Thermal tensor renormalization group simulations of square-lattice quantum spin models

This paper describes an improvement in the method of exact diagonalization of Hamiltonians of quantum spin models on finite square lattices and the statistical analysis of the data so obtained to estimate the physical properties of the models on the infinite square lattices at zero temperature. The geometry and topology of finite square lattices are described. The models studied are the spin one-half XY and Heisenberg antiferromagnets using 28 finite square lattices with up to 32 vertices. Our estimates of the energy and magnetization on each model on the infinite lattice at zero temperature compare very well with recent estimates using quantum Monte Carlo, series expansion, and spin wave estimates. Estimates of spin wave velocity and transverse susceptibilities are more scattered.PACS No.: 75.10J

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Exactly soluble quantum spin models on a double layer: The net spin model

Physical Review B ◽

10.1103/physrevb.66.184402 ◽

2002 ◽

Vol 66 (18) ◽

Cited By ~ 16

Author(s):

H. Q. Lin ◽

J. L. Shen ◽

H. Y. Shik

Keyword(s):

Double Layer ◽

Spin Model ◽

Quantum Spin ◽

Spin Models ◽

Quantum Spin Models

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Extension of the Method of Exact Diagonalization of Quantum Spin Models to Finite Face Centred Cubic Lattices and Estimation of theT=0Properties of theS=1/2XYFerromagnet on the Infinite fcc Lattice

Journal of the Physical Society of Japan ◽

10.1143/jpsj.66.3231 ◽

1997 ◽

Vol 66 (10) ◽

pp. 3231-3236 ◽

Cited By ~ 6

Author(s):

Gregory E. Stewart ◽

Donald D. Betts ◽

James S. Flynn

Keyword(s):

Exact Diagonalization ◽

Quantum Spin ◽

Spin Models ◽

Cubic Lattices ◽

Fcc Lattice ◽

Quantum Spin Models

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THOULESS NUMBER AND SPIN DIFFUSION IN QUANTUM HEISENBERG FERROMAGNETS

Modern Physics Letters B ◽

10.1142/s0217984993001788 ◽

1993 ◽

Vol 07 (27) ◽

pp. 1747-1759 ◽

Cited By ~ 7

Author(s):

PETER KOPIETZ

Keyword(s):

Spin Diffusion ◽

Nearest Neighbor ◽

Arbitrary Dimension ◽

Quantum Spin ◽

Spin Systems ◽

Heisenberg Ferromagnet ◽

Electronic Systems ◽

Dimensionless Frequency ◽

Spin Models ◽

Quantum Spin Models

Using an analogy between the conductivity tensor of electronic systems and the spin stiffness tensor of spin systems, we introduce the concept of the Thouless number g0 and the dimensionless frequency-dependent conductance g(ω) for quantum spin models. It is shown that spin diffusion implies the vanishing of the Drude peak of g(ω), and that the spin diffusion coefficient Ds is proportional to g0. We develop a new method based the Thouless number to calculate D s , and present results for D s in the nearest-neighbor quantum Heisenberg ferromagnet at infinite temperatures for arbitrary dimension d and spin S.

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