We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, nonperturbative version of the Luttinger theorem that holds in the Higgs phase.

arXiv:1711.09925Proceedings of the National Academy of SciencesApr 2, 2018107 citations

Topological States in Strongly Correlated Systems

V. Yu. Irkhin, Yu. N. Skryabin

arXiv:2209.04336Journal of Superconductivity and Novel MagnetismMay 2, 20225 citations

Z 4 parafermions in one-dimensional fermionic lattices

Alessio Calzona, Tobias Meng, Maura Sassetti +1 more

Nonlocal (topological) order and local (Landau-type) order are often viewed as opposing principles. Here, the authors study strongly interacting quantum wires that exhibit hybrid order, composed of local Ising magnetization and a topological order parameter. Based on an exact mapping of the corresponding strongly interacting electronic Hamiltonian onto \ensuremath{\mathbb{Z}} ${}_{n}$ parafermions, they show that the system can be in a hybrid phase which is distinct from the topological and from the Ising phase. Moreover, the system has remarkable similarities to superconducting hybrid devices built from fractional quantum Hall edge states, which can host parafermions useful for quantum computation.Nonlocal (topological) order and local (Landau-type) order are often viewed as opposing principles. Here, the authors study strongly interacting quantum wires that exhibit hybrid order, composed of local Ising magnetization and a topological order parameter. Based on an exact mapping of the corresponding strongly interacting electronic Hamiltonian onto \ensuremath{\mathbb{Z}}${}_{n}$ parafermions, they show that the system can be in a hybrid phase which is distinct from the topological and from the Ising phase. Moreover, the system has remarkable similarities to superconducting hybrid devices built from fractional quantum Hall edge states, which can host parafermions useful for quantum computation.

arXiv:1802.06061Physical review. B./Physical review. BNov 14, 201841 citations

Two-dimensional topological order of kinetically constrained quantum particles

Stefanos Kourtis, Claudio Castelnovo

We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a generalization of strongly interacting particle systems in which hoppings are given by flux-lattice Hamiltonians and may be relevant to optically driven cold-atom systems. After introducing a broad class of models, we focus on particular realizations and show numerically that they exhibit topological order, as witnessed by topological ground-state degeneracies and the quantization of corresponding invariants. These results demonstrate that the correlations responsible for fractional quantum Hall states in lattices can arise in models involving terms other than density-density interactions.We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a generalization of strongly interacting particle systems in which hoppings are given by flux-lattice Hamiltonians and may be relevant to optically driven cold-atom systems. After introducing a broad class of models, we focus on particular realizations and show numerically that they exhibit topological order, as witnessed by topological ground-state degeneracies and the quantization of corresponding invariants. These results demonstrate that the correlations responsible for fractional quantum Hall states in lattices can arise in models involving terms other than density-density interactions.

arXiv:1501.06917Physical Review BApr 20, 20158 citations

Topological order in correlated topological insulators

Joseph Maciejko, Andreas R uegg, Victor Chua +1 more

Bulletin of the American Physical SocietyMar 6, 20140 citations

{}_{n}

parafermions, they show that the system can be in a hybrid phase which is distinct from the topological and from the Ising phase. Moreover, the system has remarkable similarities to superconducting hybrid devices built from fractional quantum Hall edge states, which can host parafermions useful for quantum computation.