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Physical Review Letters

Phase separation in thet-Jmodel

Victor J. Emery, Steven Allan Kivelson, H. Q. Lin

Published Jan 22, 1990• 872 citations
Publisher

Abstract

It is shown that, for the t-J model, dilute holes in an antiferromagnet are unstable against phase separation into a hole-rich and a no-hole phase. When the spin-exchange interaction J exceeds a critical value ${J}_{c}$, the hole-rich phase has no electrons. It is proposed that for J slightly less than ${J}_{c}$ the hole-rich phase is a low-density superfluid of electron pairs. A brief discussion of phase separation in other related models is given.

DOI
10.1103/physrevlett.64.475

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The bound state of electron pairs in the t-J model is investigated. It is shown that for 2t<J<3.828t the hole-rich phase is a low-density superfluid of electron pairs.Received 1 April 1991DOI:https://doi.org/10.1103/PhysRevB.44.4674©1991 American Physical Society

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Physical review. B, Condensed matter•May 1, 1992•13 citations
It is shown that, for the t-J model, dilute holes in an antiferromagnet are unstable against phase separation into a hole-rich and a no-hole phase. When the spin-exchange interaction J exceeds a critical value Jc{J}_{c}Jc​, the hole-rich phase has no electrons. It is proposed that for J slightly less than Jc{J}_{c}Jc​ the hole-rich phase is a low-density superfluid of electron pairs. A brief discussion of phase separation in other related models is given.
We study the phase diagram of the two-dimensional t-J-V model of holes in a two-dimensional antiferromagnet in the J\ensuremath{\gg}t limit. Here t is the hole hopping parameter, J is the exchange coupling between nearest-neighbor spins, and V is the nearest-neighbor electron-electron repulsion. We also include the possibility of Heisenberg-Ising anisotropy, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\ne}Jz{\mathit{J}}_{\mathit{z}}Jz​. We obtain a complete description for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\ll}Jz{\mathit{J}}_{\mathit{z}}Jz​ and approximate results for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$=Jz{\mathit{J}}_{\mathit{z}}Jz​. There is no region of the zero-temperature phase diagram that supports a dilute gas of holes in an antiferromagnet. Rather, the system always phase separates into hole-rich and no-hole phases, a result we believe to be more general than the model we have considered. We find various hole-crystal phases and, at high hole density, we find a ``Fermi-liquid'' phase and at least two superfluid phases, one with a charge 2e and one with a charge 4e order parameter.
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/tJ/tJ/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<0.2,0<J/t<0.2,0<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/tJ/tJ/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 xc=1.{x}_{c}=1.xc​=1.
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/tJ/tJ/t. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.