Numerical lattice simulation confirms spontaneous time-reversal symmetry breaking and gap opening in a helical Luttinger liquid at the Dirac point above a critical Luttinger parameter.
The termK n is again a second derivative, X n Kn = 2 X k (1−cos 2ka)c † k↑ck↓,(A10) which becomes irrelevant in the long-wave length regime
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Lattice fermion simulation of spontaneous time-reversal symmetry breaking in a helical Luttinger liquid
Numerical lattice simulation confirms spontaneous time-reversal symmetry breaking and gap opening in a helical Luttinger liquid at the Dirac point above a critical Luttinger parameter.