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Physical review. B, Condensed matter

Fluctuations around the magnetic and nonmagnetic saddle points in the two-dimensional spin-1/2 frustrated Heisenberg model

Mario Di Stasio, Elisa Ercolessi, G. Morandi, A. Tagliacozzo

Published Apr 15, 1994• 1 citation
Publisher

Abstract

Fermionization of the spin operators is allowed only in the restricted Hilbert space of singly occupied sites. A method to implement this single-site occupancy constraint is applied to the frustrated Heisenberg model. This method allows us to study either magnetic or nonmagnetic phases at finite temperatures. A quantitative estimate of the relative weight of quantum fluctuations around the disordered dimer phases and the antiferromagnetic phase is given.

DOI
10.1103/physrevb.49.10908

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Fermionization of the spin operators is allowed only in the restricted Hilbert space of singly occupied sites. A method to implement this single-site occupancy constraint is applied to the frustrated Heisenberg model. This method allows us to study either magnetic or nonmagnetic phases at finite temperatures. A quantitative estimate of the relative weight of quantum fluctuations around the disordered dimer phases and the antiferromagnetic phase is given.
We implement the constraint of no-double-site occupancy exactly, in the spin-1/2 Hubbard-Heisenberg model at half filling. The staggered Peierls and the flux phase are again found to be saddle points for the effective action, also at finite temperature. Their mean-field critical temperatures are higher when the accuracy restriction is taken into account. Gaussian fluctuations of the auxiliary field are reasonably small for a large temperature range, but have to be necessarily included, when extending the free energy to finite temperatures.
Thermal properties of the ordered phase of the spin 1/2 isotropic Heisenberg Antiferromagnet on a d-dimensional hypercubical lattice are studied within the fermionic representation when the constraint of single occupancy condition is taken into account by the method suggested by Popov and Fedotov. Using saddle point approximation in path integral approach we discuss not only the leading order but also the fluctuations around the saddle point at one-loop level. The influence of taking into account the single occupancy condition is discussed at all steps.
Abstract We propose a novel two-dimensional (2D) frustrated quantum spin-1/2 anisotropic Heisenberg model with alternating ferromagnetic and antiferromagnetic magnetic chains along one direction and antiferromagnetic interactions along the other. The (mean-field) ground state is ferrimagnetic in certain range of the interaction space. Spin-wave theory analysis of the reduction of ordered moments at inequivalent spin sites and the instability of the spin waves suggest a quantum phase transition which has the characteristics of both the frustrated 2D antiferromagnetic S = 1/2 ( J 1 , J 2 ) model and 1D S 1 = 1, S 2 = 1/2 quantum ferrimagnetic model.