Quantum phase diagram of spin-1 J1−J2 Heisenberg model on the square lattice: An infinite projected entangled-pair state and density matrix renormalization group study

Reza Haghshenas, Wang-Wei Lan, Shou-Shu Gong +1 more

arXiv:1802.00874Physical review. B./Physical review. BMay 31, 201821 citations

Springer eBooks

Dmrg Studies of Stripes and Pairing in the t-J Model

Steven R. White, Douglas J. Scalapino

Published Jan 1, 2001• 0 citations

Publisher

DOI: 10.1007/978-94-010-0771-9_15

Related papers

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

Stripe structures in the t–t′-J model

Douglas J. Scalapino, Steven R. White

arXiv:1204.5212Physica C SuperconductivityApr 21, 201233 citations

Pair density wave, infinite-length stripes, and holon Wigner crystal in single-band Hubbard model on diagonal square lattice

Zhiyi Xu, Gui-Xin Liu, Yi‐Fan Jiang

We employ large-scale density-matrix renormalization group (DMRG) simulations to investigate the quantum phase diagram of the hole-doped Hubbard model on square lattices. By implementing a diagonally oriented square lattice and GPU-accelerated DMRG with up to $48000$ states, we identify three distinct quantum phases across $δ= 5\%$ to $15\%$ doping: (i) A diagonal stripe phase with short-range uniform superconductivity (SC) at lower doping $δ\lesssim 9\%$ ; (ii) An intermediate holon Wigner crystal (WC*) phase exhibiting bidirectional charge-density order and short-range SC with spatial oscillating correlations; (iii) An unprecedented infinite-length stripe (i-stripe) phase at $δ\gtrsim 12\%$ hosting long stripes spanning the whole lattice. Remarkably, as doping increases, the short-range SC in WC* phase evolves into a 2D-like pair density wave (PDW) with divergent susceptibility in the i-stripe phase, constituting probably the first controlled numerical evidence of dominant PDW in the single-band square-lattice Hubbard model. The established 2D-like PDW and its interplay with charge orders provide new perspectives on dynamical layer decoupling phenomena in cuprates and multifaceted relationships between charge, spin and SC orders in quantum materials.We employ large-scale density-matrix renormalization group (DMRG) simulations to investigate the quantum phase diagram of the hole-doped Hubbard model on square lattices. By implementing a diagonally oriented square lattice and GPU-accelerated DMRG with up to $48000$ states, we identify three distinct quantum phases across $δ= 5\%$ to $15\%$ doping: (i) A diagonal stripe phase with short-range uniform superconductivity (SC) at lower doping $δ\lesssim 9\%$; (ii) An intermediate holon Wigner crystal (WC*) phase exhibiting bidirectional charge-density order and short-range SC with spatial oscillating correlations; (iii) An unprecedented infinite-length stripe (i-stripe) phase at $δ\gtrsim 12\%$ hosting long stripes spanning the whole lattice. Remarkably, as doping increases, the short-range SC in WC* phase evolves into a 2D-like pair density wave (PDW) with divergent susceptibility in the i-stripe phase, constituting probably the first controlled numerical evidence of dominant PDW in the single-band square-lattice Hubbard model. The established 2D-like PDW and its interplay with charge orders provide new perspectives on dynamical layer decoupling phenomena in cuprates and multifaceted relationships between charge, spin and SC orders in quantum materials.

arXiv:2409.18833Sep 27, 20240 citations

On the nature of pairing in the two-dimensional t–J model

Thomas Maier

Physica B Condensed MatterFeb 15, 20058 citations

Investigation of stripe formation in an extended t-J model

Tôru Sakai, Didier Poilblanc

APSMar 1, 20020 citations

Quantum phase diagram of spin-1 J1−J2 Heisenberg model on the square lattice: An infinite projected entangled-pair state and density matrix renormalization group study

Reza Haghshenas, Wang-Wei Lan, Shou-Shu Gong +1 more

We study the spin-1 Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor ${J}_{1}$ and the next-nearest-neighbor ${J}_{2}$ couplings by using the infinite projected entangled-pair state (iPEPS) ansatz and the density matrix renormalization group (DMRG) calculation. The iPEPS simulation, which studies the model directly in the thermodynamic limit, finds a crossing of the ground state from the N\'eel magnetic state to the stripe magnetic state at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$, showing a direct phase transition. In the finite-size DMRG calculation on the cylinder geometry up to the cylinder width ${L}_{y}=10$ , we find that around the same critical point the N\'eel and the stripe orders are strongly suppressed, which implies the absence of an intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$. Our results indicate that unlike the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square model, quantum fluctuations in the spin-1 model may not be strong enough to stabilize an intermediate nonmagnetic phase.We study the spin-1 Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor ${J}_{1}$ and the next-nearest-neighbor ${J}_{2}$ couplings by using the infinite projected entangled-pair state (iPEPS) ansatz and the density matrix renormalization group (DMRG) calculation. The iPEPS simulation, which studies the model directly in the thermodynamic limit, finds a crossing of the ground state from the N\'eel magnetic state to the stripe magnetic state at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$, showing a direct phase transition. In the finite-size DMRG calculation on the cylinder geometry up to the cylinder width ${L}_{y}=10$, we find that around the same critical point the N\'eel and the stripe orders are strongly suppressed, which implies the absence of an intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$. Our results indicate that unlike the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square model, quantum fluctuations in the spin-1 model may not be strong enough to stabilize an intermediate nonmagnetic phase.

arXiv:1802.00874Physical review. B./Physical review. BMay 31, 201821 citations

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 ${\ensuremath{\rho}}_{l}\ensuremath{\sim}0.75\text{--}0.8$.

48000

states, we identify three distinct quantum phases across

δ= 5\%

15\%

doping: (i) A diagonal stripe phase with short-range uniform superconductivity (SC) at lower doping

δ\lesssim 9\%

; (ii) An intermediate holon Wigner crystal (WC*) phase exhibiting bidirectional charge-density order and short-range SC with spatial oscillating correlations; (iii) An unprecedented infinite-length stripe (i-stripe) phase at

δ\gtrsim 12\%

hosting long stripes spanning the whole lattice. Remarkably, as doping increases, the short-range SC in WC* phase evolves into a 2D-like pair density wave (PDW) with divergent susceptibility in the i-stripe phase, constituting probably the first controlled numerical evidence of dominant PDW in the single-band square-lattice Hubbard model. The established 2D-like PDW and its interplay with charge orders provide new perspectives on dynamical layer decoupling phenomena in cuprates and multifaceted relationships between charge, spin and SC orders in quantum materials.

We study the spin-1 Heisenberg model on the square lattice with the antiferromagnetic nearest-neighbor

{J}_{1}

and the next-nearest-neighbor

{J}_{2}

couplings by using the infinite projected entangled-pair state (iPEPS) ansatz and the density matrix renormalization group (DMRG) calculation. The iPEPS simulation, which studies the model directly in the thermodynamic limit, finds a crossing of the ground state from the N\'eel magnetic state to the stripe magnetic state at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$, showing a direct phase transition. In the finite-size DMRG calculation on the cylinder geometry up to the cylinder width

{L}_{y}=10

, we find that around the same critical point the N\'eel and the stripe orders are strongly suppressed, which implies the absence of an intermediate phase. Both calculations identify that the stripe order comes with a first-order transition at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.549$. Our results indicate that unlike the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ square model, quantum fluctuations in the spin-1 model may not be strong enough to stabilize an intermediate nonmagnetic phase.