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Physical Review Letters

Phase Separation in Mixtures of Hard Core Bosons

Massimo Boninsegni

Published Aug 1, 2001• 53 citations
Publisher

Abstract

A theoretical investigation of boson versions of the t-J and t-J(z) models on the square lattice is carried out. In the t-J(z) model, phase separation between a hole-rich and a hole-free phase occurs, at sufficiently low hole doping, for arbitrarily small values of J(z). The boson t-J model, instead, features a uniform ground state at any doping for J/t< or =1.5. No evidence of a striped ground state is found. Relevance of this study to the corresponding fermion models is discussed. Fermi statistics is found to enhance the tendency toward phase separation; in particular, phase separation is predicted, at low doping, in the fermion t-J(z) model, at all values of J(z).

DOI
10.1103/physrevlett.87.087201

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We use the t-t'- U model as a model for the normal states of the electron and hole doped high temperature superconductors. We solve this model on a 4 x 4 square lattice using exact diagonalizat ion. We focus on two controversial issues: the possibility of phase separation and the validity of the rigid band approximation for both hole doped and electron doped system. To study the possibility of phase separation, we calculate the binding energies of carrier clusters as well as the chemical potentials at different carrier concentrations. For the hole doped system, evidence of phase separation is found in the strong coupling regime, but not in the intermediate coupling regime. For electron doped system, tendency towards carrier pairing instead of phase separation is found. To study the validity of the rigid band approximation, we calculate the momentum distributions and the spectral functions. We find that the rigid band filling picture describes the electron doped system well. For the hole doped system, redistribution of particle density in momentum space occurs on doping. This implies that many body effect is significant and the rigid band filling picture may not be valid in the hole doped system.

•Jan 1, 1996•0 citations
A theoretical investigation of boson versions of the t-J and t-J(z) models on the square lattice is carried out. In the t-J(z) model, phase separation between a hole-rich and a hole-free phase occurs, at sufficiently low hole doping, for arbitrarily small values of J(z). The boson t-J model, instead, features a uniform ground state at any doping for J/t< or =1.5. No evidence of a striped ground state is found. Relevance of this study to the corresponding fermion models is discussed. Fermi statistics is found to enhance the tendency toward phase separation; in particular, phase separation is predicted, at low doping, in the fermion t-J(z) model, at all values of J(z).
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 Jz,{J}_{z},Jz​, 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 Jz>0.{J}_{z}>0.Jz​>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.
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 have studied by quantum Monte Carlo simulations the low temperature phase diagram of a mixture of isotopic, hard core bosons, described by the $t\text{\ensuremath{-}}{J}_{z}\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}$ model, with ${J}_{\ensuremath{\perp}}=\ensuremath{\alpha}{J}_{z}$. The coexistence of superfluid hole-rich and insulating, antiferromagnetically ordered hole-free phases is observed at sufficiently low hole density for any $\ensuremath{\alpha}<1$. A two-component checkerboard supersolid phase is not observed. The experimental relevance and possible broader implications of these findings are discussed.
Effective models of hard-core hole pair bosons and triplets are derived from the $t\ensuremath{-}J$ model in ladders and on the square lattice by performing a change from site to dimer basis. The Hilbert space is truncated by projecting out single-occupied electron states and only nearest-neighbor interactions are retained. The resulting effective models in one and two dimensions are studied by numerical techniques. In both spatial dimensions, the main result is that each hole pair is surrounded by a singlet cloud expelling triplet excitations from its vicinity. It is suggested an interpretation of this feature as a phase-separated state between a hole-pair-rich singlet phase and an undoped triplet phase with antiferromagnetic correlations. The possible relevance of this result to other theoretical scenarios and experimental results is discussed.
We study the phase diagram of two different mixed-dimensional $t\text{\ensuremath{-}}{J}_{z}\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}$ models on the square lattice, in which the hopping amplitude ttt is only nonzero along the xxx direction. In the first model, which is bosonic, the spin-exchange amplitude ${J}_{\ensuremath{\perp}}$ is negative and isotropic along the xxx and yyy directions of the lattice, and Jz{J}_{z}Jz​ is isotropic and positive. The low-energy physics is characterized by spin-charge separation: the holes hop as free fermions in an easy-plane ferromagnetic background. In the second model, ${J}_{\ensuremath{\perp}}$ is restricted to the xxx axis while Jz{J}_{z}Jz​ remains isotropic and positive. The model is agnostic to particle statistics, and shows stripe patterns with antiferromagnetic N\'eel order at low temperature and high hole densities, in resemblance of the mixed-dimensional $t\text{\ensuremath{-}}{J}_{z}$ and $t\text{\ensuremath{-}}J$ models. At lower hole density, a very strong first-order transition and hysteresis loop is seen extending to a remarkably high 14(1)% hole doping.
We use the t-t'- U model as a model for the normal states of the electron and hole doped high temperature superconductors. We solve this model on a 4 x 4 square lattice using exact diagonalizat ion. We focus on two controversial issues: the possibility of phase separation and the validity of the rigid band approximation for both hole doped and electron doped system. To study the possibility of phase separation, we calculate the binding energies of carrier clusters as well as the chemical potentials at different carrier concentrations. For the hole doped system, evidence of phase separation is found in the strong coupling regime, but not in the intermediate coupling regime. For electron doped system, tendency towards carrier pairing instead of phase separation is found. To study the validity of the rigid band approximation, we calculate the momentum distributions and the spectral functions. We find that the rigid band filling picture describes the electron doped system well. For the hole doped system, redistribution of particle density in momentum space occurs on doping. This implies that many body effect is significant and the rigid band filling picture may not be valid in the hole doped system.