The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.The phase diagram of the frustrated 2D classical and 1D quantum XY models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.

arXiv:1308.0823Physical Review LettersApr 14, 201412 citations

Universality classes of Ising models

Prabodh Shukla, Nenad M. Svrakic

Physics Letters ADec 1, 19780 citations

Ground-state phase diagram of the frustrated spin- 12 two-leg honeycomb ladder

Qiang Luo, Shijie Hu, Jize Zhao +3 more

We investigate a spin- $1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chains coupled with ${J}_{\ensuremath{\perp}}$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: a Haldane phase, a NNN-Haldane phase, and a staggered dimer phase when ${J}_{\ensuremath{\perp}}<0$; a rung singlet phase and a columnar dimer phase when ${J}_{\ensuremath{\perp}}>0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration ${J}_{2}$ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with a central charge $c=1/2$ . The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has a central charge $c=2$ .We investigate a spin-$1/2$ two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chains coupled with ${J}_{\ensuremath{\perp}}$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: a Haldane phase, a NNN-Haldane phase, and a staggered dimer phase when ${J}_{\ensuremath{\perp}}<0$; a rung singlet phase and a columnar dimer phase when ${J}_{\ensuremath{\perp}}>0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration ${J}_{2}$ increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with a central charge $c=1/2$. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has a central charge $c=2$.

arXiv:1804.00008Physical review. B./Physical review. BJun 27, 201814 citations

We investigate a spin-

1/2

two-leg honeycomb ladder with frustrating next-nearest-neighbor (NNN) coupling along the legs, which is equivalent to two ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ spin chains coupled with ${J}_{\ensuremath{\perp}}$ at odd rungs. The full parameter region of the model is systematically studied using conventional and infinite density-matrix renormalization group as well as bosonization. The rich phase diagram consists of five distinct phases: a Haldane phase, a NNN-Haldane phase, and a staggered dimer phase when ${J}_{\ensuremath{\perp}}<0$; a rung singlet phase and a columnar dimer phase when ${J}_{\ensuremath{\perp}}>0$. An interesting reentrant behavior from the dimerized phase into the Haldane phase is found as the frustration

{J}_{2}

increases. The universalities of the critical phase transitions are fully analyzed. Phase transitions between dimerized and disordered phases belong to the two-dimensional Ising class with a central charge

c=1/2

. The transition from the Haldane phase to NNN-Haldane phase is of a weak topological first order, while the continuous transition between the Haldane phase and rung singlet phase has a central charge

c=2