optical lattice. The Fermi surface and effective interaction pick up interesting momentum dependence. *Phys. Rev. A *95, 063619 (2017).

##### Cosine edge mode

We construct a minimal model for Floquet topological matter in two dimensions and surprise: all its edge modes are described by a single cosine function. *Phys. Rev. B* 94, 245128 (2016).

##### Running couplings and density waves

To find the phase diagram of 2D dipolar Fermi gas, we trace the functional renormalization group flow of over 11 thousand running couplings (interaction vertices). The winners include an unsuspected, counterintuitive density wave phase. *Phys. Rev. A* 94, 033616 (2016).

##### Topological p-wave superconductivity from kicking

Periodic driving turns coupled Kitaev chains to a topological superconductor with chiral edge modes. Why and how? *Zeitschrift fur Naturforschung A*, 71(10), 883 (2016).

##### Unification of the Ising, Kitaev, and 120-degree model

We invent a new quantum spin model, dubbed the tripod model, to unify the three models. Then we solve for its phase diagram using tensor networks. *New J. Phys. * 18, 053040 (2016).

**Spin-orbital exchange in quantum gas **

Fermionic atoms on the p-band settle for an unusual spin-disordered ground state, in the midst of the intertwined spin and orbital fluctuations. *Phys. Rev. Lett.* 114, 100406 (2015).

**Edge modes in a kicked quantum Hall system**

The edge of a quantum Hall system is a one-way street for electrons. We show that periodic kicking leads to a fundamental change to this picture: it is now two-way traffic. *Phys. Rev. Lett.* 112, 026805 (2014).

**Quadrupolar Fermi gas**

What are the many-body phases of fermions with quadrupole-quadrupole interaction? Our exact calculation in the weak-coupling limit reveals. *Phys. Rev. Lett.* 110, 155301 (2013)

**Topological ladder**

On a two-leg ladder, the orbital hopping pattern of fermions leads to a topological insulating phase, in the absence of spin-orbit coupling or gauge field. *Nature Communications* 4, 1523 (2013).

**A new phase of matter: Bond order solid**

Interacting fermions with dipole moments form solids with periodic modulations of bonds, rather than density. *Phys. Rev. Lett.* 108, 145301 (2012).

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.