Bilayer Quantum Antiferromagnet

We have seen that dissipation can lead to an effective long-range interaction in time and thus break the symmetry between space and time directions in the last example. Another mechanism to break this symmetry is quenched disorder (i.e., impurities and defects), because this disorder is random in space but perfectly correlated in the time direction. 

The quantum-to-classical mapping follows the same procedure as for the clean bilayer quantum Heisenberg model above. The result is an unusual diluted three-dimensional classical Heisenberg model. Because the impurities in the quantum system are quenched (time-independent), the equivalent classical Heisenberg model has line defects parallel to the imaginary time direction. The classical Hamiltonian is given by 

L for four impurity concentrations. The solid lines are fits to ) with 2 = 1.31, CO = 0.48. (Taken with permission from Ref. 71.) 

Vojta and Sknepnek also performed analogous calculations for the quantum percolation transition at p = pp, J 0.16/ and the multicritical point 2itp=pp,J = 0.16/. A summary of the critical exponents for all three transitions is found in Table 3. The results for the percolation transition are in reasonable agreement with theoretical predictions of a recent general scaling theory of percolation quantum phase transitions P/v = 5/48, y/v = 59/16 and a dynamical exponent oi z = Df = (coinciding with the fractal dimension of the critical percolation cluster). 

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The simplest case is when the parameter A multiplies all terms on a subset of the bonds. An example is the bilayer Heisenberg quantum antiferromagnet with Hamiltonian... 

The Hamiltonian of the resulting bilayer Heisenberg quantum antiferromagnet reads... 

Figure 4 Sketch of the bilayer Heisenberg quantum antiferromagnet. Each lattice site is occupied by a quantum spin-J,...

Table 3 Critical Exponents of the Generic Transition, Percolation Transition, and Multicritical Point of the Dimer-Diluted Bilayer Quantum Heisenberg Antiferromagnet...

Gonventional Scaling and Universality in a Disordered Bilayer Quantum Heisenberg Antiferromagnet. 

Finite-Size Scaling Analysis of the Quantum Critical Point of S = 1/2 Heisenberg Antiferromagnetic Bilayers. 

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