The critical behaviour of the 2D Ising model in Transverse Field; a Density Matrix Renormalization calculation

TL;DR

This paper extends the Density Matrix Renormalization method to 2D systems with symmetries, enabling the study of phase transitions and critical behavior in the 2D Ising model in a Transverse Field.

Contribution

It introduces a symmetry-aware extension of the Density Matrix Renormalization method for 2D systems, allowing precise analysis of phase transitions.

Findings

Determined the phase transition point for the 2D Ising model in a Transverse Field.

Calculated the critical exponent for the energy gap.

Analyzed systems up to 30x6 size with finite size scaling.

Abstract

We have adjusted the Density Matrix Renormalization method to handle two dimensional systems of limited width. The key ingredient for this extension is the incorporation of symmetries in the method. The advantage of our approach is that we can force certain symmetry properties to the resulting ground state wave function. Combining the results obtained for system sizes up-to $30 \times 6$ and finite size scaling, we derive the phase transition point and the critical exponent for the gap in the Ising model in a Transverse Field on a two dimensional square lattice.