Finite momentum condensates in Zeeman fields on a lattice
Date
2020
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We study superfluid states in two-dimensional fermionic attractive Hubbard models with Zeeman coupling to an external field. For singlet pairing in the strong coupling regime, we reveal a rich phase diagram of finite momentum condensates which exhibits both Fulde-Ferrell and Larkin-Ovchinnikov orders at zero and finite temperatures. The latter are commensurate stripe states that spontaneously break a lattice symmetry. Many stable wavevectors are found as a function of particle density and Zeeman field. Stronger coupling significantly enhances the stability of the finite momentum condensates, but our numerical mean-field calculations underestimate the effect of fluctuations and indicate a possible localization near half-filling. We furthermore study the effect of Rashba spin-orbit coupling on the formation of finite-momentum condensates in Zeeman fields. The spin orbit coupling stimulates pairing in the spin-triplet channels and stabilizes condensates with spin current vortices or spin-triplet pair density waves in certain parameter regimes. We show that Zeeman field enhances the stability of spin-polarized triplet condensates, and stabilizes additional FFLO condensates of unpolarized Cooper pair triplets. We calculate the phase diagram of condensates by a numerical minimization of mean field free energy under variations of the condensate order parameter. The phase diagrams contain numerous first-order phase transitions between competing orders, so we combine multiple algorithms and repeated minimizations with random seeds in order to distinguish between the true ground states from metastable states. In addition to conventional data analysis, we explore the ability of machine learning algorithm known as a Support Vector Classifier (SVC) to automatically discover phase boundaries from our data. We sub-sample the output collected during our search for finite momentum condensates and find that using an SVC should preclude performing expensive calculations deep within normal or uniform superfluid regions, and result in a more efficient use of compute time. The application of the procedure we describe is straightforward and should be applicable in any computational search of phase boundaries.