TY - JOUR

T1 - Ground-state correlations of quantum antiferromagnets

T2 - A Green-function Monte Carlo study

AU - Trivedi, Nandini

AU - Ceperley, D. M.

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1990

Y1 - 1990

N2 - We have studied via a Green-function Monte Carlo (GFMC) method the S=(1/2 Heisenberg quantum antiferromagnet in two dimensions. We use a well-known transformation to map the spin problem onto a system of hard-core bosons that allows us to exploit interesting analogies between magnetism and superfluidity. The GFMC method is a zero-temperature stochastic method that projects out the component of the true ground state in a given variational wave function. This method is complementary to previously used finite-temperature Monte Carlo methods and is well suited to studying the ground state and low-lying excited states. Starting with even a simple wave function, e.g., the classical Néel state, the GFMC method can obtain the short-range correlations very accurately, and we find the ground-state energy per site E0/J=-0.6692(2). We show that it is important to include the zero-point motion of the elementary excitations in the ground state and by a spin-wave analysis find that it produces long-range correlations in the wave function. Upon inclusion of such long-range correlations, we obtain a staggered magnetization m°=0.31(2) and the structure factor scrS(q)q at long wavelengths. Using the Feynman-Bijl relation, from the slope we deduce the renormalization of the spin-wave velocity by quantum fluctuations to be Zc==c/cs=1.14(5).

AB - We have studied via a Green-function Monte Carlo (GFMC) method the S=(1/2 Heisenberg quantum antiferromagnet in two dimensions. We use a well-known transformation to map the spin problem onto a system of hard-core bosons that allows us to exploit interesting analogies between magnetism and superfluidity. The GFMC method is a zero-temperature stochastic method that projects out the component of the true ground state in a given variational wave function. This method is complementary to previously used finite-temperature Monte Carlo methods and is well suited to studying the ground state and low-lying excited states. Starting with even a simple wave function, e.g., the classical Néel state, the GFMC method can obtain the short-range correlations very accurately, and we find the ground-state energy per site E0/J=-0.6692(2). We show that it is important to include the zero-point motion of the elementary excitations in the ground state and by a spin-wave analysis find that it produces long-range correlations in the wave function. Upon inclusion of such long-range correlations, we obtain a staggered magnetization m°=0.31(2) and the structure factor scrS(q)q at long wavelengths. Using the Feynman-Bijl relation, from the slope we deduce the renormalization of the spin-wave velocity by quantum fluctuations to be Zc==c/cs=1.14(5).

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U2 - 10.1103/PhysRevB.41.4552

DO - 10.1103/PhysRevB.41.4552

M3 - Article

AN - SCOPUS:25544467191

VL - 41

SP - 4552

EP - 4569

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 7

ER -