Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1405.1233 · The European Physical Journal B

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

M. Sadrzadeh, A. Langari

Published Oct 1, 2015• 10 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2015-60142-2

Related papers

Tensor networ simulation of phase diagram of frustrated J1-J2 Heisenberg model on a checkerboard lattice

Yang‐Hao Chan, Yong‐Jian Han, L.-M. Duan

Bulletin of the American Physical Society•Feb 29, 2012•0 citations

Transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

M. Sadrzadeh, A. Langari

We study the effect of quantum fluctuations by means of a transverse magnetic field ($\Gamma$) on the antiferromagnetic $J_1-J_2$ Ising model on the checkerboard lattice, the two dimensional version of pyrochlore lattice. A plaquette operator formalism has been implemented to bosonise the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered state, which breaks lattice rotational symmetry for $J_2>J_1$ (the collinear phase). The bosonic excitation gap vanishes at the critical boundary to N\'{e}el ($J_2 J_1$) phases, respectively. At the homogeneous coupling ($J_1=J_2$) a (canted) resonating plaquette state (RPS) is established from an-harmonic fluctuations, which lasts for low fields, $\Gamma/J_1\lesssim 0.4$, followed by a crossover to the fully polarized phase. We will show that our results predict an order-by-disorder as a results of transverse field at the critical point ($J_2=0.5 J_1$) of the antiferromagnetic $J_1-J_2$ Ising square lattice.

•May 6, 2014•0 citations

Phase diagrams of an Ising model with transverse field

Enaldo F. Sarmento, Solange Bessa Cavalcanti, R. B. Muniz

Cienc. Cult. (Sao Paulo) Supl•Jan 1, 1984•0 citations

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

M. Sadrzadeh, Reza Haghshenas, A. Langari

We investigate the ground-state phase diagram of the frustrated transverse-field Ising (TFI) model on the checkerboard lattice (CL), which consists of N\'eel, collinear, quantum paramagnet, and plaquette-valence bond solid (-VBS) phases. We implement a numerical simulation that is based on the recently developed unconstrained tree tensor network ansatz, which systematically improves the accuracy over the conventional methods as it exploits the internal gauge selections. At the highly frustrated region $({J}_{2}={J}_{1})$, we observe a second-order phase transition from the plaquette-VBS state to the paramagnet phase at the critical magnetic-field ${\mathrm{\ensuremath{\Gamma}}}_{c}=0.28$ with the associated critical exponents $\ensuremath{\nu}=1$ and $\ensuremath{\gamma}\ensuremath{\simeq}0.4$, which are obtained within the finite-size scaling analysis on different lattice sizes $N=4\ifmmode\times\else\texttimes\fi{}4,6\ifmmode\times\else\texttimes\fi{}6,8\ifmmode\times\else\texttimes\fi{}8$. The stability of the plaquette-VBS phase at low magnetic fields is examined by a spin-spin correlation function, which verifies the presence of plaquette-VBS at ${J}_{2}={J}_{1}$ and rules out the existence of a N\'eel phase. In addition, our numerical results suggest that the transition from the N\'eel (for ${J}_{2}<{J}_{1})$ to the plaquette-VBS phase is a deconfined phase transition. Moreover, we introduce a mapping, which renders the low-energy effective theory of the TFI on the CL to be the same model on the ${J}_{1}\ensuremath{-}{J}_{2}$ square lattice (SL). We show that the plaquette-VBS phase of the highly frustrated point ${J}_{2}={J}_{1}$ on the CL is mapped to the emergent string-VBS phase on the SL at ${J}_{2}=0.5{J}_{1}$.

arXiv:1901.00278•Physical review. B./Physical review. B•Apr 16, 2019•11 citations

Ground-State Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal-Field

Zhao, Jie Jie, Wei Wei +3 more

理论物理通讯：英文版•Jan 1, 2006•0 citations

Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal Field

Zhao, Jie Jie, Xu Xu +3 more

理论物理通讯：英文版•Jan 1, 2009•1 citation
We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ\GammaΓ) on the antiferromagnetic J1−J2J_1-J_2J1​−J2​ Ising model on the checkerboard lattice, the two dimensional version of pyrochlore lattice. A plaquette operator formalism has been implemented to bosonise the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered state, which breaks lattice rotational symmetry for J2>J1J_2>J_1J2​>J1​ (the collinear phase). The bosonic excitation gap vanishes at the critical boundary to N\'{e}el (J2J1J_2 J_1J2​J1​) phases, respectively. At the homogeneous coupling (J1=J2J_1=J_2J1​=J2​) a (canted) resonating plaquette state (RPS) is established from an-harmonic fluctuations, which lasts for low fields, Γ/J1≲0.4\Gamma/J_1\lesssim 0.4Γ/J1​≲0.4, followed by a crossover to the fully polarized phase. We will show that our results predict an order-by-disorder as a results of transverse field at the critical point (J2=0.5J1J_2=0.5 J_1J2​=0.5J1​) of the antiferromagnetic J1−J2J_1-J_2J1​−J2​ Ising square lattice.
We investigate the ground-state phase diagram of the frustrated transverse-field Ising (TFI) model on the checkerboard lattice (CL), which consists of N\'eel, collinear, quantum paramagnet, and plaquette-valence bond solid (-VBS) phases. We implement a numerical simulation that is based on the recently developed unconstrained tree tensor network ansatz, which systematically improves the accuracy over the conventional methods as it exploits the internal gauge selections. At the highly frustrated region (J2=J1)({J}_{2}={J}_{1})(J2​=J1​), we observe a second-order phase transition from the plaquette-VBS state to the paramagnet phase at the critical magnetic-field ${\mathrm{\ensuremath{\Gamma}}}_{c}=0.28$ with the associated critical exponents $\ensuremath{\nu}=1$ and $\ensuremath{\gamma}\ensuremath{\simeq}0.4$, which are obtained within the finite-size scaling analysis on different lattice sizes $N=4\ifmmode\times\else\texttimes\fi{}4,6\ifmmode\times\else\texttimes\fi{}6,8\ifmmode\times\else\texttimes\fi{}8$. The stability of the plaquette-VBS phase at low magnetic fields is examined by a spin-spin correlation function, which verifies the presence of plaquette-VBS at J2=J1{J}_{2}={J}_{1}J2​=J1​ and rules out the existence of a N\'eel phase. In addition, our numerical results suggest that the transition from the N\'eel (for J2<J1){J}_{2}<{J}_{1})J2​<J1​) to the plaquette-VBS phase is a deconfined phase transition. Moreover, we introduce a mapping, which renders the low-energy effective theory of the TFI on the CL to be the same model on the ${J}_{1}\ensuremath{-}{J}_{2}$ square lattice (SL). We show that the plaquette-VBS phase of the highly frustrated point J2=J1{J}_{2}={J}_{1}J2​=J1​ on the CL is mapped to the emergent string-VBS phase on the SL at J2=0.5J1{J}_{2}=0.5{J}_{1}J2​=0.5J1​.