arXiv:cond-mat/9611195 · Physical Review Letters

Phase Separation at all Interaction Strengths in thet-JModel

C. Stephen Hellberg, Efstratios Manousakis

Published Jun 16, 1997• 137 citations

Abstract

We investigate the phase diagram of the two-dimensional t-J model using a recently developed Green's function Monte Carlo method for lattice fermions. We use the technique to calculate exact ground-state energies of the model on large lattices. In contrast to many previous studies, we find the model phase separates for all values of $J/t$. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.

DOI: 10.1103/physrevlett.78.4609

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arXiv:cond-mat/9611195 · Physical Review Letters

Phase Separation at all Interaction Strengths in thet-JModel

C. Stephen Hellberg, Efstratios Manousakis

Published Jun 16, 1997• 137 citations

arXiv HTML PDF

Abstract

J/t

. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.

DOI: 10.1103/physrevlett.78.4609

Related papers

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.

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We show how the Green's function Monte Carlo method can be used to compute accurately the ground-state energy of two-dimensional t-J model for lattices of large size. This is demonstrated for the case of a single hole, with the aid of suitable initial and guidance functions. Our transient estimates for the ground-state energy of the 4\ifmmode\times\else\texttimes\fi{}4 lattice are in remarkable agreement with the exact values; we report results for lattices of significantly larger size than 4\ifmmode\times\else\texttimes\fi{}4.We show how the Green's function Monte Carlo method can be used to compute accurately the ground-state energy of two-dimensional t-J model for lattices of large size. This is demonstrated for the case of a single hole, with the aid of suitable initial and guidance functions. Our transient estimates for the ground-state energy of the 4\ifmmode\times\else\texttimes\fi{}4 lattice are in remarkable agreement with the exact values; we report results for lattices of significantly larger size than 4\ifmmode\times\else\texttimes\fi{}4.

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A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of ${J}_{z},$ at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any ${J}_{z}>0.$ The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.A theoretical investigation of boson versions of the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}_{z}$ models on the square lattice is carried out, by means of Green's function Monte Carlo simulations. Accurate ground-state energy estimates as a function of hole doping are obtained, allowing one to investigate the stability of the uniform phase against separation of the system into hole-rich and hole-free phases. In the boson $t\ensuremath{-}{J}_{z}$ model, such a separation is found to occur for arbitrarily small values of ${J}_{z},$ at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any ${J}_{z}>0.$ The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.

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Two-holed-wave binding in the physical region of thet-Jmodel: A Green’s-function Monte Carlo study

Massimo Boninsegni, Efstratios Manousakis

We investigate numerically the ground state of two holes with ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value ${\mathit{J}}_{\mathit{c}}$ \ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J ${\mathit{J}}_{\mathit{c}}$ .We investigate numerically the ground state of two holes with ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value ${\mathit{J}}_{\mathit{c}}$\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J${\mathit{J}}_{\mathit{c}}$.

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Phase separation in the two-dimensional Hubbard model: A fixed-node quantum Monte Carlo study

Andrea C. Cosentini, Massimo Capone, Leonardo Guidoni +1 more

Fixed-node Green's-function Monte Carlo calculations have been performed for very large 16\ifmmode\times\else\texttimes\fi{}16 two-dimensional Hubbard lattices, large interaction strengths $U=10,20,$ and $40$ , and many $(15\ensuremath{\sim}20)$ densities between empty and half-filling. The nodes were fixed by a simple Slater-Gutzwiller trial wave function. For each value of U we obtained a sequence of ground-state energies which is consistent with the possibility of a phase separation close to half-filling, with a hole density in the hole-rich phase which is a decreasing function of $U$ . The energies suffer, however, from a fixed-node bias: more accurate nodes are needed to confirm this picture. Our extensive numerical results and their test against size, shell, shape, and boundary-condition effects also suggest that phase separation is quite a delicate issue, on which simulations based on smaller lattices than considered here are unlikely to give reliable predictions.Fixed-node Green's-function Monte Carlo calculations have been performed for very large 16\ifmmode\times\else\texttimes\fi{}16 two-dimensional Hubbard lattices, large interaction strengths $U=10,20,$ and $40$, and many $(15\ensuremath{\sim}20)$ densities between empty and half-filling. The nodes were fixed by a simple Slater-Gutzwiller trial wave function. For each value of U we obtained a sequence of ground-state energies which is consistent with the possibility of a phase separation close to half-filling, with a hole density in the hole-rich phase which is a decreasing function of $U$. The energies suffer, however, from a fixed-node bias: more accurate nodes are needed to confirm this picture. Our extensive numerical results and their test against size, shell, shape, and boundary-condition effects also suggest that phase separation is quite a delicate issue, on which simulations based on smaller lattices than considered here are unlikely to give reliable predictions.

arXiv:cond-mat/9801299Physical review. B, Condensed matterDec 1, 199835 citations

J/t

. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.

242

lattice sites. By studying the energy as a function of hole doping we conclude that there is no phase separation in the physical region relevant for high-

{T}_{c}

superconductors. This finding is further supported by the hole-hole correlation function calculation. Remarkably, near the phase separation instability, for ${J}_{c}/t\ensuremath{\sim}0.5$ this function displays enhanced fluctuations at incommensurate wave vectors that scale linearly with the doping, in agreement with experimental findings.

{J}_{z},

at sufficiently low hole doping. Phase separation is suppressed in the boson $t\ensuremath{-}J$ model, which features a uniform ground state at any doping, for $J/t\ensuremath{\lesssim}1.5.$ Relevance of this study to the corresponding fermion models is discussed. Fermi statistics enhances the tendency toward phase separation; in particular, phase separation at low doping is predicted in the fermion $t\ensuremath{-}{J}_{z}$ model at any

{J}_{z}>0.

The possible formation of stripes of holes is investigated for systems featuring both periodic and cylindrical boundary conditions. No evidence of a striped ground state is found in either the $t\ensuremath{-}J$ or $t\ensuremath{-}{J}_{z}$ boson models.

We investigate numerically the ground state of two holes with

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

{\mathit{y}}^{2}

symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value

{\mathit{J}}_{\mathit{c}}

\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J

{\mathit{J}}_{\mathit{c}}

Fixed-node Green's-function Monte Carlo calculations have been performed for very large 16\ifmmode\times\else\texttimes\fi{}16 two-dimensional Hubbard lattices, large interaction strengths

U=10,20,

and

40

, and many $(15\ensuremath{\sim}20)$ densities between empty and half-filling. The nodes were fixed by a simple Slater-Gutzwiller trial wave function. For each value of U we obtained a sequence of ground-state energies which is consistent with the possibility of a phase separation close to half-filling, with a hole density in the hole-rich phase which is a decreasing function of

U

. The energies suffer, however, from a fixed-node bias: more accurate nodes are needed to confirm this picture. Our extensive numerical results and their test against size, shell, shape, and boundary-condition effects also suggest that phase separation is quite a delicate issue, on which simulations based on smaller lattices than considered here are unlikely to give reliable predictions.