erratum: bose condensation in quasi-one-dimensional antiferromagnets in strong fields

PHYSICAL REVIEW B VOLUME 45, NUMBER 9

Errata

1 MARCH 1992-I

Erratum: Single-particle excitations in a quantum antiferromagnet[Phys. Rev. B 41, 2017 (1990)]

K. J. von Szczepanski, P. Horsch, W. Stephan, and M. Ziegler

We note a typing mistake in Eq. (3) of our paper. The second term, proportional to t IU, must have a negative sign,corresponding to Eq. (4).

Because of a numerical error in one of our computer programs, wrong values for all E~& ~ and two wrong values ofE', were given in Table II of the paper. E', (E', ) is the total energy of the lowest state for one hole in the t Jm-odel(t-J model, i.e., the t-J model with three-site terms) on a ten-site lattice in two dimensions. The correct table follows.

TABLE II. Total energy of the ground state for the t-J, t-J, and Hubbard model on a ten-site lattice in two dimensions for allnonequivalent momenta. E0 is the energy for half filling, El for one hole in the half-filled band. The value of total spin S in(S~)=S(S+1)is given in brackets. The parameters Jand Uare connected via J =4t~/U.

Et-J0

EHub0

E 1

Et-J1

EHub1

(0,0)

—6.1500 (0)—5.1041 (0)—6.1898 (-')—6.3206 (2 }

—6.0669 (-', )

(3m/5, m/5)

J/t =0.5 U/t =8—4.7381 (1)—4.1980 (1)—6.8930 ( —')—7.1920 (-')—6.5679 (1)

(2m /5, 4m/5)

—4.7500 (1)—4.1227 (1)—6.7807 (2)—7.0970 (2)—6.3097 (2)

—5.7321 (1)—4.8633 {1)—6.1885 ( 2)—6.3554 (2)—5.7947 ( —)

Et-J0

EHub0

Et-J1

Et-J1

EHub1

—2.4600 (0}—2.3517 (0)—4.2514 ( —)

—4.3354 ( —)

—4.3129 (-,')

J/t =0.2 U/t =20—1.8952 (1)—1.8439 (1)—4.3420 (-,' )

—4.4835 (-,')—4.4490 ( —')

—1.9000 (1)—1.8449 (1)—4.3528 (2)—4.4735 (2)—4.3978 (2)

—2.2928 (1)—2.2123 (1)—4.3190 (-,')—4.3892 (2)—4.3362 (2)

The energy of the t-J model (i.e., including the three-site terms) is always lower than the corresponding energy ofone hole in the Hubbard model, consistent with the one-dimensional case depicted in Fig. 4 of our paper.

The errors do not affect any further considerations of the paper, nor do they alter the conclusions drawn.

1992 The American Physical Society

Erratum: Bose condensation in quasi-one-dimensional antiferromagnets in strong fields[Phys. Rev. B 43, 3215 (1991)]

lan AfBeck

(1) Equation (27) should read

)ty(O) ) (8(x)g(0))i2 qln[x~

(2) Some of these results were obtained earlier by H. J. Schulz in Phys. Rev. B 34, 6372 (1986).

45 5118 1992 The American Physical Society