Exactly Solvable Points and Symmetry-Protected Topological Phases of Quantum Spins on a Zig-Zag Lattice

TL;DR

This paper presents exactly solvable points for symmetry-protected topological phases in a spin model of ultracold polar molecules on a zigzag lattice, providing analytical insights into their wave functions and phase transitions.

Contribution

It introduces exactly solvable points for SPT phases in a tunable spin model of ultracold polar molecules, enhancing understanding of their wave functions and phase diagrams.

Findings

Exact ground state wave functions for two SPT phases.

Phase diagram obtained via infinite TEBD simulations.

Identification of experimental signatures of phase transitions.

Abstract

A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation, and discuss the phase transitions between the two SPT phases and their experimental signatures.