Phase diagram of the anti-ferromagnetic xxz model in the presence of an external magnetic field

TL;DR

This paper investigates the phase transitions and critical behavior of the anisotropic anti-ferromagnetic Heisenberg chain under an external magnetic field using quantum renormalization group methods, providing insights into phase boundaries and critical exponents.

Contribution

It applies the standard quantum renormalization group to analyze the phase diagram and critical properties of the anisotropic Heisenberg chain in a magnetic field, highlighting the relevance of anisotropy.

Findings

Critical line for transition from partially magnetized to saturated ferromagnetic phase identified.

Crossover exponent between PM and AFI phases evaluated.

Magnetization, correlation functions, and ground state energy compared with exact results.

Abstract

The anisotropic s=1/2 anti-ferromagnetic Heisenberg chain in the presence of an external magnetic field is studied by using the standard quantum renormalization group. We obtain the critical line of the transition from partially magnetized (PM) phase to the saturated ferromagnetic (SFM) phase. The crossover exponent between the PM phase and anti-ferromagnetic Ising (AFI) phase is evaluated. Our results show that the anisotropy($\d$) term is relevant and causes crossover. These results indicate that the standard RG approach yields fairly good values for the critical points and their exponents. The magnetization curve, correlation functions and the ground state energy per site are obtained and compared with the known exact results.