Physical review. B, Condensed matter

Stripes in a three-chain Hubbard ladder: A comparison of density-matrix renormalization group and constrained-path Monte Carlo results

J. Bonča, James E. Gubernatis, M. Guerrero, Eric Jeckelmann, Steven R. White

Published Feb 1, 2000• 30 citations

Abstract

DOI: 10.1103/physrevb.61.3251

Related papers

Stripes in a three-chain Hubbard ladder: a comparison of density-matrix renormalization group and constrained-path Monte Carlo results

J. Bonča, James E. Gubernatis, M. Guerrero +2 more

arXiv:cond-mat/9712018Dec 1, 19970 citations

Stripes in a Three-Chain Hubbard Ladder: a Comparison of Density-Matrix Renormalization Group and Constrained-Path Monte Carlo Results

J. Bonča, James E. Gubernatis, M. Guerrero +2 more

APSMar 1, 19980 citations

Stripe formation in doped Hubbard ladders

Georg Hager, Gerhard Wellein, Eric Jeckelmann +1 more

arXiv:cond-mat/0409321Physical Review BFeb 10, 200586 citations

Ground-state phase diagram of the one-dimensional extended Hubbard model: A density-matrix renormalization-group approach

G. P. Zhang

Physical review. B, Condensed matterOct 15, 199745 citations

Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

G. Ehlers, Steven R. White, R. M. Noack

arXiv:1701.03690Physical review. B./Physical review. BMar 21, 201790 citations

Study of the triangular-lattice Hubbard model with constrained-path quantum Monte Carlo

Shu Fay Ung, Ankit Mahajan, David R. Reichman

cond-mat.str-elCross-listedarXiv:2603.14808Physical review. B./Physical review. BMar 17, 20261 citation

Physical review. B, Condensed matter

Stripes in a three-chain Hubbard ladder: A comparison of density-matrix renormalization group and constrained-path Monte Carlo results

J. Bonča, James E. Gubernatis, M. Guerrero, Eric Jeckelmann, Steven R. White

Published Feb 1, 2000• 30 citations

Publisher

Abstract

Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we studied the ground-state energies and the spin and hole densities of a

12\ifmmode\times\else\texttimes\fi{}3

Hubbard model with open boundary conditions and six holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate U regimes. For

U/t>~6

we find a ground-state with charge inhomogeneities consistent with stripes.

DOI: 10.1103/physrevb.61.3251

Related papers

Stripes in a three-chain Hubbard ladder: a comparison of density-matrix renormalization group and constrained-path Monte Carlo results

J. Bonča, James E. Gubernatis, M. Guerrero +2 more

Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we have studied the ground-state energies and the spin and hole densities of a $12 \times 3$ Hubbard model with open boundary conditions and 6 holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate $U$ regimes. For $U/t \geq 6$ we find a ground-state with stripes.Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we have studied the ground-state energies and the spin and hole densities of a $12 \times 3$ Hubbard model with open boundary conditions and 6 holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate $U$ regimes. For $U/t \geq 6$ we find a ground-state with stripes.

arXiv:cond-mat/9712018Dec 1, 19970 citations

Stripes in a Three-Chain Hubbard Ladder: a Comparison of Density-Matrix Renormalization Group and Constrained-Path Monte Carlo Results

J. Bonča, James E. Gubernatis, M. Guerrero +2 more

Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we studied the ground-state energies and the spin and hole densities of a 12x3 Hubbard model with open boundary conditions and six holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate U regimes. For U/t{>=}6 we find a ground-state with charge inhomogeneities consistent with stripes. (c) 2000 The American Physical Society.Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we studied the ground-state energies and the spin and hole densities of a 12x3 Hubbard model with open boundary conditions and six holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate U regimes. For U/t{>=}6 we find a ground-state with charge inhomogeneities consistent with stripes. (c) 2000 The American Physical Society.

APSMar 1, 19980 citations

Stripe formation in doped Hubbard ladders

Georg Hager, Gerhard Wellein, Eric Jeckelmann +1 more

We investigate the formation of stripes in $7r\ifmmode\times\else\texttimes\fi{}6$ Hubbard ladders with $4r$ holes doped away from half filling using the density-matrix renormalization group (DMRG) method. A parallelized code allows us to keep enough density-matrix eigenstates (up to $m=8000$ ) and to study sufficiently large systems (with up to $7r=21$ rungs) to extrapolate the stripe amplitude to the limits of vanishing DMRG truncation error and infinitely long ladders. Our work gives strong evidence that stripes exist in the ground state for strong coupling $(U=12t)$ but that the structures found in the hole density at weaker coupling $(U=3t)$ are an artifact of the DMRG approach.We investigate the formation of stripes in $7r\ifmmode\times\else\texttimes\fi{}6$ Hubbard ladders with $4r$ holes doped away from half filling using the density-matrix renormalization group (DMRG) method. A parallelized code allows us to keep enough density-matrix eigenstates (up to $m=8000$) and to study sufficiently large systems (with up to $7r=21$ rungs) to extrapolate the stripe amplitude to the limits of vanishing DMRG truncation error and infinitely long ladders. Our work gives strong evidence that stripes exist in the ground state for strong coupling $(U=12t)$ but that the structures found in the hole density at weaker coupling $(U=3t)$ are an artifact of the DMRG approach.

arXiv:cond-mat/0409321Physical Review BFeb 10, 200586 citations

Ground-state phase diagram of the one-dimensional extended Hubbard model: A density-matrix renormalization-group approach

G. P. Zhang

We use the density-matrix renormalization group to calculate the phase diagram of the one-dimensional extended Hubbard chain at half filling. We find that for one specific $U,$ the critical value of ${V}_{c}$ for the charge-density-wave versus spin-density-wave phase transition is smaller than that predicted from the Monte Carlo simulation. Our results are consistent with the strong- and weak-coupling limit results, whereas the previous results from the Monte Carlo simulations deviate from the weak-coupling limit result. As $U$ increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at ${U}_{c}=4--6,$ not ${U}_{c}=3$ as previously predicted from the Monte Carlo simulation. Due to the topological difference, we observe that with the periodic boundary condition, the phase transition is more abrupt for finite chains of length $N=4M$ than for chains of $N=4M+2,$ where $M$ is an integer, for the same $U$ and $V.$ The difference will diminish in the thermodynamic limit.We use the density-matrix renormalization group to calculate the phase diagram of the one-dimensional extended Hubbard chain at half filling. We find that for one specific $U,$ the critical value of ${V}_{c}$ for the charge-density-wave versus spin-density-wave phase transition is smaller than that predicted from the Monte Carlo simulation. Our results are consistent with the strong- and weak-coupling limit results, whereas the previous results from the Monte Carlo simulations deviate from the weak-coupling limit result. As $U$ increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at ${U}_{c}=4--6,$ not ${U}_{c}=3$ as previously predicted from the Monte Carlo simulation. Due to the topological difference, we observe that with the periodic boundary condition, the phase transition is more abrupt for finite chains of length $N=4M$ than for chains of $N=4M+2,$ where $M$ is an integer, for the same $U$ and $V.$ The difference will diminish in the thermodynamic limit.

Physical review. B, Condensed matterOct 15, 199745 citations

Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

G. Ehlers, Steven R. White, R. M. Noack

The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid--real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at $n=0.875$ filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both $U/t=4.0$ and $8.0$ . We find that the strength of the charge ordering depends on $U/t$ and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid--real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at $n=0.875$ filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both $U/t=4.0$ and $8.0$. We find that the strength of the charge ordering depends on $U/t$ and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.

arXiv:1701.03690Physical review. B./Physical review. BMar 21, 201790 citations

Study of the triangular-lattice Hubbard model with constrained-path quantum Monte Carlo

Shu Fay Ung, Ankit Mahajan, David R. Reichman

We benchmark constrained-path Monte Carlo (CPMC) on the triangular-lattice Hubbard model for several fillings and $U$ values and show that symmetry-adapted trial wave functions substantially improve quantitative accuracy. Away from half-filling, simple free-electron-based trials that preserve the ground state symmetry yield energy deviations $\lesssim 1\%$ from exact diagonalization and density matrix renormalization group results. At half-filling, strong frustration in the intermediate to large $U$ regimes necessitates symmetry-projected trials to reach comparable accuracy, where both free-electron and symmetry-broken Hartree-Fock trials incur substantial constraint bias. Since the computational cost of CPMC with symmetry projection scales polynomially with system size, our results motivate its use as a practical route for studying competing ground states in strongly correlated, frustrated systems.We benchmark constrained-path Monte Carlo (CPMC) on the triangular-lattice Hubbard model for several fillings and $U$ values and show that symmetry-adapted trial wave functions substantially improve quantitative accuracy. Away from half-filling, simple free-electron-based trials that preserve the ground state symmetry yield energy deviations $\lesssim 1\%$ from exact diagonalization and density matrix renormalization group results. At half-filling, strong frustration in the intermediate to large $U$ regimes necessitates symmetry-projected trials to reach comparable accuracy, where both free-electron and symmetry-broken Hartree-Fock trials incur substantial constraint bias. Since the computational cost of CPMC with symmetry projection scales polynomially with system size, our results motivate its use as a practical route for studying competing ground states in strongly correlated, frustrated systems.

cond-mat.str-elCross-listedarXiv:2603.14808Physical review. B./Physical review. BMar 17, 20261 citation

Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we studied the ground-state energies and the spin and hole densities of a

12\ifmmode\times\else\texttimes\fi{}3

Hubbard model with open boundary conditions and six holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate U regimes. For

U/t>~6

we find a ground-state with charge inhomogeneities consistent with stripes.

Using both the density-matrix renormalization group method and the constrained-path quantum Monte Carlo method, we have studied the ground-state energies and the spin and hole densities of a

12 \times 3

Hubbard model with open boundary conditions and 6 holes doped away from half-filling. Results obtained with these two methods agree well in the small and intermediate

U

regimes. For

U/t \geq 6

we find a ground-state with stripes.

We investigate the formation of stripes in $7r\ifmmode\times\else\texttimes\fi{}6$ Hubbard ladders with

4r

holes doped away from half filling using the density-matrix renormalization group (DMRG) method. A parallelized code allows us to keep enough density-matrix eigenstates (up to

m=8000

) and to study sufficiently large systems (with up to

7r=21

rungs) to extrapolate the stripe amplitude to the limits of vanishing DMRG truncation error and infinitely long ladders. Our work gives strong evidence that stripes exist in the ground state for strong coupling

(U=12t)

but that the structures found in the hole density at weaker coupling

(U=3t)

are an artifact of the DMRG approach.

We use the density-matrix renormalization group to calculate the phase diagram of the one-dimensional extended Hubbard chain at half filling. We find that for one specific

U,

the critical value of

{V}_{c}

for the charge-density-wave versus spin-density-wave phase transition is smaller than that predicted from the Monte Carlo simulation. Our results are consistent with the strong- and weak-coupling limit results, whereas the previous results from the Monte Carlo simulations deviate from the weak-coupling limit result. As

U

increases, we find that the first-order phase transition develops gradually. The tricritical point is estimated to occur at

{U}_{c}=4--6,

not

{U}_{c}=3

as previously predicted from the Monte Carlo simulation. Due to the topological difference, we observe that with the periodic boundary condition, the phase transition is more abrupt for finite chains of length

N=4M

than for chains of

N=4M+2,

where

M

is an integer, for the same

U

and

V.

The difference will diminish in the thermodynamic limit.

n=0.875

filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both

U/t=4.0

and

8.0

. We find that the strength of the charge ordering depends on

U/t

and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.

We benchmark constrained-path Monte Carlo (CPMC) on the triangular-lattice Hubbard model for several fillings and

U

values and show that symmetry-adapted trial wave functions substantially improve quantitative accuracy. Away from half-filling, simple free-electron-based trials that preserve the ground state symmetry yield energy deviations

\lesssim 1\%

from exact diagonalization and density matrix renormalization group results. At half-filling, strong frustration in the intermediate to large

U

regimes necessitates symmetry-projected trials to reach comparable accuracy, where both free-electron and symmetry-broken Hartree-Fock trials incur substantial constraint bias. Since the computational cost of CPMC with symmetry projection scales polynomially with system size, our results motivate its use as a practical route for studying competing ground states in strongly correlated, frustrated systems.