We review the fact that $U(1)$ gauge symmetry enables the mapping of one-dimensional Hubbard chains with Rashba-type spin-orbit coupling to renormalized Hubbard Hamiltonians. The existence of the mapping has important consequences for the interpretation of ARPES experiments on one-dimensional chains subject to Rashba spin-orbit coupling and can be exploited to check for the applicability of the mapping. We show numerical applications of the mapping and consider the implications for bosonization as well as for the Heisenberg limit of the Hubbard model. In addition we point out the consequences for various generalized Hubbard models.
We review the fact that U(1) gauge symmetry enables the mapping of one-dimensional Hubbard chains with Rashba-type spin-orbit coupling to renormalized Hubbard Hamiltonians. The existence of the mapping has important consequences for the interpretation of ARPES experiments on one-dimensional chains subject to Rashba spin-orbit coupling and can be exploited to check for the applicability of the mapping. We show numerical applications of the mapping and consider the implications for bosonization as well as for the Heisenberg limit of the Hubbard model. In addition we point out the consequences for various generalized Hubbard models.
Uniform spin-orbit coupling in an open single-band Hubbard chain is an exactly removable SU(2) gauge field at the Hamiltonian level, but not at the level of laboratory-frame spin correlations. We study this separation using density matrix renormalization group calculations for the repulsive one-dimensional Rashba-Hubbard chain. For open boundary conditions, a site-dependent spin rotation maps the model with hopping t and Rashba spin-orbit strength λ onto the ordinary Hubbard chain with renormalized hopping tλ=t2+λ2. Consequently, charge and energy diagnostics are affected only through the bandwidth renormalization, which is quadratic in weak λ/t. Spin correlations, however, respond already at linear order because the same transformation rotates the local spin basis by the wave vector kso=2arctan(λ/t). We use DMRG to verify this observable consequence across the filling diagram of finite open chains. The filling structure follows the gauge-equivalent Hubbard model, whereas the spin structure factor shows the predicted spin-orbit sidebands. A dominant Hubbard-chain magnetic wave vector k0 is transformed into components at k0±kso, folded into the open-chain Brillouin zone. At half filling, where k0=π, the two sidebands fold onto a single, in-plane, spin spiral wave with k=π−kso<π. Away from half filling, the incommensurate Hubbard spin response splits into two distinct spin-orbit-shifted components, producing a real-space beating pattern. Our results provide a filling-resolved tensor-network benchmark for the exactly removable limit of one-dimensional spin-orbit coupling, and establish a controlled reference point for ladders, multiorbital chains, rings, proximitized wires, and higher-dimensional Hubbard systems where spin-orbit coupling can no longer be gauged away.
We study the symmetry properties of the Hubbard model with spin-orbit interactions of Rashba and Dresselhaus type. These interactions break the rotational symmetry in spin space, so that the magnetic order cannot be excluded by using the Bogoliubov inequality method. Nevertheless, we rigorously show that the existence of the magnetic long-range orders may be ruled out when the Rashba and Dresselhaus coupling constants are equal in modulus, whereas the $\ensuremath{\eta}$ pairing can be always ruled out, regardless of the microscopic parameters of the model. These results are obtained by imposing locally the SU(2) gauge symmetry on the lattice, and rewriting the spin-orbit interactions in such a way that they are included in the path order of the gauge field on the lattice.
The Hubbard model is a simple but profound theoretical tool for understanding the physics underlying strongly correlated systems. This phenomenology includes, but is not limited to, metal-insulating transitions, charge and spin order (charge density/spin density waves), superconducting phases, non-Fermi liquid physics, among others. Examining one dimensional physical models described by the Hubbard Hamiltonian can teach us much about the related physics of higher dimensional systems. Applying advanced numerical computational techniques such as density matrix numerical renormalization group (DMRG) to one-dimensional manypbody model Hamiltonians allows for the calculation of ground state energies and dynamical spectral functions with extremely high precision and accuracy. This thesis explores the application of DMRG numerical techniques to one-dimensional physical systems described by Hamiltonians beyond the conventional Hubbard model, and the nuanced physical effects observed for these systems across various regimes and phases. A Wannier Hubbard chain composed of non-orthogonal overlapping atomic orbitals was transformed to an orthogonal atomic basis using a non-unitary Lowdin transformation. The calculation of energies, dynamical spectral functions and the photoemission spectrum for this Wannier Hubbard chain revealed phases not previously observed for Hubbard chains at half-filling. Additional analysis and calculations were performed for a CuO chain described by the Luther-Emery Hamiltonian that epitomizes charge-transfer physics. The motivation for studying this CuO chain was previous literature on transition metal oxides (TMOs) and the mapping of multiband Hamiltonians to single band models in certain energy regimes. Finally, we performed computational analysis for a spin-3/2 generalized Hubbard chain. By spanning the full phase space of our spin-3/2 Hubbard chain in terms of chemical potential μ and external magnetic field h we observed non-typical Cooper pairing states and novel phases for different symmetries of our Hamiltonian.--Author's abstract
Hidden local gauge invariance in the one-dimensional (1-D) Hubbard model and its equivalent coupled spin model is studied. It is found that Abelian U(1)⊗U(1) gauge transformations appear in both cases. Furthermore, it is shown that the energy spectrum is gauge invariant whereas the eigenvectors are explicitly gauge dependent. However, this result relies heavily on Shastry’s conjecture about the eigenvalue of the transfer matrix for the 1-D Hubbard model. Lastly, there is also a discrete symmetry associated to Z2⊗Z2. Once this symmetry is broken, one immediately obtains another nontrivial solution to the Yang–Baxter relations. UFaipxr
The Rashba-Hubbard model on the square lattice is the paradigmatic case for studying the effect of spin-orbit coupling, which breaks spin and inversion symmetry, in a correlated electron system. We employ a truncated-unity variant of the functional renormalization group which allows us to analyze magnetic and superconducting instabilities on equal footing. We derive phase diagrams depending on the strengths of Rasbha spin-orbit coupling, real second-neighbor hopping, and electron filling. We find commensurate and incommensurate magnetic phases which compete with d-wave superconductivity. Due to the breaking of inversion symmetry, singlet and triplet components mix; we quantify the mixing of d-wave singlet pairing with f-wave triplet pairing.
The composite-spin representation of the spin-1 Heisenberg chain is used to transform it through the Jordan-Wigner transformation to the one-dimensional fermion gas. To properly include the xy couplings between spins, we also consider the bosonized version of the fermion model. Phase diagrams deduced from the two versions of the fermion model are compared against numerical results for finite Heisenberg chains. One of the symmetries of the spin model is lost in the fermionization, and this leads to a topologically incorrect phase diagram in at least one part of the parameter space. There are clear indications of significant coupling of spin and charge degrees of freedom in the fermion model and of strong renormalization of the coupling constants in the continuum limit. The existence of the Haldane gap is discussed in connection with these results.