Thermal Pure Quantum States at Finite Temperature

An equilibrium state can be represented by a pure quantum state, which we call a thermal pure quantum (TPQ) state. We propose a new TPQ state and a simple method of obtaining it. A single realization of the TPQ state suffices for calculating all statistical-mechanical properties, including correlation functions and genuine thermodynamic variables, of a quantum system at finite temperature.

Figure 1

$m_z$ vs $h_z$ for $J=-1$. Solid lines: exact results for $N\to \infty$, for various values of $u$ [10]. Circles: results of our formulation for $N=24$. Results for $N=4–20$ are also shown for $u=-0.3J$.

Figure 2

$\varphi (j)$ for $J=+1$ and $h_z=0$. Solid lines: exact results for $N\to \infty$, for various values of $u$ [11]. Circles: results of our formulation for $N=24$. (left inset) Results for $N=16–24$ at $j=2$ for $u=-0.36J$. (right inset) $\varphi (j)$ at finite $h_z$, obtained from a single realization of the TPQ state at $T\simeq 0.45J$.

Figure 3

$T$ vs $u$ for $J=+1$. Solid lines: exact results for $N\to \infty$, for $h_z=0-0.8J$ [13]. Triangles and squares: our results for ${\beta }^{-1}(u;N)$ (triangles) and ${\tilde{\beta }}^{-1}(u;\infty )$ (squares) for $N=24$. (inset) ${\tilde{\beta }}^{-1}(u;\infty )$ for $N=8–24$.