Quantum phase transitions and string orders in the spin-1/2 Heisenberg-Ising alternating chain with Dzyaloshinskii-Moriya interaction

TL;DR

This study explores quantum phase transitions and string orders in a spin-1/2 Heisenberg-Ising alternating chain with Dzyaloshinskii-Moriya interaction, revealing a rich phase diagram with topological and symmetry-breaking phases using matrix-product-state methods.

Contribution

It identifies and characterizes multiple phases, including odd- and even-Haldane phases, and analyzes the nature of phase transitions in the model with Dzyaloshinskii-Moriya interactions.

Findings

Discovery of four distinct phases: AF, AF stripe, odd-Haldane, even-Haldane.

Continuous topological phase transition between odd- and even-Haldane phases with central charge c=1.

Phase transitions between other phases have central charge c=1/2.

Abstract

Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e., the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, respectively. A rich phase diagram including four different phases, i.e., an antiferromagnetic (AF), AF stripe, odd- and even-Haldane phases, is obtained. These phases are found to be separated by continuous QPTs: the topological QPT between the odd- and even-Haldane phases is verified to be continuous and corresponds to conformal field theory with central charge $c$=1; while the rest phase transitions in the phase diagram are found to be $c$=1/2. We also revisit, with our MPS method, the exactly solvable case of HIAC model with DM interactions only on odd bonds, and find that the even-Haldane phase disappears, but the other three phases, i.e., the AF, AF stripe, and odd-Haldane phases, still remain in the phase diagram. We exhibit the evolution of the even-Haldane phase by tuning the DM interactions on the even bonds gradually.