, it is always possible to close the magnetic translation algebra using fermionic bilinears, whether in the continuum or on the lattice. We also show that these generators are complete in even, but not odd, dimensions, in the sense that any fermionic Hamiltonian in even dimensions that conserves particle number can be represented in terms of the generators of this algebra, whether or not time-reversal symmetry is broken. As an example, we reproduce the

f

-sum rule of interacting electrons at vanishing magnetic field using this representation. We also show that interactions can significantly change the bare bandwidth of lattice Hamiltonians when represented in terms of the generators of the magnetic translation algebra.

DOI: 10.1103/physrevb.86.195125

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d

f

d

f

T=0

in the physical limit of vanishing renormalization group parameter

Λ

. We explore the capabilities and limitations of this method extension for Heisenberg models on the square, honeycomb and triangular lattices. While the zero-field magnetizations of these systems are systematically overestimated, the types of magnetic orders are correctly captured, even if the local orientations of the seed field are chosen differently than the spin orientations of the realized magnetic order. Furthermore, the magnetization curve of the square lattice Heisenberg antiferromagnet shows good agreement with error controlled methods. In the future, the inclusion of magnetic fields in the pseudo-fermion functional renormalization group, which is also possible in three dimensional spin systems, will enable a variety of additional interesting applications such as the investigation of magnetization plateaus.

T=0

in the physical limit of vanishing renormalization group parameter $\mathrm{\ensuremath{\Lambda}}$. We explore the capabilities and limitations of this method extension for Heisenberg models on the square, honeycomb, and triangular lattices. While the zero-field magnetizations of these systems are systematically overestimated, the types of magnetic orders are correctly captured, even if the local orientations of the seed field are chosen differently than the spin orientations of the realized magnetic order. Furthermore, the magnetization curve of the square lattice Heisenberg antiferromagnet shows good agreement with error controlled methods. In the future, the inclusion of magnetic fields in the pseudo-fermion functional renormalization group, which is also possible in three-dimensional spin systems, will enable a variety of additional interesting applications such as the investigation of magnetization plateaus.

^{3}\mathrm{He}

\frac{A}{B}

interface, are discussed.

Symmetry-enforced quantum spin Hall insulators in

π

-flux models

We prove a Lieb-Schultz-Mattis theorem for the quantum spin Hall effect (QSHE) in two-dimensional

π

-flux models. In the presence of time reversal,

U(1)

charge conservation and magnetic translation (with

π

-flux per unit cell) symmetries, if a generic interacting Hamiltonian has a unique gapped symmetric ground state at half filling (i.e. an odd number of electrons per unit cell), it can only be a QSH insulator. In other words, a trivial Mott insulator is forbidden by symmetries at half filling. We further show that such a symmetry-enforced QSHE can be realized in cold atoms, by shaking an optical lattice and applying a time-dependent Zeeman field.