Wavefunction renormalization for the Coulomb gas by the Wegner-Houghton renormalization group method

VII.D Renormalization Group for the Coulomb Gas

To construct an RG for the Coulomb gas, note that the partition for the system, eq.(VII.59), involves two parameters, (K, y0), and has an implicit cutoff, a, related to the minimum separation between vortices. As discussed earlier, the distinction between regions inside and outside the core of a vortex are arbitrary. Increasing the core size to ba modifies not only the core energy, hence y0, bu...

VII.C Renormalization Group for the Coulomb Gas

The two partition functions in eq.(VII.58) are independent and can be calculated separately. As the Gaussian partition function is analytic, any phase transitions of the XY model must originate in the Coulomb gas. As briefly discussed earlier, in the low temperature phase the charges appear only in the small density of tightly bound dipole pairs. The dipoles dissociate in the high temperature p...

Time-Dependent Real-Space Renormalization Group Method

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

Renormalization Group Flow of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two–dimensional hierarchical Coulomb system in the limit as the size of the block L ↓ 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t → ∞, to one of the countably infinite equilibrium solutions. The j–th...

Renormalization Group Renormalization Group