# Phase diagram of the spin-1/2 Heisenberg alternating chain in a magnetic field

## TL;DR

This paper investigates the phase diagram of the spin-1/2 Heisenberg alternating chain in a magnetic field using tensor network methods, revealing various quantum phases and their entanglement properties.

## Contribution

It provides a detailed phase diagram including Haldane, dimer, Luttinger liquid, and paramagnetic phases, with analysis of entanglement entropy and quantum coherence.

## Key findings

- Identification of multiple quantum phases under magnetic field
- Scaling of entanglement entropy with central charge c=1 in Luttinger liquid phase
- Correlation between quantum coherence, string order, and quantum phase transitions

## Abstract

By using the infinite time-evolving block decimation, we study quantum fidelity and entanglement entropy in the spin-1/2 Heisenberg alternating chain under an external magnetic field. The effects of the magnetic field on the fidelity are investigated, and its relation with the quantum phase transition (QPT) is analyzed. The phase diagram of the model is given accordingly, which supports the Haldane phase, the singlet-dimer phase, the Luttinger liquid phase and the paramagnetic phase. The scaling of entanglement entropy in the gapless Luttinger liquid phase is studied, and the central charge c = 1 is obtained. We also study the relationship between the quantum coherence, string order parameter and QPTs. Results obtained from these quantum information observations are consistent with the previous reports.