New Ward-Takahashi identities in statistical mechanics of many-fermion systems

Theoretical Physics Institute

Tadashi Toyoda

Marian Apostol

Pierluigi Falco

Two dimensional toy models display, in a gentler setting, manysalient aspects of Quantum Field Theory. Here I discuss a concrete two dimensional case, the Thirring model, which illustrates several important concepts of this theory: the anomalous dimension of the fields; the exact solvability; the anomalies of the Ward-Takahashi identities. Besides, I give a glimpse of the decisive role that this model plays in the study of an apparently unrelated topic: correlation critical exponents of two dimensional lattice systems of Statistical Mechanics.

節夫 三沢

Hui Li, Zhipeng Sun, Yingze Su +3 more

The calculation of response functions in correlated electronic systems is one of the most important problems in the condensed matter physics. To obtain a physical response function, preserving both the Ward-Takahashi identity and the fluctuation-dissipation theorem are crucial. Here we propose a self-consistent many body method within the GW framework to calculate the response functions based on the fluctuation-dissipation theorem, which also satisfies the Ward-Takahashi identity. The validity of this methodology is demonstrated on the two-dimensional one-band Hubbard model, where both the Ward-Takahashi identity and fluctuation-dissipation theorem are verified numerically. Moreover, comparing to the accurate spin susceptibility of the determinantal Monte Carlo approach, the results obtained from our method are quite satisfactory and the computational cost are greatly reduced.