Recent Progress on High Tc Superconductivity and Related Problems

The most interesting states of the cuprate compounds are not the superconductors with high critical temperatures. Instead, the novelty lies primarily in the higher temperature metallic "normal" states from which the superconductors descend, and in competing low temperature states with density wave…

The ground state phase diagram of spin-1/2 J1-J2 antiferromagnetic Heisenberg model on square lattice around the maximally frustrated regime (J2~0.5J1) has been debated for decades. I will discuss some progresses on this old problem based on recent numerical results from density matrix…

In underdoped cuprate superconductors, a rich competition occurs between superconductivity and charge density wave order (CDW). Under debate, however, is whether rotational symmetry breaking (nematicity) also plays a central role -- whether it occurs intrinsically and generically or merely as a…

We discuss two basic principles to unify the understanding of both cuprates and iron-based superconductors: (1) the correspondence principle— the short range magnetic exchange interactions and the Fermi surfaces act collaboratively to achieve high Tc superconductivity and determine pairing…

We studied t1-t2-J1-J2 model on Honeycomb lattice at finite doping. We find that when t_1 is very small, the t1-t2-J1-J2 model on Honeycomb lattice may be in a supperconducting phase. Such a supperconducting phase is not driven by the pairing, but by entanglement.

Motivated by results of DMRG and tensor network simulations on doped $t$-$J$ model on honeycomb lattice, we study superconductivity of singlet and triplet pairing in this model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the…

We study non-Fermi liquids that arise at the quantum critical points associated with the spin and charge density wave transitions in metals with the C2 symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in 3 − epsilon dimensional momentum space…

Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor of spin liquid states on the kagome lattice. As their ground state, spin-1 excited states for spin liquids…