We study the nature of edge states in extrinsically and spontaneously dimerized states of two-dimensional spin- $\frac{1}{2}$ antiferromagnets, by performing quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the wide region of the dimerized phases, and the critical exponent of spin correlators along the edge deviates from the value of Tomonaga-Luttinger liquid (TLL) universality in large but finite systems at low temperatures. We also demonstrate that the gapless nature at edges is stable against several perturbations such as external magnetic field, easy-plane XXZ anisotropy, Dzyaloshinskii-Moriya interaction, and further-neighbor exchange interactions. The edge states exhibit non-TLL behavior, depending strongly on model parameters and kinds of perturbations. Possible ways of detecting these edge states are discussed. Properties of edge states we show in this paper could also be used as reference points to study other edge states of more exotic gapped magnetic phases such as spin liquids.We study the nature of edge states in extrinsically and spontaneously dimerized states of two-dimensional spin-$\frac{1}{2}$ antiferromagnets, by performing quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the wide region of the dimerized phases, and the critical exponent of spin correlators along the edge deviates from the value of Tomonaga-Luttinger liquid (TLL) universality in large but finite systems at low temperatures. We also demonstrate that the gapless nature at edges is stable against several perturbations such as external magnetic field, easy-plane XXZ anisotropy, Dzyaloshinskii-Moriya interaction, and further-neighbor exchange interactions. The edge states exhibit non-TLL behavior, depending strongly on model parameters and kinds of perturbations. Possible ways of detecting these edge states are discussed. Properties of edge states we show in this paper could also be used as reference points to study other edge states of more exotic gapped magnetic phases such as spin liquids.

arXiv:1209.3097Physical Review BDec 14, 201211 citations

Selective Population of Edge States in a 2D Topological Band System

Bogdan Galilo, Derek K. K. Lee, Ryan Barnett

We consider a system of interacting spin-one atoms in a hexagonal lattice under the presence of a synthetic gauge field. Quenching the quadratic Zeeman field is shown to lead to a dynamical instability of the edge modes. This, in turn, leads to a spin current along the boundary of the system which grows exponentially fast in time following the quench. Tuning the magnitude of the quench can be used to selectively populate edge modes of different momenta. Implications of the intrinsic symmetries of the Hamiltonian on the dynamics are discussed. The results hold for atoms with both antiferromagnetic and ferromagnetic interactions.We consider a system of interacting spin-one atoms in a hexagonal lattice under the presence of a synthetic gauge field. Quenching the quadratic Zeeman field is shown to lead to a dynamical instability of the edge modes. This, in turn, leads to a spin current along the boundary of the system which grows exponentially fast in time following the quench. Tuning the magnitude of the quench can be used to selectively populate edge modes of different momenta. Implications of the intrinsic symmetries of the Hamiltonian on the dynamics are discussed. The results hold for atoms with both antiferromagnetic and ferromagnetic interactions.

arXiv:1506.05818Physical Review LettersDec 11, 201549 citations

Numerical and analytical studies of physical properties of 2D antiferromagnetic spin systems

P. J. Freitas

Jan 1, 20000 citations

Spin-disordered superfluid state for spin-1 bosons with fractional spin and statistics

W. Vincent Liu, Xiao-Gang Wen

We study a strongly correlated spin-1 Bose gas in 2D space by using the projective construction. A spin-disordered superfluid state is constructed and proposed as a candidate competing with the conventional polar condensate when interaction is antiferromagnetic. This novel state has a non-trivial topological order whose low energy excitations carry fractional spin, charge, and statistics. The spin excitations become gapless only at the edge and are described by level-1 SU(2) Kac-Moody algebra. The edge state is identical to the edge state of the chiral spin liquid or the right moving sector of spin-1/2 chain.We study a strongly correlated spin-1 Bose gas in 2D space by using the projective construction. A spin-disordered superfluid state is constructed and proposed as a candidate competing with the conventional polar condensate when interaction is antiferromagnetic. This novel state has a non-trivial topological order whose low energy excitations carry fractional spin, charge, and statistics. The spin excitations become gapless only at the edge and are described by level-1 SU(2) Kac-Moody algebra. The edge state is identical to the edge state of the chiral spin liquid or the right moving sector of spin-1/2 chain.

arXiv:cond-mat/0201187Jan 11, 20021 citation

We study the nature of edge states in extrinsically and spontaneously dimerized states of two-dimensional spin-

\frac{1}{2}

antiferromagnets, by performing quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the wide region of the dimerized phases, and the critical exponent of spin correlators along the edge deviates from the value of Tomonaga-Luttinger liquid (TLL) universality in large but finite systems at low temperatures. We also demonstrate that the gapless nature at edges is stable against several perturbations such as external magnetic field, easy-plane XXZ anisotropy, Dzyaloshinskii-Moriya interaction, and further-neighbor exchange interactions. The edge states exhibit non-TLL behavior, depending strongly on model parameters and kinds of perturbations. Possible ways of detecting these edge states are discussed. Properties of edge states we show in this paper could also be used as reference points to study other edge states of more exotic gapped magnetic phases such as spin liquids.