This thesis introduces the concept of "thermal pure quantum (TPQ) states", which are pure quantum states in equilibrium. The author establishes a new formulation of statistical mechanics based on the TPQ states. This formulation allows us to obtain not only mechanical variables but also thermodynamic variables such as entropy and free energy from a single TPQ state. Furthermore, the formulation provides a new physical description in which all fluctuations including thermally driven ones are uniquely identified to be quantum fluctuations.

The use of TPQ formulation has practical advantages in its application to numerical computations and allows for significant reduction in computation cost in numerics. For demonstration purposes, a numerical computation based on TPQ formulation is applied to a frustrated two-dimensional quantum spin model, and the result is also included in this book.

Nominated as an outstanding contribution by the Physics Department of The University of Tokyo in 2014 Is the only book that formulates quantum statistical mechanics based on a single pure quantum state Shows that pure quantum state formulation of statistical mechanics is a strong tool to investigate quantum many-body systems Is based on two papers designated Editor's suggestion in Physical Review Letters Includes supplementary material: sn.pub/extras

Inhalt
Introduction to thermal pure quantum state formulation of statistical mechanics.- Typicality And Ergodicity.- Canonical Thermal Pure Quantum State.- Microcanonical Thermal Pure Quantum State.- Equilibrium State And Entanglement.- Relation Among TPQ States.- Application To Numerical Calculation.- Conclusion. <p