This study is a 13-week, open-label study of 8 participants with schizophrenia and minimal thought disorder; they will have 12 weeks of treatment and week for assessment. They will receive linagliptin, 5 mg by mouth once per day, while continuing their antipsychotic treatment. The principal outcome measures will be the concentrations of the long and short forms of SDF1-α (stromal cell-derived factor alpha) in blood.