Events

The spectral gap of quantum many-body Hamiltonians is an important but difficult concept in condensed matter. Its identification is complicated and, quite often, controversial because the gap, together with the ground-state degeneracy is a thermdynamic limit notion rather than any finite-size energy splitting. In this talk, we will discuss a gaplessness indicator. Specifically, we prove that the ground state(s) of an SO(3)-symmetric gapped spin chain must be spin singlet(s), and the expectation value of a twisting operator asymptotically approaches unity in the thermodynamic limit, where finite-size corrections are inversely proportional to the system size. This theorem provides (i) supporting evidence for various conjectured gapped phases, and, contrapositively, (ii) a sufficient criterion for identifying gapless spin chains. We test the efficiency of our theorem by numerical simulations for a variety of spin models and show that it indeed offers a novel efficient way to identify gapless phases in spin chains with spin-rotation symmetry.

Transforming the concept of band topology fostered in electron systems to electromagnetic waves opens a completely new direction for harnessing propagation of light. It is observed that electromagnetic modes in honeycomb photonic crystals exhibit Dirac-type frequency dispersions, which are accompanied by emergent spin degree of freedom, and that deforming the honeycomb structure in a designed way gives birth to a photonic analogue of quantum spin Hall effect. In this talk I will first show that the main physics can be captured phenomenologically by the k∙p theory, and discuss that the photonic topology can be characterized in terms of the Wilson loops based on the C_2 T symmetry. Then I will introduce examples to demonstrate how the recipe can be exploited for harnessing light and deriving advanced optic properties.

Transforming the concept of band topology fostered in electron systems to electromagnetic waves opens a completely new direction for harnessing propagation of light. It is observed that electromagnetic modes in honeycomb photonic crystals exhibit Dirac-type frequency dispersions, which are accompanied by emergent spin degree of freedom, and that deforming the honeycomb structure in a designed way gives birth to a photonic analogue of quantum spin Hall effect. In this talk I will first show that the main physics can be captured phenomenologically by the k∙p theory, and discuss that the photonic topology can be characterized in terms of the Wilson loops based on the C_2 T symmetry. Then I will introduce examples to demonstrate how the recipe can be exploited for harnessing light and deriving advanced optic properties.