Low-Lying Energy Properties of a Frustrated Antiferromagnetic Spin-$\frac 1 2$ Ladder

TL;DR

This study maps the phase diagram of a frustrated antiferromagnetic spin-1/2 ladder, revealing two gapped phases and the nature of their phase transition, with implications for ladder materials.

Contribution

It provides the first detailed phase diagram of the frustrated spin-1/2 ladder using DMRG, identifying phase boundaries and transition orders.

Findings

Identified Haldane and singlet gapped phases.

Discovered phase transition changes from second to first order with increasing frustration.

Predicted significant frustration effects in ladder materials.

Abstract

Using the Density Matrix Renormalization Group method, we determined the phase diagram of a frustrated antiferromagnetic spin-$\frac 1 2$ ladder at zero temperature. Two spin-gapped phases, the Haldane phase and the singlet phase, are identified. A phase transition between the two phases occurs at any non-zero value of frustration coupling $J_{\times}$. On the phase boundary, the spin gap vanishes for sufficiently small $J_{\times}$. Crossing this non-gapped line, the transition is of second order, while of first order for larger $J_{\times}$. Striking frustration effects are predicted for ladder materials.