Quantum transfer-matrix method and thermo-quantum dynamics

The quantum transfer-matrix (QTM) method is reviewed and thermo-quantum dynamics is formulated on the basis of the QTM. The free energy of the relevant quantum system (e.g. the one-dimensional Heisenberg model) is expressed only in terms of the maximum eigenvalue λmax of the QTM. Even the correlation length ξ(T) is expressed in terms of the ratio of λmax over the next largest eigenvalue λ2 as ξ(T)−1=log(λmax/λ2). This new formulation has the great merit that the thermal average Q for any local observable Q in the thermodynamic limit is expressed as an expectation value over a temperature-dependent state vector in the single (conjugate) Hilbert space in contrast to the usage of the double Hilbert space in the thermo-field dynamics.