Ground-state fidelity and quantum criticality in a two-leg ladder with cyclic four-spin exchange

TL;DR

This paper uses a tensor network algorithm to map out the phase diagram of a two-leg Heisenberg spin ladder with cyclic four-spin exchange, identifying six distinct quantum phases and critical points.

Contribution

It introduces an efficient tensor network method to compute ground-state fidelity per lattice site for phase diagram determination in complex quantum systems.

Findings

Identified six different quantum phases in the model.

Established the ground-state phase diagram with critical points.

Results agree with previous exact diagonalization and DMRG studies.

Abstract

We investigate a two-leg Heisenberg spin ladder with cyclic four-spin exchange by exploiting a newly-developed tensor network algorithm. The algorithm allows to efficiently compute the ground-state fidelity per lattice site, which enables us to establish the ground-state phase diagram for quantum lattice many-body systems. The latter is based on the observation that, for an infinite-size system, any singularity on a ground-state fidelity surface characterizes a critical point, at which the system undergoes a phase transition. For the two-leg Heisenberg spin-1/2 ladder with cyclic four-spin exchange, six different phases are identified: the ferromagnetic phase, the rung singlet phase, the staggered dimer phase, the scalar chirality phase, the dominant vector chirality region, and the dominant collinear spin region. Our findings are in a good agreement with the previous studies from the exact diagonalization and the density-matrix renormalization group.