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The transverse field Ising model is a quan … The transverse field Ising model is a quantum version of the classical Ising model. It features a lattice with nearest neighbour interactions determined by the alignment or anti-alignment of spin projections along the axis, as well as an external magnetic field perpendicular to the axis (without loss of generality, along the axis) which creates an energetic bias for one x-axis spin direction over the other. An important feature of this setup is that, in a quantum sense, the spin projection along the axis and the spin projection along the axis are not commuting observable quantities. That is, they cannot both be observed simultaneously. This means classical statistical mechanics cannot describe this model, and a quantum treatment is needed. Specifically, the model has the following quantum Hamiltonian: Here, the subscripts refer to lattice sites, and the sum is done over pairs of nearest neighbour sites and . and are representations of elements of the spin algebra (Pauli matrices, in the case of spin 1/2) acting on the spin variables of the corresponding sites. They anti-commute with each other if on the same site and commute with each other if on different sites. is a prefactor with dimensions of energy, and is another coupling coefficient that determines the relative strength of the external field compared to the nearest neighbour interaction.ared to the nearest neighbour interaction.
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| rdfs:comment |
The transverse field Ising model is a quan … The transverse field Ising model is a quantum version of the classical Ising model. It features a lattice with nearest neighbour interactions determined by the alignment or anti-alignment of spin projections along the axis, as well as an external magnetic field perpendicular to the axis (without loss of generality, along the axis) which creates an energetic bias for one x-axis spin direction over the other. Specifically, the model has the following quantum Hamiltonian:del has the following quantum Hamiltonian:
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| rdfs:label |
Transverse-field Ising model
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