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Physical review. B, Condensed matter

Quantum Monte Carlo study of a single hole in a quantum antiferromagnet

Sandro Sorella

Published Nov 1, 1992• 29 citations
Publisher

Abstract

Using the standard quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a quantum antiferromagnet. The calculation is very well stabilized, using selected-size systems and a special choice of the trial wave function that satisfies the ``closed-shell condition'' in the presence of an arbitrarily weak Zeeman magnetic field. First it is shown that the presence of this magnetic field does not affect the thermodynamic properties of the half-filled system. Then I use the same selected sizes for the one-hole ground state. I investigate the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator behaves as a conventional insulator with an upper and lower Hubbard band. By comparing the present finite-size scaling with several techniques that predict a finite quasiparticle weight, the data seem more consistent with a vanishing quasiparticle weight, i.e., the Mott-Hubbard insulator should be characterized by nontrivial excitations that cannot be interpreted in a simple picture. However, one cannot exclude, based only on numerical grounds, a very small but nonvanishing quasiparticle weight. In the last part I give some theoretical arguments to explain the results of the Monte Carlo simulation.

DOI
10.1103/physrevb.46.11670

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Using the standard quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a quantum antiferromagnet. The calculation is very well stabilized, using selected-size systems and a special choice of the trial wave function that satisfies the ``closed-shell condition'' in the presence of an arbitrarily weak Zeeman magnetic field. First it is shown that the presence of this magnetic field does not affect the thermodynamic properties of the half-filled system. Then I use the same selected sizes for the one-hole ground state. I investigate the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator behaves as a conventional insulator with an upper and lower Hubbard band. By comparing the present finite-size scaling with several techniques that predict a finite quasiparticle weight, the data seem more consistent with a vanishing quasiparticle weight, i.e., the Mott-Hubbard insulator should be characterized by nontrivial excitations that cannot be interpreted in a simple picture. However, one cannot exclude, based only on numerical grounds, a very small but nonvanishing quasiparticle weight. In the last part I give some theoretical arguments to explain the results of the Monte Carlo simulation.
Using the standard Quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a Quantum Antiferromagnet. The calculation is very well stabilized, using selected sized systems and special use of the trial wavefunction that satisfy the “close shell condition” in presence of an arbitrarily weak Zeeman magnetic field, vanishing in the thermodynamic limit. It will be shown in a forthcoming publication1 that the presence of this magnetic field does not affect thermodynamic properties for the half filled system. Then I have used the same selected sizes for the one hole ground state. I have investigated the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator should behave just as conventional insulator with an upper and lower Hubbard band. By comparing the present finite size scaling with several techniques predicting a finite quasiparticle weight (see Fig.1) the data seem more consistent with a vanishing quasiparticle weight, i.e. , as recently suggested by P.W. Anderson2 the Hubbard-Mott insulator should be characterized by non-trivial excitations which cannot be interpreted in a simple quasi-particle picture. However it cannot be excluded , based only on numerical grounds, that a very small but non vanishing quasiparticle weight should survive in the thermodynamic limit.
Dynamic properties of the three-dimensional single-band Hubbard model are studied using quantum Monte Carlo combined with the maximum entropy technique. At half-filling, there is a clear gap in the density of states and well-defined quasiparticle peaks at the top (bottom) of the lower (upper) Hubbard band. We find an antiferromagnetically induced weight above the naive Fermi momentum. Upon hole doping, the chemical potential \ensuremath{\mu} moves to the top of the lower band where a robust peak is observed. Results are compared with spin-density-wave mean-field and self-consistent Born approximation results, and also with the infinite-dimensional (D=\ensuremath{\infty}) Hubbard model, and experimental photoemission for three-dimensional transition-metal oxides. \textcopyright{} 1996 The American Physical Society.
We study a ground-state ansatz for the single-hole-doped $t\text{\ensuremath{-}}J$ model in two dimensions via a variational Monte Carlo method. Such a single-hole wave function possesses finite angular momenta generated by hidden spin currents, which give rise to a novel ground-state degeneracy in agreement with recent exact diagonalization (ED) and density matrix renormalization group (DMRG) results. We further show that the wave function can be decomposed into a quasiparticle component and an incoherent momentum distribution in excellent agreement with the DMRG results up to an $8\ifmmode\times\else\texttimes\fi{}8$ lattice. Such a two-component structure indicates the breakdown of Landau's one-to-one correspondence principle, and in particular, the quasiparticle spectral weight vanishes by a power law in the large sample size limit. By contrast, turning off the phase string induced by the hole hopping in the so-called $\ensuremath{\sigma}\ifmmode\cdot\else\textperiodcentered\fi{}t\text{\ensuremath{-}}J$ model, a conventional Bloch-wave wave function with a finite quasiparticle spectral weight can be recovered, also in agreement with the ED and DMRG results. The present study shows that a singular effect already takes place in the single-hole-doped Mott insulator, by which the bare hole is turned into a non-Landau quasiparticle with translational-symmetry breaking. Generalizations to pairing and finite doping are briefly discussed.
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The ground state of the 2D (square lattice) finite-size Hubbard model is studied at half filling with a newly developed Quantum Monte Carlo method. We have studied square cells from 18 to 242 sites for U=3 with high statistical accuracy to perform a reliable size scaling analysis. The results confirm that the system is an antiferromagnetic insulator. The finite size scaling results are discussed in detail, focusing on the behaviour of magnetization, and most particularly of momentum distribution.
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,U=10,20,U=10,20, and 404040, 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 UUU. 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.