Note on twisted order in the frustrated quantum Heisenberg model

Using a Lanczos technique we study the frustrated spin-(1/2 Heisenberg model on square lattices of 16 and 20 sites. Frustration is introduced by an interaction along the diagonals of the plaquettes with coupling ${J}_{2}$ \ensuremath{\ge}0. For large ${J}_{2}$ we found that the ground state breaks (spontaneously) the lattice rotational symmetry. For intermediate values of ${J}_{2}$ , the squares of order parameters associated with spin-Peierls and ``twisted'' states have a peak while a similar quantity for a chiral state shows no interesting structure.Using a Lanczos technique we study the frustrated spin-(1/2 Heisenberg model on square lattices of 16 and 20 sites. Frustration is introduced by an interaction along the diagonals of the plaquettes with coupling ${J}_{2}$\ensuremath{\ge}0. For large ${J}_{2}$ we found that the ground state breaks (spontaneously) the lattice rotational symmetry. For intermediate values of ${J}_{2}$, the squares of order parameters associated with spin-Peierls and ``twisted'' states have a peak while a similar quantity for a chiral state shows no interesting structure.

Physical Review LettersNov 6, 1989329 citations

Fractionally quantized Berry phase in spin-1/2 frustrated Heisenberg model

Shin Miyahara

Spin-1/2 frustrated Heisenberg model show novel ground states due to the quantum fluctulation. To classify the ground states with toprogical invariant, we introduce fractionally quantized Berry phase. The Berry phase for the Heisenberg model is defined by local spin twists in the spin xy plane. As typical examples, we consider plateau states in frustrated magnets, e.g., a multimer ( N -mer) chains. Fractional quantization of the Berry phase comes from rotational symmetry of the twisted cluster. The Z N Berry phases are obtained from the numerical integration with using the ground states calculated by the Lanczos method. As a result, we obtained fractional quantization of Z 2 and Z 4 Berry phases in dimer ( N =2) and tetramer ( N =4) chains respectively.Spin-1/2 frustrated Heisenberg model show novel ground states due to the quantum fluctulation. To classify the ground states with toprogical invariant, we introduce fractionally quantized Berry phase. The Berry phase for the Heisenberg model is defined by local spin twists in the spin xy plane. As typical examples, we consider plateau states in frustrated magnets, e.g., a multimer ( N -mer) chains. Fractional quantization of the Berry phase comes from rotational symmetry of the twisted cluster. The Z N Berry phases are obtained from the numerical integration with using the ground states calculated by the Lanczos method. As a result, we obtained fractional quantization of Z 2 and Z 4 Berry phases in dimer ( N =2) and tetramer ( N =4) chains respectively.

StatPhys 27 Main ConferenceApr 16, 20190 citations

{J}_{2}

\ensuremath{\ge}0. For large

{J}_{2}

we found that the ground state breaks (spontaneously) the lattice rotational symmetry. For intermediate values of

{J}_{2}

, the squares of order parameters associated with spin-Peierls and ``twisted'' states have a peak while a similar quantity for a chiral state shows no interesting structure.