Detailed Lanczos study of one- and two-hole band structure and finite-size effects in the t - J model

Journal Article · Wed Jan 01 04:00:00 EST 1992 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.45.256· OSTI ID:5001041

Barnes, T ^[1]; Jacobs, A E ^[2]; Kovarik, M D ^[1]; Macready, W G ^[2]

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1. Physics Division and Center for Computationally Intensive Physics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6373 (United States) Department of Physics, University of Tennessee, Knoxville, Tennessee 37996-1200 (United States)
2. Department of Physics, University of Toronto, Toronto, Ontario, M5S1A7 (Canada)

We present accurate numerical results for low-lying one- and two-hole states in the {ital t}-{ital J} model on a 4{times}4 lattice. We find six level crossings in the one-hole ground state for 0{lt}{ital t}/{ital J}{lt}{infinity}; accurate {ital t}/{ital J} values of these crossings and the associated ground-state quantum numbers are given. A degeneracy of {bold k}=(0,0) S=1/2, and {ital S}=3/2 one-hole levels at {ital t}/{ital J}=1/2 is noted, which is consistent with a recent analytical result. For small {ital t}/{ital J}, the {ital S}=1/2 one-hole and {ital S}=0 two-hole bandwidths on the 4{times}4 lattice are {ital W}{sub {ital h}}=(1.190 445 7(1)){ital t} and {ital W}{sub hh}=(2.575(4)){ital t}{sup 2}/{ital J}, respectively. The origin of these qualitatively different behaviors is discussed, and a simple relation is found between the small-({ital t}/{ital J}) one-hole bandwidth and a static-hole ground-state matrix element. The linear-{ital t} term in {ital W}{sub {ital h}} is apparently a finite-lattice artifact. As a measure of finite-size effects we determined the rms hole-hole separation in the two-hole ground states; we find evidence of important finite-size effects for {ital t}/{ital J}{approx gt}1, for which the rms hole-hole separation is clearly constrained by the 4{times}4 lattice. Intermediate-({ital t}/{ital J}) hole separations and binding energies for 0.3{approx lt}{ital t}/{ital J}{approx lt}1, however, scale approximately as powers of {ital t}/{ital J}, and can be used to give bulk-limit estimates for {ital t}/{ital J}=3. In particular, we estimate that the bulk-limit ground-state rms hole-hole separation at {ital t}/{ital J}=3 is {approx}1.8{ital a}{sub 0}, corresponding to 7 A in the high-temperature superconductors.

• DOE Contract Number: AC05-84OR21400
• OSTI ID: 5001041
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 45:1; ISSN 0163-1829; ISSN PRBMD
• Country of Publication: United States
• Language: English

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ANTIFERROMAGNETISM
COOPER PAIRS
COULOMB FIELD
CRYSTAL MODELS
ELECTRIC FIELDS
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