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Physical review. B, Condensed matter

Effective-field renormalization-group study for the transverse Ising model in a quantum-spin system

Qing Jiang, Z. Y. Li

Published Dec 1, 1989• 21 citations
Publisher

Abstract

In this paper we suggest a method that combines the effective-field renormalization group with the discretized path-integral method to study the critical behavior of the transverse Ising model in a quantum-spin system. We find the results on a critical transverse field and critical exponent at zero temperature to be closely comparable to other results. This demonstrates the utility of this method in studying critical properties of quantum-spin systems.

DOI
10.1103/physrevb.40.11264

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In this paper we suggest a method that combines the effective-field renormalization group with the discretized path-integral method to study the critical behavior of the transverse Ising model in a quantum-spin system. We find the results on a critical transverse field and critical exponent at zero temperature to be closely comparable to other results. This demonstrates the utility of this method in studying critical properties of quantum-spin systems.
A zero-temperature real-space renormalization-group method is presented and applied to the quantum Ising model with a transverse field in one dimension. The transition between the low-field and high-field regimes is studied. Magnetization components, spin correlation functions, and critical exponents are derived and checked against the exact results. It is shown that increasing the size of the blocks in the iterative procedure yields more accurate results, especially for the critical "magnetic" exponents near the transition.
A newly developed zero-temperature real-space renormalization-group method is applied to the quantum Ising model with a transverse field on different two-dimensional lattices: hexagonal, triangular, and quadratic. The order parameter, spin-spin correlation functions, the critical fields, and the critical exponents describing the low-field-large-field transition are calculated. The influence of size and shape of the spin blocks used in the iterative process is discussed. The results for triangular and hexagonal lattices are new; for the quadratic lattice the calculations show an encouraging agreement with previous series-expansion results. The expected equivalence to the critical behavior of the three-dimensional Ising model is discussed: A reasonable agreement is obtained for the hexagonal lattice.
The critical behavior of an Ising model of classical spins in a transverse field HHH is derived for dimension $d=4\ensuremath{-}\ensuremath{\epsilon}$ using an $\ensuremath{\epsilon}$ expansion based on the Wilson renormalization group. To first order in $\ensuremath{\epsilon}$ the model exhibits a line of critical points Tc(H){T}_{c}(H)Tc​(H) with the same fixed point and critical exponents as in previous studies of the Wilson effective Hamiltonian.