Thermo quantum dynamics in the transverse Ising chain

Thermo quantum dynamics, which is formulated by using the eigenstate of the quantum transfer-matrix with the maximum eigenvalue (where m denotes the Trotter number and β=1/kBT), is applied to a transverse Ising chain. In order to exemplify the formulation of the thermo quantum dynamics for “local” operators, we show how to evaluate both the thermal average and the correlation function . Furthermore, it is demonstrated for the first time that the limit m→∞ of the thermal state vector exists in the diagonalized representation and that this thermal state vector can be regarded as the ground state vector of the corresponding virtual system.