The spin- $\frac{1}{2}$ ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on square lattices is investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combined with Monte Carlo sampling techniques, we are able to obtain the ground state energies that are competitive with the best results. The calculations show that there is no N\'eel order, dimer order, or plaquette order in the region of $0.42\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer, and plaquette correlation functions all have power law decay behaviors, which provide strong evidence that the intermediate nonmagnetic phase is a single gapless spin liquid state.The spin-$\frac{1}{2}$ ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on square lattices is investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combined with Monte Carlo sampling techniques, we are able to obtain the ground state energies that are competitive with the best results. The calculations show that there is no N\'eel order, dimer order, or plaquette order in the region of $0.42\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer, and plaquette correlation functions all have power law decay behaviors, which provide strong evidence that the intermediate nonmagnetic phase is a single gapless spin liquid state.

arXiv:1806.07031Physical review. B./Physical review. BDec 17, 201871 citations

Gapless chiral spin liquid in spin-1/2 triangular Heisenberg model

Shou-Shu Gong, Mac Lee, D. N. Sheng

Bulletin of the American Physical SocietyMar 6, 20190 citations

Gapless spin liquid and valence-bond solid in the J1 - J2 Heisenberg model on the square lattice: Insights from singlet and triplet excitations

Francesco Ferrari, Federico Becca

The spin- $1/2$ ${J}_{1}$ - ${J}_{2}$ Heisenberg model on the square lattice represents one of the simplest examples in which the effects of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for ${J}_{2}/{J}_{1}\ensuremath{\approx}0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.54$) and a valence-bond solid (for $0.54\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)], reconcile the contradicting results obtained within different approaches over the years.The spin-$1/2$ ${J}_{1}$-${J}_{2}$ Heisenberg model on the square lattice represents one of the simplest examples in which the effects of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for ${J}_{2}/{J}_{1}\ensuremath{\approx}0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.54$) and a valence-bond solid (for $0.54\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)], reconcile the contradicting results obtained within different approaches over the years.

arXiv:2005.12941Physical review. B./Physical review. BJul 10, 202079 citations

Spin Liquid in the Triangular Lattice Heisenberg Model

Ian P. McCulloch, S. N. Saadatmand

Bulletin of the American Physical SocietyMar 14, 20160 citations

Comment on “Gapless spin liquid ground state of the spin- 12 J1−J2 Heisenberg model on square lattices”

Bowen Zhao, Jun Takahashi, Anders W. Sandvik

Liu et al. [Phys. Rev. B 98, 241109 (2018)] used Monte Carlo sampling of the physical degrees of freedom of a projected entangled pair state type wave function for the $S=1/2$ frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on the square lattice and found a nonmagnetic state argued to be a gapless spin liquid when the coupling ratio $g={J}_{2}/{J}_{1}$ is in the range $g\ensuremath{\in}[0.42,0.6]$. Here we show that their definition of the order parameter for another candidate ground state within this coupling window---a spontaneously dimerized state---is problematic. The order parameter as defined will not detect dimer order when lattice symmeties are broken due to open boundaries or asymmetries originating from the calculation itself. Thus, a dimerized phase for some range of $g$ cannot be excluded (and is likely based on several other recent works).Liu et al. [Phys. Rev. B 98, 241109 (2018)] used Monte Carlo sampling of the physical degrees of freedom of a projected entangled pair state type wave function for the $S=1/2$ frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on the square lattice and found a nonmagnetic state argued to be a gapless spin liquid when the coupling ratio $g={J}_{2}/{J}_{1}$ is in the range $g\ensuremath{\in}[0.42,0.6]$. Here we show that their definition of the order parameter for another candidate ground state within this coupling window---a spontaneously dimerized state---is problematic. The order parameter as defined will not detect dimer order when lattice symmeties are broken due to open boundaries or asymmetries originating from the calculation itself. Thus, a dimerized phase for some range of $g$ cannot be excluded (and is likely based on several other recent works).

arXiv:1909.12788Physical review. B./Physical review. BApr 9, 20208 citations

Gapless Chiral Spin Liquid Phase in Spin-

1/2

Triangular Heisenberg Model

The spin-

\frac{1}{2}

${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on square lattices is investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combined with Monte Carlo sampling techniques, we are able to obtain the ground state energies that are competitive with the best results. The calculations show that there is no N\'eel order, dimer order, or plaquette order in the region of $0.42\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer, and plaquette correlation functions all have power law decay behaviors, which provide strong evidence that the intermediate nonmagnetic phase is a single gapless spin liquid state.

The spin-

1/2

{J}_{1}

{J}_{2}

Heisenberg model on the square lattice represents one of the simplest examples in which the effects of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for ${J}_{2}/{J}_{1}\ensuremath{\approx}0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.54$) and a valence-bond solid (for $0.54\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A. W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)], reconcile the contradicting results obtained within different approaches over the years.

Liu et al. [Phys. Rev. B 98, 241109 (2018)] used Monte Carlo sampling of the physical degrees of freedom of a projected entangled pair state type wave function for the

S=1/2

frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on the square lattice and found a nonmagnetic state argued to be a gapless spin liquid when the coupling ratio

g={J}_{2}/{J}_{1}

is in the range $g\ensuremath{\in}[0.42,0.6]$. Here we show that their definition of the order parameter for another candidate ground state within this coupling window---a spontaneously dimerized state---is problematic. The order parameter as defined will not detect dimer order when lattice symmeties are broken due to open boundaries or asymmetries originating from the calculation itself. Thus, a dimerized phase for some range of

g

cannot be excluded (and is likely based on several other recent works).