Thermo quantum dynamics in the transverse Ising chain

Thermo quantum dynamics, which is formulated by using the eigenstate |Ψmax(m)(β)〉 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 〈σjx〉 and the correlation function 〈σjxσj+rx〉. Furthermore, it is demonstrated for the first time that the limit m→∞ of the thermal state vector |Ψmax(m)(β)〉 exists in the diagonalized representation and that this thermal state vector can be regarded as the ground state vector of the corresponding virtual system.