arXiv:cond-mat/9705156 · Physical review. B, Condensed matter

Phase separation of the two-dimensional t−J model

C. T. Shih, Y. C. Chen, Ting-Kuo Lee

Published Jan 1, 1998• 42 citations

Abstract

The boundary of phase separation of the two-dimensional $t\ensuremath{-}J$ model is investigated by the power-Lanczos method and Maxwell construction. The method is similar to a variational approach and it determines the lower bound of the phase-separation boundary with ${J}_{c}/t=0.6\ifmmode\pm\else\textpm\fi{}0.1$ in the limit ${n}_{e}\ensuremath{\sim}1.$ In the physically interesting regime of high-${T}_{c}$ superconductors where $0.3<J/t<0.5$ there is no phase separation.

DOI: 10.1103/physrevb.57.627

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Ground-state properties of the two-dimensional t-J model

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Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method

C.T Shih, Y.C Chen, T.K Lee

arXiv:cond-mat/0104067Journal of Physics and Chemistry of SolidsSep 1, 200110 citations

Phase separation based on a U(1) slave-boson functional integral approach to the t−J model

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Green’s-function Monte Carlo for lattice fermions: Application to the t−J model

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Limits on phase separation for two-dimensional strongly correlated electrons

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Superconductivity near phase separation in models of correlated electrons

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arXiv:cond-mat/9705156 · Physical review. B, Condensed matter

Phase separation of the two-dimensional t−J model

C. T. Shih, Y. C. Chen, Ting-Kuo Lee

Published Jan 1, 1998• 42 citations

arXiv HTML PDF

Abstract

The boundary of phase separation of the two-dimensional

t\ensuremath{-}J

model is investigated by the power-Lanczos method and Maxwell construction. The method is similar to a variational approach and it determines the lower bound of the phase-separation boundary with

{J}_{c}/t=0.6\ifmmode\pm\else\textpm\fi{}0.1

in the limit

{n}_{e}\ensuremath{\sim}1.

In the physically interesting regime of high-

{T}_{c}

superconductors where

0.3<J/t<0.5

there is no phase separation.

DOI: 10.1103/physrevb.57.627

Related papers

Ground-state properties of the two-dimensional t-J model

Masanori Kohno

The two-dimensional t-J model in the ground state is investigated by the power Lanczos method. The pairing-pairing correlation function for ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave symmetry is enhanced in the realistic parameter regime for high- ${\mathrm{T}}_{\mathrm{c}}$ superconductors. The charge susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$ shows divergent behavior as ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling for the doping concentration \ensuremath{\delta}, indicating that the value of the dynamical exponent z is four under the assumption of hyperscaling. The peak height of the spin structure factor ${\mathrm{S}}_{\mathrm{max}}$ (Q) also behaves as ${\mathrm{S}}_{\mathrm{max}}$ (Q)\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling, which leads to the divergence of the antiferromagnetic correlation length ${\ensuremath{\xi}}_{\mathrm{m}}$ as ${\ensuremath{\xi}}_{\mathrm{m}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1\mathrm{/}2}$. The boundary of phase separation is estimated on the basis of the Maxwell construction. Numerical results are compared with experimental features observed in high- ${\mathrm{T}}_{\mathrm{c}}$ cuprates.The two-dimensional t-J model in the ground state is investigated by the power Lanczos method. The pairing-pairing correlation function for ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$-wave symmetry is enhanced in the realistic parameter regime for high-${\mathrm{T}}_{\mathrm{c}}$ superconductors. The charge susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$ shows divergent behavior as ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling for the doping concentration \ensuremath{\delta}, indicating that the value of the dynamical exponent z is four under the assumption of hyperscaling. The peak height of the spin structure factor ${\mathrm{S}}_{\mathrm{max}}$(Q) also behaves as ${\mathrm{S}}_{\mathrm{max}}$(Q)\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling, which leads to the divergence of the antiferromagnetic correlation length ${\ensuremath{\xi}}_{\mathrm{m}}$ as ${\ensuremath{\xi}}_{\mathrm{m}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1\mathrm{/}2}$. The boundary of phase separation is estimated on the basis of the Maxwell construction. Numerical results are compared with experimental features observed in high-${\mathrm{T}}_{\mathrm{c}}$ cuprates.

arXiv:cond-mat/9610081Physical review. B, Condensed matterJan 15, 199759 citations

Revisit phase separation of the two-dimensional t-J model by the power-Lanczos method

C.T Shih, Y.C Chen, T.K Lee

arXiv:cond-mat/0104067Journal of Physics and Chemistry of SolidsSep 1, 200110 citations

Phase separation based on a U(1) slave-boson functional integral approach to the t−J model

Tae-Hyoung Gimm, Sung‐Ho Suck Salk

Based on the U(1) slave-boson functional integral approach to the $t\ensuremath{-}J$ model Hamiltonian, we investigate the phase diagram of phase separation for the hole-doped two-dimensional system of antiferromagnets. We discuss the phase separation (into a hole-rich and a hole-free phase) as a function of $J/t$ where J is the Heisenberg (antiferromagnetic) coupling constant and t the hopping energy. For the physically interesting region of relatively small Heisenberg coupling, $0<J/t<0.2,$ we find that the phase separation occurs in a region of hole doping concentration below ${x}_{c}\ensuremath{\sim}0.1$ and that in the same region the critical hole doping concentrations remain robust with nearest-neighbor hole-hole repulsive interactions. On the other hand, in the region of larger $J/t$ the phase separation boundary is found to be highly sensitive to the variation of the repulsive hole-hole interactions. In agreement with other studies, we find that the phase separation occurs at a critical value of ${J}_{c}\ensuremath{\approx}3.4t$ corresponding to the critical hole concentration ${x}_{c}=1.$ Based on the U(1) slave-boson functional integral approach to the $t\ensuremath{-}J$ model Hamiltonian, we investigate the phase diagram of phase separation for the hole-doped two-dimensional system of antiferromagnets. We discuss the phase separation (into a hole-rich and a hole-free phase) as a function of $J/t$ where J is the Heisenberg (antiferromagnetic) coupling constant and t the hopping energy. For the physically interesting region of relatively small Heisenberg coupling, $0<J/t<0.2,$ we find that the phase separation occurs in a region of hole doping concentration below ${x}_{c}\ensuremath{\sim}0.1$ and that in the same region the critical hole doping concentrations remain robust with nearest-neighbor hole-hole repulsive interactions. On the other hand, in the region of larger $J/t$ the phase separation boundary is found to be highly sensitive to the variation of the repulsive hole-hole interactions. In agreement with other studies, we find that the phase separation occurs at a critical value of ${J}_{c}\ensuremath{\approx}3.4t$ corresponding to the critical hole concentration ${x}_{c}=1.$

arXiv:cond-mat/9909409Physical review. B, Condensed matterDec 1, 200012 citations

Green’s-function Monte Carlo for lattice fermions: Application to the t−J model

C. Stephen Hellberg, Efstratios Manousakis

We develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.We develop a general numerical method to study the zero-temperature properties of strongly correlated electron models on large lattices. The technique, which resembles Green's-function Monte Carlo, projects the ground-state component from a trial wave function with no approximations. We use this method to determine the phase diagram of the two-dimensional $t\ensuremath{-}J$ model, using the Maxwell construction to investigate electronic phase separation. The shell effects of fermions on finite-sized periodic lattices are minimized by keeping the number of electrons fixed at a closed-shell configuration and varying the size of the lattice. Results obtained for various electron numbers corresponding to different closed shells indicate that the finite-size effects in our calculation are small. For any value of interaction strength, we find that there is always a value of the electron density above which the system can lower its energy by forming a two-component phase separated state. Our results are compared with other calculations on the $t\ensuremath{-}J$ model. We find that the most accurate results are consistent with phase separation at all interaction strengths.

arXiv:cond-mat/9911071Physical review. B, Condensed matterMay 1, 200046 citations

Limits on phase separation for two-dimensional strongly correlated electrons

W. O. Putikka, Marco U. Luchini

From calculations of the high-temperature series for the free energy of the two-dimensional t- $J$ model we construct a series for ratios of the free energy per hole. The ratios can be extrapolated very accurately to low temperatures and used to investigate phase separation. Our results confirm that phase separation occurs only for $J/t\ensuremath{\gtrsim}1.2.$ Also, the phase transition into the phase-separated state has ${T}_{c}\ensuremath{\approx}0.25J$ for large $J/t.$ From calculations of the high-temperature series for the free energy of the two-dimensional t-$J$ model we construct a series for ratios of the free energy per hole. The ratios can be extrapolated very accurately to low temperatures and used to investigate phase separation. Our results confirm that phase separation occurs only for $J/t\ensuremath{\gtrsim}1.2.$ Also, the phase transition into the phase-separated state has ${T}_{c}\ensuremath{\approx}0.25J$ for large $J/t.$

arXiv:cond-mat/9912294Physical review. B, Condensed matterJul 15, 200023 citations

Superconductivity near phase separation in models of correlated electrons

Elbio R. Dagotto, José A. Riera, Y.-C. Chen +4 more

Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ , but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high- ${\mathit{T}}_{\mathit{c}}$ cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-${\mathit{T}}_{\mathit{c}}$ cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.

arXiv:cond-mat/9309028Physical review. B, Condensed matterFeb 1, 1994129 citations

The boundary of phase separation of the two-dimensional

t\ensuremath{-}J

model is investigated by the power-Lanczos method and Maxwell construction. The method is similar to a variational approach and it determines the lower bound of the phase-separation boundary with

{J}_{c}/t=0.6\ifmmode\pm\else\textpm\fi{}0.1

in the limit

{n}_{e}\ensuremath{\sim}1.

In the physically interesting regime of high-

{T}_{c}

superconductors where

0.3<J/t<0.5

there is no phase separation.

{\mathrm{T}}_{\mathrm{c}}

superconductors. The charge susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$ shows divergent behavior as ${\mathrm{\ensuremath{\chi}}}_{\mathrm{c}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling for the doping concentration \ensuremath{\delta}, indicating that the value of the dynamical exponent z is four under the assumption of hyperscaling. The peak height of the spin structure factor

{\mathrm{S}}_{\mathrm{max}}

(Q) also behaves as

{\mathrm{S}}_{\mathrm{max}}

(Q)\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1}$ near half filling, which leads to the divergence of the antiferromagnetic correlation length ${\ensuremath{\xi}}_{\mathrm{m}}$ as ${\ensuremath{\xi}}_{\mathrm{m}}$\ensuremath{\propto}${\mathrm{\ensuremath{\delta}}}^{\mathrm{\ensuremath{-}}1\mathrm{/}2}$. The boundary of phase separation is estimated on the basis of the Maxwell construction. Numerical results are compared with experimental features observed in high-

{\mathrm{T}}_{\mathrm{c}}

cuprates.

J/t

where J is the Heisenberg (antiferromagnetic) coupling constant and t the hopping energy. For the physically interesting region of relatively small Heisenberg coupling,

0<J/t<0.2,

we find that the phase separation occurs in a region of hole doping concentration below ${x}_{c}\ensuremath{\sim}0.1$ and that in the same region the critical hole doping concentrations remain robust with nearest-neighbor hole-hole repulsive interactions. On the other hand, in the region of larger

J/t

the phase separation boundary is found to be highly sensitive to the variation of the repulsive hole-hole interactions. In agreement with other studies, we find that the phase separation occurs at a critical value of ${J}_{c}\ensuremath{\approx}3.4t$ corresponding to the critical hole concentration

{x}_{c}=1.

From calculations of the high-temperature series for the free energy of the two-dimensional t-

J

model we construct a series for ratios of the free energy per hole. The ratios can be extrapolated very accurately to low temperatures and used to investigate phase separation. Our results confirm that phase separation occurs only for $J/t\ensuremath{\gtrsim}1.2.$ Also, the phase transition into the phase-separated state has ${T}_{c}\ensuremath{\approx}0.25J$ for large

J/t.

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-

{\mathit{T}}_{\mathit{c}}

cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.