Topological quantum phase transition in bond-alternating spin-1/2 Heisenberg chains

TL;DR

This paper studies a topological quantum phase transition in an infinite bond-alternating spin-1/2 Heisenberg chain using advanced numerical methods, revealing long-range string order changes and critical properties characteristic of the Gaussian universality class.

Contribution

It demonstrates the occurrence of a topological quantum phase transition characterized by long-range string order and provides critical exponents and central charge, advancing understanding of topological phases in spin chains.

Findings

Identification of a topological phase transition with different long-range string orders.

Critical exponent β=1/12 for string order.

Central charge c≈1 indicating Gaussian universality class.

Abstract

We investigate string correlations in an infinite-size spin-1/2 bond-alternating Heisenberg chain. By employing the infinite matrix product state representation with the infinite time evolving block decimation method, a finite string correlation for extremely large lattice distances is directly observed, contrast to an extrapolated extreme value for finite size chains. We find that a topological quantum phase transition occurs between two different phases separated and characterized by two different long-range string orders in the space of bond-alternating interactions. Also, the critical exponent $\beta$ from the long-range string orders is obtained as $\beta=1/12$ and the central charge at the critical point is obtained as $c \simeq 1$, which shows that the topological phase transition belongs to the Gussian universality class. In addition, it is shown that, for the topological quantum phase transition, the phase boundary can be captured by the singular behavior of the von Neumann entropy and the pinch point of the fidelity per site.