In this study, it is investigated the effect of quantum fluctuations on the J1−J2 Blume–Capel model. The cluster mean field theory in the four site approximation is used to find the minimal (free) energy solutions. The ground state and finite temperature phase diagrams for the model with competitive ferromagnetic nearest neighbors (J1) and antiferromagnetic next nearest neighbors interactions (J2) are explored. It is found that the nature of phase transitions changes when quantum fluctuations and single-ion anisotropy parameter are varied. It is discussed the existence of tricritical points.In this study, it is investigated the effect of quantum fluctuations on the J1−J2 Blume–Capel model. The cluster mean field theory in the four site approximation is used to find the minimal (free) energy solutions. The ground state and finite temperature phase diagrams for the model with competitive ferromagnetic nearest neighbors (J1) and antiferromagnetic next nearest neighbors interactions (J2) are explored. It is found that the nature of phase transitions changes when quantum fluctuations and single-ion anisotropy parameter are varied. It is discussed the existence of tricritical points.

Jan 1, 20250 citations

Physical observable for one-dimensional the spin-1 Blume–Capel model

Chunhuan Xiang, Ai Min Chen, Su Yao +1 more

Physica A Statistical Mechanics and its ApplicationsFeb 1, 20202 citations

Plaquette valence bond state in the spin- 12 J1−J2 XY model on the square lattice

Yang‐Hao Chan, Hong‐Chen Jiang, Ying-Cheng Chen

We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor ${J}_{1}$ and second-neighbor ${J}_{2}$ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at ${J}_{2}/{J}_{1}<0.50$ and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor ${J}_{1}$ and second-neighbor ${J}_{2}$ antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at ${J}_{2}/{J}_{1}<0.50$ and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.

arXiv:2212.04863Physical review. B./Physical review. BJun 1, 20233 citations

Quantum simulation of the t–J model

Fumiko Yamaguchi, Y. Yamamoto

Superlattices and MicrostructuresOct 1, 20023 citations

Quantum phase transitions in the two-dimensional J1−J2 model

Oleg P. Sushkov, J. Oitmaa, Zheng Weihong

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the ${J}_{1}{\ensuremath{-}J}_{2}$ model, in two dimensions. Two quantum phase transitions in the model are already known: the second-order transition from the N\'eel state to the spin liquid state at ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38,$ and the first-order transition from the spin liquid state to the collinear state at ${(J}_{2}{/J}_{1}{)}_{c4}\ensuremath{\approx}0.60.$ We have found evidence for two second-order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette-type modulation at ${(J}_{2}{/J}_{1}{)}_{c3}=0.50\ifmmode\pm\else\textpm\fi{}0.02,$ and the transition from the simple N\'eel state to the N\'eel state with spin columnar dimerization at ${(J}_{2}{/J}_{1}{)}_{c1}=0.34\ifmmode\pm\else\textpm\fi{}0.04.$ We also present an independent calculation of ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38$ using another approach.We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the ${J}_{1}{\ensuremath{-}J}_{2}$ model, in two dimensions. Two quantum phase transitions in the model are already known: the second-order transition from the N\'eel state to the spin liquid state at ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38,$ and the first-order transition from the spin liquid state to the collinear state at ${(J}_{2}{/J}_{1}{)}_{c4}\ensuremath{\approx}0.60.$ We have found evidence for two second-order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette-type modulation at ${(J}_{2}{/J}_{1}{)}_{c3}=0.50\ifmmode\pm\else\textpm\fi{}0.02,$ and the transition from the simple N\'eel state to the N\'eel state with spin columnar dimerization at ${(J}_{2}{/J}_{1}{)}_{c1}=0.34\ifmmode\pm\else\textpm\fi{}0.04.$ We also present an independent calculation of ${(J}_{2}{/J}_{1}{)}_{c2}\ensuremath{\approx}0.38$ using another approach.

arXiv:cond-mat/0007329Physical review. B, Condensed matterFeb 20, 2001151 citations

We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor

{J}_{1}

and second-neighbor

{J}_{2}

antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at

{J}_{2}/{J}_{1}<0.50

and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.