Spin-1/2 Heisenberg ladder: variation of entanglement and fidelity measures close to quantum critical points

TL;DR

This paper investigates how entanglement and fidelity measures behave near quantum critical points in a spin-1/2 Heisenberg ladder under a magnetic field, revealing divergent derivatives at one critical point and fidelity signatures at both.

Contribution

It analyzes the divergence of entanglement measure derivatives and the effectiveness of fidelity measures in detecting quantum phase transitions in a Heisenberg ladder.

Findings

Derivatives of entanglement measures diverge at Hc2 but not at Hc1.

Fidelity and fidelity susceptibility effectively signal both critical points.

Numerical and analytical methods confirm the behavior of measures near QPTs.

Abstract

We consider a two-chain, spin-1/2 antiferromagnetic Heisenberg spin ladder in an external magnetic field H. The spin ladder is known to undergo second order quantum phase transitions (QPTs) at two critical values, Hc1 and Hc2, of the magnetic field. There are now known examples of strongly coupled (rung exchange interaction much stronger than nearest-neighbour intrachain exchange interaction) organic ladder compounds in which QPTs have been experimentally observed. In this paper, we investigate whether well-known bipartite entanglement meaures like one-site von Neumann entropy, two-site von Neumann entropy and concurrence develop special features close to the quantum critical points. As suggested by an earlier theorem, the first derivatives of the measures with respect to magnetic field are expected to diverge as H tends to Hc1 and Hc2. Based on numerical diagonalization data and a mapping of the strongly-coupled ladder Hamiltonian onto the XXZ chain Hamiltonian, for which several analytical results are known, we find that the derivatives of the entanglement measures diverge as H tends to Hc2 but remain finite as H tend to Hc1. The reason for this discrepancy is analysed. We further calculate two recently proposed quantum information theoretic measures, the reduced fidelity and reduced fidelity susceptibility, and show that these measures provide appropriate signatures of the QPTs occuring at the critical points H=Hc1 and H=Hc2.