Details
| Original language | English |
|---|---|
| Article number | L032203 |
| Number of pages | 6 |
| Journal | Physical Review E |
| Volume | 110 |
| Issue number | 3 |
| Publication status | Published - 27 Sept 2024 |
Abstract
We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few-body operators in chaotic many-body systems, truncated below a certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below a certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in the context of previous works exploring the emergence of random-matrix behavior at small energy scales.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Physics and Astronomy(all)
- Condensed Matter Physics
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In: Physical Review E, Vol. 110, No. 3, L032203, 27.09.2024.
Research output: Contribution to journal › Letter › Research › peer review
}
TY - JOUR
T1 - Emergence of unitary symmetry of microcanonically truncated operators in chaotic quantum systems
AU - Wang, Jiaozi
AU - Richter, Jonas
AU - Lamann, Mats H.
AU - Steinigeweg, Robin
AU - Gemmer, Jochen
AU - Dymarsky, Anatoly
N1 - Publisher Copyright: © 2024 American Physical Society.
PY - 2024/9/27
Y1 - 2024/9/27
N2 - We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few-body operators in chaotic many-body systems, truncated below a certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below a certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in the context of previous works exploring the emergence of random-matrix behavior at small energy scales.
AB - We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few-body operators in chaotic many-body systems, truncated below a certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below a certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in the context of previous works exploring the emergence of random-matrix behavior at small energy scales.
UR - http://www.scopus.com/inward/record.url?scp=85206126775&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2310.20264
DO - 10.48550/arXiv.2310.20264
M3 - Letter
C2 - 39425330
AN - SCOPUS:85206126775
VL - 110
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 3
M1 - L032203
ER -