arXiv:1908.10000

Stable diagonal stripes in the t-J model at $\bar{n}_h$=1/8 doping from fPEPS calculations

Shaojun Dong, Chao Wang, Yong‐Jian Han, Chao Yang, Lixin He

Published Aug 27, 2019• 0 citations

Abstract

We investigate the 2D t-J model at a hole doping of $\bar{n}_h$=1/8 using recently developed high accuracy fermionic projected entangled pair states(fPEPS) method. By applying stochastic gradient descent method combined with Monte Carlo sampling technique, we obtain the ground state hole energy $E_{\rm hole}$=-1.6186 for $J/t$=0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with width of 4 unit cells, and stripe filling $ρ_l$=0.5. We further show that the long range superconductivity order is suppressed at this point.

DOI: 10.48550/arxiv.1908.10000

Related papers

Stable diagonal stripes in the t–J model at nh = 1/8 doping from fPEPS calculations

Shaojun Dong, Chao Wang, Yong‐Jian Han +2 more

Abstract We investigate the two-dimensional t–J model at a hole doping of $${\bar{n}}_{{\rm{h}}}=1/8$$ n ¯ h = 1 / 8 using recently developed high accuracy fermionic projected entangled pair states method. By applying the stochastic gradient descent method combined with the Monte Carlo sampling technique, we obtain the ground state hole energy Ehole = −1.621 for J/t = 0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with a width of 4 unit cells, and stripe filling ρl = 0.5. We further show that the long-range superconductivity order is suppressed at this point.

npj Quantum MaterialsMay 8, 202011 citations

Absence of static stripes in the two-dimensional t − J model determined using an accurate and systematic quantum Monte Carlo approach

Wen-Jun Hu, Federico Becca, Sandro Sorella

arXiv:1111.5158Physical Review BFeb 28, 201240 citations

Stripes in the two-dimensional t - J model with infinite projected entangled-pair states

Philippe Corboz, Steven R. White, Guifré Vidal +1 more

arXiv:1104.5463Physical Review BJul 29, 2011211 citations

Diagonal Stripe States in the Light-doping Region in the Two-dimensional Hubbard Model

Mitake Miyazaki, Takashi Yanagisawa, Yamaji K.

Journal of the Physical Society of JapanJul 15, 200434 citations

Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States

Wen-Yuan Liu, Huanchen Zhai, Ruojing Peng +2 more

arXiv:2502.13454Physical Review LettersJun 3, 202522 citations

Phase separation and stripes in a boson version of a doped quantum antiferromagnet

Massimo Boninsegni

Physical review. B, Condensed matterMar 12, 200214 citations

arXiv:1908.10000

Stable diagonal stripes in the t-J model at $\bar{n}_h$ =1/8 doping from fPEPS calculationsStable diagonal stripes in the t-J model at $\bar{n}_h$=1/8 doping from fPEPS calculations

Shaojun Dong, Chao Wang, Yong‐Jian Han, Chao Yang, Lixin He

Published Aug 27, 2019• 0 citations

arXiv HTML PDF

Abstract

We investigate the 2D t-J model at a hole doping of

\bar{n}_h

=1/8 using recently developed high accuracy fermionic projected entangled pair states(fPEPS) method. By applying stochastic gradient descent method combined with Monte Carlo sampling technique, we obtain the ground state hole energy

E_{\rm hole}

=-1.6186 for

J/t

=0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with width of 4 unit cells, and stripe filling

ρ_l

=0.5. We further show that the long range superconductivity order is suppressed at this point.

DOI: 10.48550/arxiv.1908.10000

Related papers

Stable diagonal stripes in the t–J model at nh = 1/8 doping from fPEPS calculations

Shaojun Dong, Chao Wang, Yong‐Jian Han +2 more

Abstract We investigate the two-dimensional t–J model at a hole doping of ${\bar{n}}_{{\rm{h}}}=1/8$ n ¯ h = 1 / 8 using recently developed high accuracy fermionic projected entangled pair states method. By applying the stochastic gradient descent method combined with the Monte Carlo sampling technique, we obtain the ground state hole energy Ehole = −1.621 for J/t = 0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with a width of 4 unit cells, and stripe filling ρl = 0.5. We further show that the long-range superconductivity order is suppressed at this point.Abstract We investigate the two-dimensional t–J model at a hole doping of $${\bar{n}}_{{\rm{h}}}=1/8$$ n ¯ h = 1 / 8 using recently developed high accuracy fermionic projected entangled pair states method. By applying the stochastic gradient descent method combined with the Monte Carlo sampling technique, we obtain the ground state hole energy Ehole = −1.621 for J/t = 0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with a width of 4 unit cells, and stripe filling ρl = 0.5. We further show that the long-range superconductivity order is suppressed at this point.

npj Quantum MaterialsMay 8, 202011 citations

Absence of static stripes in the two-dimensional t − J model determined using an accurate and systematic quantum Monte Carlo approach

Wen-Jun Hu, Federico Becca, Sandro Sorella

We examine the two-dimensional $t\ensuremath{-}J$ model by using variational approach combined with well established quantum Monte Carlo techniques [S. Sorella et al., Phys. Rev. Lett. 88, 117002 (2002).] that are used to improve systematically the accuracy of the variational ansatz. Contrary to recent density-matrix renormalization group and projected entangled-pair state calculations [P. Corboz et al., Phys. Rev. B 84, 041108(R) (2011).], a uniform phase is found for $J/t=0.4$ , even when the calculation is biased with an ansatz that explicitly contains stripe order. Moreover, in the small hole doping regime, that is, $\ensuremath{\delta}\ensuremath{\lesssim}0.1$, our results support the coexistence of antiferromagnetism and superconductivity.We examine the two-dimensional $t\ensuremath{-}J$ model by using variational approach combined with well established quantum Monte Carlo techniques [S. Sorella et al., Phys. Rev. Lett. 88, 117002 (2002).] that are used to improve systematically the accuracy of the variational ansatz. Contrary to recent density-matrix renormalization group and projected entangled-pair state calculations [P. Corboz et al., Phys. Rev. B 84, 041108(R) (2011).], a uniform phase is found for $J/t=0.4$, even when the calculation is biased with an ansatz that explicitly contains stripe order. Moreover, in the small hole doping regime, that is, $\ensuremath{\delta}\ensuremath{\lesssim}0.1$, our results support the coexistence of antiferromagnetism and superconductivity.

arXiv:1111.5158Physical Review BFeb 28, 201240 citations

Stripes in the two-dimensional t - J model with infinite projected entangled-pair states

Philippe Corboz, Steven R. White, Guifré Vidal +1 more

We simulate the $t$ - $J$ model in two dimensions by means of infinite projected entangled-pair states (iPEPS) generalized to arbitrary unit cells, finding results similar to those previously obtained by the density-matrix renormalization group (DMRG) for wide ladders. In particular, we show that states exhibiting stripes, that is, a unidirectional modulation of hole-density and antiferromagnetic order with a $\ensuremath{\pi}$-phase shift between adjacent stripes, have a lower variational energy than uniform phases predicted by variational and fixed-node Monte Carlo simulations. For a fixed unit-cell size the energy per hole is minimized for a hole density ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.5$ per unit length of a stripe. The superconducting order parameter is maximal around ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.75\text{--}0.8$.We simulate the $t$-$J$ model in two dimensions by means of infinite projected entangled-pair states (iPEPS) generalized to arbitrary unit cells, finding results similar to those previously obtained by the density-matrix renormalization group (DMRG) for wide ladders. In particular, we show that states exhibiting stripes, that is, a unidirectional modulation of hole-density and antiferromagnetic order with a $\ensuremath{\pi}$-phase shift between adjacent stripes, have a lower variational energy than uniform phases predicted by variational and fixed-node Monte Carlo simulations. For a fixed unit-cell size the energy per hole is minimized for a hole density ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.5$ per unit length of a stripe. The superconducting order parameter is maximal around ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.75\text{--}0.8$.

arXiv:1104.5463Physical Review BJul 29, 2011211 citations

Diagonal Stripe States in the Light-doping Region in the Two-dimensional Hubbard Model

Mitake Miyazaki, Takashi Yanagisawa, Yamaji K.

We studied the ground state of the two-dimensional Hubbard model near half filling on the square lattice. Using Variational Monte Carlo method, we show that the diagonal stripe state of bond-centered type, in which the domain wall is located between two sites, becomes more stable than the vertical stripe state when the doping hole density x is as low as x ≃0.06. The inverse of stripe periodicity δ and the hole density x are observed to have the relationship δ∼ x (δ< x ) for the bond-centered diagonal stripe state (the vertical stripe state) in the light-doping region. These results are in good agreement with elastic neutron scattering experiments in La 2- x Sr x CuO 4 .We studied the ground state of the two-dimensional Hubbard model near half filling on the square lattice. Using Variational Monte Carlo method, we show that the diagonal stripe state of bond-centered type, in which the domain wall is located between two sites, becomes more stable than the vertical stripe state when the doping hole density x is as low as x ≃0.06. The inverse of stripe periodicity δ and the hole density x are observed to have the relationship δ∼ x (δ< x ) for the bond-centered diagonal stripe state (the vertical stripe state) in the light-doping region. These results are in good agreement with elastic neutron scattering experiments in La 2- x Sr x CuO 4 .

Journal of the Physical Society of JapanJul 15, 200434 citations

Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States

Wen-Yuan Liu, Huanchen Zhai, Ruojing Peng +2 more

We demonstrate the use of finite-size fermionic projected entangled pair states, in conjunction with variational Monte Carlo, to perform accurate simulations of the ground state of the 2D Hubbard model. Using bond dimensions of up to D=28, we show that we can surpass state-of-the-art density matrix renormalization group energies that use up to m=32 000 SU(2) multiplets on eight-leg ladders. We further apply our methodology to 10×16, 12×16, and 16×16 lattices at 1/8 hole doping and observe the dimensional crossover between stripe orientations. Our Letter shows the power of finite-size fermionic tensor networks to resolve the physics of the 2D Hubbard model and related problems.We demonstrate the use of finite-size fermionic projected entangled pair states, in conjunction with variational Monte Carlo, to perform accurate simulations of the ground state of the 2D Hubbard model. Using bond dimensions of up to D=28, we show that we can surpass state-of-the-art density matrix renormalization group energies that use up to m=32 000 SU(2) multiplets on eight-leg ladders. We further apply our methodology to 10×16, 12×16, and 16×16 lattices at 1/8 hole doping and observe the dimensional crossover between stripe orientations. Our Letter shows the power of finite-size fermionic tensor networks to resolve the physics of the 2D Hubbard model and related problems.

arXiv:2502.13454Physical Review LettersJun 3, 202522 citations

Phase separation and stripes in a boson version of a doped quantum antiferromagnet

Massimo Boninsegni

A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of ${J}_{z},$ at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any ${J}_{z}>0.$ The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of ${J}_{z},$ at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any ${J}_{z}>0.$ The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.

Physical review. B, Condensed matterMar 12, 200214 citations

Stable diagonal stripes in the t-J model at

\bar{n}_h

=1/8 doping from fPEPS calculations

We investigate the 2D t-J model at a hole doping of

\bar{n}_h

E_{\rm hole}

=-1.6186 for

J/t

=0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with width of 4 unit cells, and stripe filling

ρ_l

=0.5. We further show that the long range superconductivity order is suppressed at this point.

Abstract We investigate the two-dimensional t–J model at a hole doping of

{\bar{n}}_{{\rm{h}}}=1/8

n ¯ h = 1 / 8 using recently developed high accuracy fermionic projected entangled pair states method. By applying the stochastic gradient descent method combined with the Monte Carlo sampling technique, we obtain the ground state hole energy Ehole = −1.621 for J/t = 0.4. We show that the ground state has stable diagonal stripes instead of vertical stripes with a width of 4 unit cells, and stripe filling ρl = 0.5. We further show that the long-range superconductivity order is suppressed at this point.

J/t=0.4

, even when the calculation is biased with an ansatz that explicitly contains stripe order. Moreover, in the small hole doping regime, that is, $\ensuremath{\delta}\ensuremath{\lesssim}0.1$, our results support the coexistence of antiferromagnetism and superconductivity.

We simulate the

t

J

model in two dimensions by means of infinite projected entangled-pair states (iPEPS) generalized to arbitrary unit cells, finding results similar to those previously obtained by the density-matrix renormalization group (DMRG) for wide ladders. In particular, we show that states exhibiting stripes, that is, a unidirectional modulation of hole-density and antiferromagnetic order with a $\ensuremath{\pi}$-phase shift between adjacent stripes, have a lower variational energy than uniform phases predicted by variational and fixed-node Monte Carlo simulations. For a fixed unit-cell size the energy per hole is minimized for a hole density ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.5$ per unit length of a stripe. The superconducting order parameter is maximal around ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.75\text{--}0.8$.

{J}_{z},

at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any

{J}_{z}>0.

The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.