Ground State Phase Diagram of the One Dimensional S=1/2 XXZ Model with Dimerization and Quadrumerization

TL;DR

This paper maps the ground state phase diagram of a one-dimensional S=1/2 XXZ model with dimerization and quadrumerization, revealing various quantum states and their transitions using numerical and theoretical methods.

Contribution

It provides a detailed phase diagram for the model, identifying multiple quantum states and analyzing critical exponents with conformal field theory and level spectroscopy.

Findings

Identification of ground states: Haldane, S=1 dimer, S=1 large-D, S=1/2 dimer.

Calculation of the phase diagram with respect to anisotropy and dimerization.

Determination of the critical exponent  of the energy gap.

Abstract

The one dimensional S=1/2 XXZ model with dimerization (1-j) and quadrumerization \delta is studied by the numerical exact diagonalization of finite size systems. Using the conformal field theory and the level spectroscopy method, we calculate the ground state phase diagram with XY-like anisotropy \Delta (0<\Delta<1). The ground states of this model contain the Haldane state, S=1 dimer state, S=1 large-D state and S=1/2 dimer state as limiting cases. The \Delta and \delta-dependence of the critical exponent \nu of the energy gap is determined from the conformal dimensions of excited states.