arXiv:2001.04951 · Physical Review Research

Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory

Zhi‐Hao Cui, Chong Sun, Ushnish Ray, Bo-Xiao Zheng, Qiming Sun, Garnet Kin‐Lic Chan

Published Nov 19, 2020• 47 citations

Abstract

The authors use a density matrix embedding theory to characterize the ground-state phase diagram of the three-band Hubbard model, and focus on the atomic-scale nature of the antiferromagnetic and superconducting orders by including the oxygen degrees of freedom.

DOI: 10.1103/physrevresearch.2.043259

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arXiv:2001.04951 · Physical Review Research

Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory

Zhi‐Hao Cui, Chong Sun, Ushnish Ray, Bo-Xiao Zheng, Qiming Sun, Garnet Kin‐Lic Chan

Published Nov 19, 2020• 47 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevresearch.2.043259

Related papers

Ground-state phase diagram of the three-band Hubbard model in various parametrizations from density matrix embedding theory

Zhi‐Hao Cui, Chong Sun, Ushnish Ray +3 more

We compute the ground-state phase diagram of the three-band Hubbard model in various published parametrizations using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AF) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. In the case of the AF order, as expected, the local magnetic moment localizes entirely at the copper sites and decays with doping, while in the SC phase we observe a local $p_{x (y)}$ [or $d_{xz (yz)}$ ]-symmetry modulation of the pair density on the Cu-O bonds within the larger scale $d_{x^2 - y^2}$ -wave SC pairing order between Cu-Cu and O-O. While all parametrizations of the model display AF and SC phases, the decay of AF order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AF and SC orders occurs in all parameter sets. Our work highlights the importance of the oxygen degrees of freedom in the study of atomic-scale SC orders, as well as the necessity of re-evaluating current parametrizations of the three-band Hubbard model.We compute the ground-state phase diagram of the three-band Hubbard model in various published parametrizations using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AF) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. In the case of the AF order, as expected, the local magnetic moment localizes entirely at the copper sites and decays with doping, while in the SC phase we observe a local $p_{x (y)}$ [or $d_{xz (yz)}$]-symmetry modulation of the pair density on the Cu-O bonds within the larger scale $d_{x^2 - y^2}$-wave SC pairing order between Cu-Cu and O-O. While all parametrizations of the model display AF and SC phases, the decay of AF order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AF and SC orders occurs in all parameter sets. Our work highlights the importance of the oxygen degrees of freedom in the study of atomic-scale SC orders, as well as the necessity of re-evaluating current parametrizations of the three-band Hubbard model.

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Takashi Yanagisawa

We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$ , where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion $U$ , the band parameter $t'$ and the electron density $n_e$ . We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $ψ=\exp(-λK)P_Gψ_0$, where $ψ_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $λ$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion $U$, the band parameter $t'$ and the electron density $n_e$. We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.

arXiv:1903.09368Journal of the Physical Society of JapanApr 5, 201913 citations

p_{x (y)}

[or

d_{xz (yz)}

]-symmetry modulation of the pair density on the Cu-O bonds within the larger scale

d_{x^2 - y^2}

-wave SC pairing order between Cu-Cu and O-O. While all parametrizations of the model display AF and SC phases, the decay of AF order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AF and SC orders occurs in all parameter sets. Our work highlights the importance of the oxygen degrees of freedom in the study of atomic-scale SC orders, as well as the necessity of re-evaluating current parametrizations of the three-band Hubbard model.

{T}_{c}

in the cuprates and on the scale of contributions in real materials that are neglected in the Hubbard model.

U

at ${U}_{\mathrm{c}1}\ensuremath{\sim}7.8t$ and ${U}_{\mathrm{c}2}\ensuremath{\sim}9.9t$ (

t

being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for $0\ensuremath{\le}U<{U}_{\mathrm{c}1}$ implies a metallic phase in this regime. For

U>{U}_{\mathrm{c}2}

, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the ${120}^{\ensuremath{\circ}}$ N\'eel-ordered state realized in the limit of $U\ensuremath{\rightarrow}\ensuremath{\infty}$. For

{U}_{\mathrm{c}1}<U<{U}_{\mathrm{c}2}

, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the

\mathrm{K}

and ${\mathrm{K}}^{\ensuremath{'}}$ points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing

U

and thus the superconductivity is unlikely in the intermediate phase.

ψ=\exp(-λK)P_Gψ_0

, where

ψ_0

is a one-particle state,

P_G

is the Gutzwiller operator,

K

is the kinetic operator, and

λ

is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion

U

, the band parameter

t'

and the electron density

n_e

. We show a phase diagram that includes superconducting and antiferromagnetic phases and that

t'=0

is most favorable for superconductivity.