Speaker: Shoki Sugimoto / 杉本昇大氏（東大理）

Date: Jan. 11th, 2022, 17:00-

Title: Thermalization of isolated quantum systems and its typicality

Abstract: Recent developments in experiments have enabled us to realize isolated quantum systems with unprecedented accuracy, and local relaxations of such systems to thermal equilibrium have been observed [1]. These results have resurged interest in the problem of how an isolated quantum system relaxes to thermal equilibrium under unitary dynamics, and substantial progress has been made over the last few decades. Among such progress, the notions of ‘typicality’ and the eigenstate thermalization hypothesis are prominent.It has been shown that almost all pure states are practically indistinguishable from a statistical ensemble with the corresponding energy, and therefore thermal equilibrium is typical [2]. Eigenstate thermalization hypothesis (ETH) [3] states that eigenstates of a many-body Hamiltonian are in thermal equilibrium by themselves and are considered to be a primary scenario for thermalization of isolated quantum systems. However, the rigorous proof of this hypothesis has remained elusive because of extreme difficulty in calculating the eigenstate properties of a generic many-body Hamiltonian. In this seminar, I will talk about our results [4] which numerically provide the first evidence that the ETH typically holds in realistic systems with O(1)-body and O(1)-local interactions as well as those with two-body but long-range interactions r^-α for α ≧ 0.6. On the other hand, we find that the distribution of the maximum difference between the eigenstate expectation values of a local observable and the microcanonical average significantly deviates from that expected from the conventional random matrix theory. This fact implies that the mechanism behind the typicality of the ETH in realistic systems is different from that proposed earlier based on the concentration of measure phenomenon on a high-dimensional sphere.

References:

References:

[1] S. Trotzky et al., Nature Physics 8 325 (2012)

A. Kaufman et al., Science 353 794 (2016)

[2] S. Goldstein et al., Physical Review Letters 96 050403 (2006)

S. Popescu et al., Nature Physics 2 754 (2006)

[3] J. von Neumann, Z. Phys. 57, 30 (1929)

J. Deutch, Physical Review A 43, 2046 (1991)

M. Srednicki, Physical Review E 50, 888 (1994)

[4] S. Sugimoto, R. Hamazaki, and M. Ueda, Physical Review Letters 126 120602 (2021)

S. Sugimoto, R. Hamazaki, and M. Ueda, arXiv:2111.12484 (2021)