Proceedings of the Samahang Pisika ng Pilipinas

Correlations in an extended Hubbard model with Ising-like interaction

Robertson C. Esperanza, Francis N. C. Paraan

Published May 13, 2017• 0 citations

Abstract

Density-density and spin-spin correlations are calculated in an extended Hubbard model with an intersite Ising-like interaction. Local expectation values and correlation functions involving charge density and magnetization are obtained using the density matrix renormalization group (DMRG) for a periodic chain of L = 10 sites at half-filling. Antiferromagnetic phases with spin and charge density modulation are identified and located in a phase diagram.

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Proceedings of the Samahang Pisika ng Pilipinas

Correlations in an extended Hubbard model with Ising-like interaction

Robertson C. Esperanza, Francis N. C. Paraan

Published May 13, 2017• 0 citations

OpenAlex

Abstract

Related papers

A DMRG study of the half-filled Hubbard model on a Bethe lattice: a signature of the Mott-Hubbard transition

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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

Accurate ground-state phase diagram of the one-dimensional extended Hubbard model at half filling

G. P. Zhang

It has been well established that in both the weak- and strong-coupling limits, the phase transition from a spin-density wave (SDW) to a charge-density wave (CDW) in the half-filled extended-Hubbard model occurs precisely at the ratio ${U/V}_{c}=2,$ where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.It has been well established that in both the weak- and strong-coupling limits, the phase transition from a spin-density wave (SDW) to a charge-density wave (CDW) in the half-filled extended-Hubbard model occurs precisely at the ratio ${U/V}_{c}=2,$ where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.

Physical review. B, Condensed matterOct 2, 200328 citations

The half-filled Hubbard model on the Bethe lattice with coordination number

z=3

is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy

E

, average local magnetization $ $, its fluctuations $ - ^2$ and various spin correlation functions $ - $ are determined as a function of the Coulomb interaction strength

U/t

. The calculated local magnetic moments $ $ increase monotonically with increasing Coulomb repulsion

U/t

forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large

U/t

, $ $ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins (

| |\simeq 0.35

for

U/t\to +\infty

). $ - ^2$ shows a maximum for

U/t=2.4

--2.9 which results from the interplay between the usual increase of $ $ with increasing

U/t

and the formation of important permanent moments $ $ at large

U/t

. NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of

U/t

. The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction

{T}^{*}

is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.

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.

{U/V}_{c}=2,

where U and V are the on-site and intersite electron-electron interactions, respectively. However, a recent density-matrix renormalization group (DMRG) study and a previous Monte Carlo simulation jointly suggest a picture that challenges the well-established weak-coupling result. Here, a careful calculation shows such a picture is questionable. In particular, it clarifies the DMRG result, even with a moderate number of states kept in the density matrix, agrees with both the weak- and strong-coupling findings, and predicts a CDW/SDW phase boundary smoothly links those two coupling limits. Possible sources of these previous failures are discussed.