We present a mapping of a two-dimensional system of interacting bosons in a strong perpendicular magnetic field to an equivalent system of interacting bosons on the square lattice in the absence of the field. The mapping utilizes a magnetic Bloch and the corresponding magnetic Wannier single-particle basis in the lowest Landau level. By construction, the ground states of the resulting model of interacting bosons on the square lattice are gapped fractionalized liquids or gapless Bose metal states with broken time-reversal symmetry at specific rational filling fractions.We present a mapping of a two-dimensional system of interacting bosons in a strong perpendicular magnetic field to an equivalent system of interacting bosons on the square lattice in the absence of the field. The mapping utilizes a magnetic Bloch and the corresponding magnetic Wannier single-particle basis in the lowest Landau level. By construction, the ground states of the resulting model of interacting bosons on the square lattice are gapped fractionalized liquids or gapless Bose metal states with broken time-reversal symmetry at specific rational filling fractions.

arXiv:1601.00968Physical review. B./Physical review. BMar 16, 20161 citation

Symmetry Fractionalization in Two Dimensions

Hong Yao, Liang Fu, Xiao-Liang Qi

Bulletin of the American Physical SocietyMar 21, 20110 citations

Building Symmetry Fractionalizations from a Bipartite Lattice Construction

Jong Yeon Lee, Ari M. Turner, Ashvin Vishwanath

Bulletin of the American Physical SocietyMar 9, 20180 citations

Spectroscopic signatures of crystal momentum fractionalization

Andrew M. Essin, Michael Hermele

We consider gapped ${\mathbb{Z}}_{2}$ spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space-group symmetry. In particular, spinons can carry fractional crystal momentum. We show that such quantum number fractionalization has dramatic, spectroscopically accessible consequences, namely, enhanced periodicity of the two-spinon density of states in the Brillouin zone, which can be detected via inelastic neutron scattering. This effect is a sharp signature of certain topologically ordered spin liquids and other symmetry-enriched topological phases. Considering square lattice space-group and time-reversal symmetry, we show that exactly four distinct types of spectral periodicity are possible.We consider gapped ${\mathbb{Z}}_{2}$ spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space-group symmetry. In particular, spinons can carry fractional crystal momentum. We show that such quantum number fractionalization has dramatic, spectroscopically accessible consequences, namely, enhanced periodicity of the two-spinon density of states in the Brillouin zone, which can be detected via inelastic neutron scattering. This effect is a sharp signature of certain topologically ordered spin liquids and other symmetry-enriched topological phases. Considering square lattice space-group and time-reversal symmetry, we show that exactly four distinct types of spectral periodicity are possible.

arXiv:1401.1846Physical Review BSep 5, 201448 citations

Various delocalized phases of a disordered fermion model on a two-dimensional square lattice with π -flux

Takahiro Fukui

A disordered fermion model defined on a two-dimensional square lattice with $\ensuremath{\pi}$ flux is studied. Time-reversal symmetry and one of four possible chiral symmetries are imposed. The continuum limit of the model near zero energy yields Dirac fermions with chiral symmetry. It is shown that one of them has $\mathrm{Sp}(n)\ifmmode\times\else\texttimes\fi{}\mathrm{Sp}(n)$ symmetry whereas others have U $(2n)$ symmetry, both of which are broken to Sp $(n),$ and the fluctuation around a saddle point is described, respectively, by the Sp ${(n)}_{2}$ Wess-Zumino-Witten model and U $(2n)$ /Sp $(n)$ nonlinear sigma model.A disordered fermion model defined on a two-dimensional square lattice with $\ensuremath{\pi}$ flux is studied. Time-reversal symmetry and one of four possible chiral symmetries are imposed. The continuum limit of the model near zero energy yields Dirac fermions with chiral symmetry. It is shown that one of them has $\mathrm{Sp}(n)\ifmmode\times\else\texttimes\fi{}\mathrm{Sp}(n)$ symmetry whereas others have U$(2n)$ symmetry, both of which are broken to Sp$(n),$ and the fluctuation around a saddle point is described, respectively, by the Sp${(n)}_{2}$ Wess-Zumino-Witten model and U$(2n)$/Sp$(n)$ nonlinear sigma model.

arXiv:cond-mat/0008119Physical review. B, Condensed matterAug 7, 20010 citations

We consider gapped

{\mathbb{Z}}_{2}

spin liquids, where spinon quasiparticles may carry fractional quantum numbers of space-group symmetry. In particular, spinons can carry fractional crystal momentum. We show that such quantum number fractionalization has dramatic, spectroscopically accessible consequences, namely, enhanced periodicity of the two-spinon density of states in the Brillouin zone, which can be detected via inelastic neutron scattering. This effect is a sharp signature of certain topologically ordered spin liquids and other symmetry-enriched topological phases. Considering square lattice space-group and time-reversal symmetry, we show that exactly four distinct types of spectral periodicity are possible.

(2n)

symmetry, both of which are broken to Sp

(n),

and the fluctuation around a saddle point is described, respectively, by the Sp

{(n)}_{2}

Wess-Zumino-Witten model and U

(2n)

/Sp

(n)

nonlinear sigma model.