Equivalence between the nonlinear /sigma/ model and the spin-(1/2 antiferromagnetic Heisenberg model: Spin correlations in La/sub 2/CuO/sub 4/

Journal Article · Tue Aug 01 04:00:00 EDT 1989 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.40.2205· OSTI ID:6051076

Manousakis, E; Salvador, R

We study the continuum limit of the quantum nonlinear /sigma/ model in 2+1 dimensions and at finite temperature /ital T/ using both Monte Carlo simulation on large-size lattices (100/sup 2//times/8 is our largest-size lattice) and saddle-point approximation. At zero temperature, we find the critical point /ital g//sub /ital c// that separates the quantum disordered phase from the phase with spontaneous symmetry breaking (nonzero staggered magnetization). We calculate the model's renormalization group /beta/ function close to the critical point. Using the /beta/ function, we rescale the correlation lengths calculated at various values of the coupling constant (spin stiffness) and temperature and find that they all collapse on the same curve /xi///ital a//sub /sigma//=f(T/T/sub /sigma//). Even though the lattice spacing vanishes, a finite unit of length /ital a//sub /sigma// and a temperature scale /ital T//sub /sigma// is generated via /ital dimensional/ /ital transmutation/. Assuming that the nonlinear /sigma/ model and the spin-1/2 antiferromagnetic (AF) Heisenberg model are equivalent at low temperature, we relate the units /ital a//sub /sigma// and /ital T//sub /sigma// to the lattice spacing /ital a//sub /ital H// and the AF coupling /ital J/ of the Heisenberg model so that the correlation lengths obtained from the simulation of the two models agree. In order to achieve this agreement we find that (a) the spin-1/2 AF Heisenberg model should order at /ital T/=0 and (b) the relationship between the scales /ital a//sub /sigma//,/ital T//sub /sigma// and /ital a//sub /ital H//, /ital J/ is obtained, and /ital f/(/ital T///ital T//sub /sigma//) can be accurately approximated by an exponential of /ital T//sub /sigma///T below /ital g//sub /ital c//.

• Research Organization: Department of Physics, Center for Materials Research and Technology Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306 (US); Control Data Corporation and Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306
• OSTI ID: 6051076
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Journal Name: Phys. Rev. B: Condens. Matter; (United States) Vol. 40:4; ISSN PRBMD
• Country of Publication: United States
• Language: English

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75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANGULAR MOMENTUM
ANTIFERROMAGNETIC MATERIALS
ANTIFERROMAGNETISM
CHALCOGENIDES
COHERENT SCATTERING
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MONTE CARLO METHOD
NEUTRON DIFFRACTION
OXIDES
OXYGEN COMPOUNDS
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