We report large-scale quantum Monte Carlo calculations at the T=0 antiferromagnetic to valence-bond-solid (VBS) transition of a two-dimensional S=1/2 XY model with four-spin interactions. Finite-size scaling suggests a discontinuous spin stiffness, but a continuous VBS order-parameter. We propose that this is a continuous VBS transition without critical spin fluctuations. We also argue that the system is close to a point, in an extended parameter space, where both the magnetic and VBS fluctuations are critical--possibly a deconfined quantum-critical point.We report large-scale quantum Monte Carlo calculations at the T=0 antiferromagnetic to valence-bond-solid (VBS) transition of a two-dimensional S=1/2 XY model with four-spin interactions. Finite-size scaling suggests a discontinuous spin stiffness, but a continuous VBS order-parameter. We propose that this is a continuous VBS transition without critical spin fluctuations. We also argue that the system is close to a point, in an extended parameter space, where both the magnetic and VBS fluctuations are critical--possibly a deconfined quantum-critical point.

arXiv:cond-mat/0604451Apr 19, 20061 citation

Plaquette-type valence bond solid state in the J 1 − J 2 square-lattice Heisenberg model

Jiale Huang, Xiangjian Qian, Mingpu Qin

We utilize density matrix renormalization group and fully augmented matrix product states (FAMPS) methods to investigate the valence bond solid (VBS) phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square lattice Heisenberg model. To differentiate between the columnar valence bond solid and plaquette valence bond solid (PVBS) phases, we introduce an anisotropy ${\mathrm{\ensuremath{\Delta}}}_{y}$ in the nearest-neighboring coupling in the $y$ direction, aiming at detecting the possible spontaneous rotational symmetry breaking in the VBS phase. In the calculations, we push the bond dimension to as large as $D=25\phantom{\rule{0.16em}{0ex}}000$ in FAMPS, simulating systems at a maximum size of $14\ifmmode\times\else\texttimes\fi{}14$. With a careful extrapolation of the truncation errors and appropriate finite-size scaling, followed by finite ${\mathrm{\ensuremath{\Delta}}}_{y}$ scaling analysis of the VBS dimer order parameters, we identify the VBS phase as a PVBS type, meaning there is no spontaneous rotational symmetry breaking in the VBS phase. This paper not only supports the presence of PVBS order in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square lattice Heisenberg model, but also highlights the capabilities of FAMPS in the study of two-dimensional quantum many-body systems.We utilize density matrix renormalization group and fully augmented matrix product states (FAMPS) methods to investigate the valence bond solid (VBS) phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square lattice Heisenberg model. To differentiate between the columnar valence bond solid and plaquette valence bond solid (PVBS) phases, we introduce an anisotropy ${\mathrm{\ensuremath{\Delta}}}_{y}$ in the nearest-neighboring coupling in the $y$ direction, aiming at detecting the possible spontaneous rotational symmetry breaking in the VBS phase. In the calculations, we push the bond dimension to as large as $D=25\phantom{\rule{0.16em}{0ex}}000$ in FAMPS, simulating systems at a maximum size of $14\ifmmode\times\else\texttimes\fi{}14$. With a careful extrapolation of the truncation errors and appropriate finite-size scaling, followed by finite ${\mathrm{\ensuremath{\Delta}}}_{y}$ scaling analysis of the VBS dimer order parameters, we identify the VBS phase as a PVBS type, meaning there is no spontaneous rotational symmetry breaking in the VBS phase. This paper not only supports the presence of PVBS order in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square lattice Heisenberg model, but also highlights the capabilities of FAMPS in the study of two-dimensional quantum many-body systems.

arXiv:2406.17417Physical review. B./Physical review. BNov 4, 20245 citations

Quantum computing for electronic structure analysis: Ground state energy and molecular properties calculations

Nouhaila Innan, Muhammad Al-Zafar Khan, Mohamed Bennai

arXiv:2305.07902Materials Today CommunicationsDec 1, 202320 citations

Computational Quantum Chemistry

Elsevier eBooksJan 1, 201923 citations

y

direction, aiming at detecting the possible spontaneous rotational symmetry breaking in the VBS phase. In the calculations, we push the bond dimension to as large as

D=25\phantom{\rule{0.16em}{0ex}}000

in FAMPS, simulating systems at a maximum size of $14\ifmmode\times\else\texttimes\fi{}14$. With a careful extrapolation of the truncation errors and appropriate finite-size scaling, followed by finite ${\mathrm{\ensuremath{\Delta}}}_{y}$ scaling analysis of the VBS dimer order parameters, we identify the VBS phase as a PVBS type, meaning there is no spontaneous rotational symmetry breaking in the VBS phase. This paper not only supports the presence of PVBS order in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square lattice Heisenberg model, but also highlights the capabilities of FAMPS in the study of two-dimensional quantum many-body systems.