I will talk on experiments and their interpretation done with Professor Lei Shu and her collaborators at Fudan University, Shanghai, and some tentative theory for the observations. Thermodynamic and magnetic relaxation measurements in zero and finite magnetic field have been performed in two related almost triangular lattices of S=1/2 spins. One of these compounds is the purest of any of the potential spin-liquid compounds investigated so far.
Recently, a new class of kagomé metals, with chemical formula AV3Sb5, where A = K, Rb, or Cs, have emerged as an exciting realization of quasi-2D correlated metals with hexagonal symmetry. These materials have been shown to display several electronic orders setting in through thermodynamic phase transitions: multi-component (“3Q”) hexagonal charge density wave (CDW) order below a Tc≈90K, andsuperconductivity with critical temperature of 2.5K or smaller, and some indications of nematicity and one-dimensional charge order in the normal and superconducting states.
I will present a new mechanism for superconductivity from strong electron-electron repulsion in multi-band systems. When the kinetic energy is small, the dynamics of nearby electrons on the lattice is strongly correlated. I will introduce a controlled expansion in the kinetic term to demonstrate pairing induced by correlated tunneling process involving a third electron in the occupied band. This mechanism can also be viewed as the real space picture of exciton-mediated pairing.
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatments, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories.
We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter. These different "symmetry-protected topological" phases are characterized by protected (gapless) surface states. After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries. I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting
We propose a new type of critical quantum liquids, dubbed Stiefel liquids, based on 2+1 dimensional Wess-Zumino-Witten models on target space SO(N)/SO(4). We show that the well known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N = 5 and N = 6, respectively. Furthermore, we conjecture that Stiefel liquids with N > 6 are non-Lagrangian, in the sense that the theories do not (at least not easily) admit any weakly-coupled UV completion.
The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between space and time on one hand, and unitarity and non-unitarity on the other, can be used to realize steady state phases of non-unitary dynamics that exhibit a rich variety of behavior in their entanglement scaling with subsystem size --- from logarithmic to extensive to fractal.
Recently, the notion of symmetry has been extended from 0-symmetry described by group to higher symmetry described by higher group. In this talk, we show that the notion of symmetry can be generalized even further to "algebraic higher symmetry". Then we will describe an even more general point of view of symmetry, which puts the (generalized) symmetry charges and topological excitations at equal footing: symmetry can be viewed gravitational anomaly, or symmetry can be viewed as shadow topological order in one higher dimension.
In this work, we introduce and study "hybrid" fracton orders, especially though a family of exactly solvable models. The hybrid fracton orders exhibit both the phenomenology of a conventional 3d topological ordered phase and a fracton phase. There are simple yet non-trivial fusion and braiding between the excitations between the two kinds. One example is the hybrid order of the Z2 topological order with the Z2 Xcube order, in which the fracton excitations fuse into the toric code charge, and in turn, the flux loop of the toric code can fuse into various lineon excitations.
Fracton models are characterized by an exponentially increasing ground state degeneracy and point excitations with constrained motion. In this talk, I will focus on a prototypical 3D fracton model -- the X-cube model -- and discuss how its ground state degeneracy can be understood from a foliation structure in the model. In particular, we show that there are hidden 2D topological layers in the 3D bulk. To calculate the ground state degeneracy, we can remove the layers until a minimal structure is reached.