Hubbard model with Rashba or Dresselhaus spin-orbit coupling and Rotated Anti-ferromagnetic Heisenberg Model

Abstract

In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin-orbit coupling (SOC) on fermionic Hubbard model in a 2d square lattice. In the strong coupling limit, it leads to the Rotated Anti-ferromagnetic Heisenberg model which is a new class of quantum spin model. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground ( Y-y ) state subject to strong quantum fluctuations at $T=0$. We evaluate the quantum fluctuations by the spin wave expansion up to order $1/S^2$. In some SOC parameter regime, the Y-y state supports a massive relativistic in-commensurate magnon ( C-IC ) with its two gap minima positions continuously tuned by the SOC parameters. The C-IC magnons dominate all the low temperature thermodynamic quantities and also lead to the separation of the peak positions between the longitudinal and the transverse spin structure factors. In the weak coupling limit, any weak repulsive interaction also leads to a weak Y-y state. There is only a crossover from the weak to the strong coupling. High temperature expansions of the specific heats in both weak and strong coupling are presented. The dramatic roles to be played by these C-IC magnons at generic SOC parameters or under various external probes are hinted. Experimental applications to both layered noncentrosymmetric materials and cold atom are discussed.

14 pages, 8 colour figures, Revtex4

References in corpus (14)

• Many-Body Physics with Ultracold Gases
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• Using photoemission spectroscopy to probe a strongly interacting Fermi gas
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Bose Hubbard Models with Synthetic Spin-Orbit Coupling: Mott Insulators, Spin Textures and Superfluidity
• Putting competing orders in their place near the Mott transition
• Exotic quantum spin models in spin-orbit-coupled Mott insulators
• Experimental observation of a topological band gap opening in ultracold Fermi gases with two-dimensional spin-orbit coupling
• Berry Phase Effect on Exciton Transport and Bose Einstein Condensate
• Duality, Magnetic space group and their applications to quantum phases and phase transitions on bipartite lattices in several experimental systems
• Pairing sizes in attractively interacting Fermi gases with Spin-orbit Couplings
• Classification of magnons in Rotated Ferromagnetic Heisenberg model and their competing responses in transverse fields
• Heat Capacity of a Strongly-Interacting Fermi Gas
• Two classes of organization principle: quantum/topological phase transitions meet complete/in-complete devil staircases and their experimental realizations

Cited by in corpus (9)

• Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates
• Phase diagram of the square lattice Hubbard model with Rashba-type antisymmetric spin-orbit coupling
• Pauli metallic ground-state in Hubbard clusters with Rashba spin-orbit coupling
• Topological depletions and sub-leading scalings across topological phase transitions
• Exotic Spin Phases in Two Dimensional Spin-orbit Coupled Models: Importance of Quantum Fluctuation Effects
• High Chern number topological superfluids and new class of topological phase transitions of Rashba spin-orbit coupled fermions on a lattice
• Transient dynamics and quantum phase diagram for the square lattice Rashba-Hubbard model at arbitrary hole doping
• Response of a strongly interacting spin-orbit coupling system to a Zeeman field
• Effective spin model with anisotropic exchange interactions for the spin-orbit coupled Hubbard model at half-filling