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

Bulletin of the American Physical Society

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

Published Feb 29, 2012• 0 citations
OpenAlex

Related papers

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

M. Sadrzadeh, A. Langari

arXiv:1405.1233•The European Physical Journal B•Oct 1, 2015•10 citations

Phase diagram and chirality of the spin-1/2 J1-J2 Heisenberg model on the kagome lattice

Shou-Shu Gong, Dong-Ning Sheng

Bulletin of the American Physical Society•Mar 20, 2013•0 citations

Simulation of fermionic and frustrated lattice models in two dimensions with tensor network algorithms

Philippe Corboz, Glen Evenbly, Jacob Jordan +6 more

Bulletin of the American Physical Society•Mar 23, 2011•0 citations

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

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

We use the recently developed tensor network algorithm based on infinite projected entangled pair states (iPEPS) to study the phase diagram of frustrated antiferromagnetic ${J}_{1}$-${J}_{2}$ Heisenberg model on a checkerboard lattice. The simulation indicates a N\'eel ordered phase when ${J}_{2}<0.88{J}_{1}$, a plaquette valence bond solid state when $0.88<{J}_{2}/{J}_{1}<1.11$, and a stripe phase when ${J}_{2}>1.11{J}_{1}$, with two first-order transitions across the phase boundaries. The calculation shows that the cross dimer state proposed before is unlikely to be the ground state of the model, although such a state indeed arises as a metastable state in some parameter region.

arXiv:1108.1595•Physical Review B•Dec 12, 2011•16 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

The phase transitions of the frustrated J1-J2 Ising model on the honeycomb lattice

Shang-Wei Li, Yuan-Heng Tseng, Fu-Jiun Jiang

arXiv:2509.11437•Physica A Statistical Mechanics and its Applications•Sep 5, 2026•0 citations
We use the recently developed tensor network algorithm based on infinite projected entangled pair states (iPEPS) to study the phase diagram of frustrated antiferromagnetic J1{J}_{1}J1​-J2{J}_{2}J2​ Heisenberg model on a checkerboard lattice. The simulation indicates a N\'eel ordered phase when J2<0.88J1{J}_{2}<0.88{J}_{1}J2​<0.88J1​, a plaquette valence bond solid state when 0.88<J2/J1<1.110.88<{J}_{2}/{J}_{1}<1.110.88<J2​/J1​<1.11, and a stripe phase when J2>1.11J1{J}_{2}>1.11{J}_{1}J2​>1.11J1​, with two first-order transitions across the phase boundaries. The calculation shows that the cross dimer state proposed before is unlikely to be the ground state of the model, although such a state indeed arises as a metastable state in some parameter region.
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​.