Fitting luttinger bases on bosonization theory of sine-Gordan action. Fitting at both bond and density channel . Discuss situation if umklapp or pairing term is relevant in the action.

Visit to Hong Kong gives inspiration on flat band kondo problem. Here I discribe their ideas and discuss something that we can do.

Describing stub , cruetz and sawtooth chain .Discussing how to define the superconducting coherence length and calculate superfluidity weight numerically

Flat band systems can also have superconductivity , whose superfluidity weight comes from quantum geometry of the multi-orbital systems. Here is introduction of the theory developed orginally by Päivi Törmä. Physically , interaction in flat band systems unlock the potential and gives effective kinetic energy to Cooper pairs. The potential of Wannier overlaps is now provided by quantum metric.

Professor Steven White talked about the MPS-VMC method at March meeting ,2026. It is a method using MPS states as direct samples. Here I discrbe the method.

Renormalization of 1-D interaction fermion models using the sine-Gordon action , showing the CDW and Bond-Order phases. Comparsion to classical 2-D XY model and elctron gases. Discuss the doped sine-Gordon action that cna lead to C-IC and LL-IC transitions

Construct the bosonization theory step by step , both the field and constructive approach.The key is to derive the bosonic identity and bosoniztion dictionary.

One dimensional spinless t-V model wth kitaev pairing can be compared to classical 2D ANNNI model , and also can be solved at weak interaction with the bosonization method. This work shows the phase diagram of this model with an ICDW phase

Introduction to Luttinger Liquid

I have read a recent work on flat band superconductivity. In flat band majorana system , quantum metric provides an additional long range decay length other than the majorana localization length . The length therefore can be detected by superconduting correlation functions numerically.