Erhai Zhao

The far-from-equilibrium dynamics of certain interacting quantum systems still defy precise understanding. One example is the so-called quantum many-body scars (QMBSs), where a set of energy eigenstates evade thermalization to give rise to long-lived oscillations. Despite the success of viewing scars from the perspectives of symmetry, commutant algebra, and quasiparticles, it remains a challenge to elucidate the mechanism underlying all QMBS and to distinguish them from other forms of ergodicity breaking. In this work, we introduce an alternative route to detect and diagnose QMBS based on Fisher zeros, i.e., the patterns of zeros of the analytically continued partition function Z on the complex β (inverse temperature) plane. For systems with scars, a continuous line of Fisher zeros will appear off the imaginary β axis and extend upward, separating the β plane into regions with distinctive thermalization behaviors. This conjecture is motivated from interpreting the complex Z as the return amplitude of the thermofield double state, and it is validated by analyzing two models with QMBS, the P[over ¯]XP[over ¯] model and the Ising chain in external fields. These models also illustrate the key difference between QMBS and strong ergodicity breaking including their distinctive renormalization group flows on the complex β plane. This "statistical mechanics" approach places QMBS within the same framework of thermal and dynamical phase transitions. It has the advantage of spotting scars without exhaustively examining each individual quantum state.

Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical implications. This mini review provides a concise overview of recent developments in complexification, primarily covering finite temperature and equilibrium quantum phase transitions, as well as their connection with dynamical quantum phase transitions and non-Hermitian physics, with a particular focus on the significance of Fisher zeros. Starting from the newly discovered self-similarity phenomenon associated with complex partition functions, we further discuss research on self-similar systems briefly. Finally, we offer a perspective on these aspects.

By setting the inverse temperature β loose to occupy the complex plane, Fisher showed that the zeros of the complex partition function Z , if approaching the real β axis, reveal a thermodynamic phase transition. More recently, Fisher zeros were used to mark the dynamical phase transition in quench dynamics. It remains unclear, however, how Fisher zeros can be employed to better understand quantum phase transitions or the nonunitary dynamics of open quantum systems. Here we answer this question by a comprehensive analysis of the analytically continued one-dimensional transverse field Ising model. We exhaust all the Fisher zeros to show that in the thermodynamic limit they congregate into a remarkably simple pattern in the form of continuous open or closed lines. These Fisher lines evolve smoothly as the coupling constant is tuned, and a qualitative change identifies the quantum critical point. By exploiting the connection between Z and the thermofield double states, we obtain analytical expressions for the short- and long-time dynamics of the survival amplitude, including its scaling behavior at the quantum critical point. We point out Z can be realized and probed in monitored quantum circuits. The exact analytical results are corroborated by the numerical tensor renormalization group. We further show that similar patterns of Fisher zeros also emerge in other spin models. Therefore, the approach outlined may serve as a powerful tool for interacting quantum systems. Published by the American Physical Society 2024

Quantum phase transitions are a fascinating area of condensed matter physics. The extension through complexification not only broadens the scope of this field but also offers a new framework for understanding criticality and its statistical implications. This mini review provides a concise overview of recent developments in complexification, primarily covering finite temperature and equilibrium quantum phase transitions, as well as their connection with dynamical quantum phase transitions and non-Hermitian physics, with a particular focus on the significance of Fisher zeros. Starting from the newly discovered self-similarity phenomenon associated with complex partition functions, we further discuss research on self-similar systems briefly. Finally, we offer a perspective on these aspects.

Rectenna is the key component in radio-frequency circuits for receiving and converting electromagnetic waves into direct current. However, it is very challenging for the conventional semiconductor diode switches to rectify high-frequency signals for 6G telecommunication (>100 GHz), medical detection (>THz), and rectenna solar cells (optical frequencies). Such a major challenge can be resolved by replacing the conventional semiconductor diodes with tunneling diodes as the rectenna switches. In this work, metal–insulator–metal (MIM) tunneling diodes based on 2D insulating materials were designed, and their performance was evaluated using a comprehensive simulation approach which includes a density-function theory simulation of 2D insulator materials, the modeling of the electrical characteristics of tunneling diodes, and circuit simulation for rectifiers. It is found that novel 2D insulators such as monolayer TiO₂ can be obtained by oxidizing sulfur-metal layered materials. The MIM diodes based on such insulators exhibit fast tunneling and excellent current rectifying properties. Such tunneling diodes effectively convert the received high-frequency electromagnetic waves into direct current.

Rectenna is the key component in radio-frequency circuits for receiving and converting electromagnetic waves into direct current. However, it is very challenging for the conventional semiconductor diode switches to rectify high-frequency signals for 6G telecommunication (>100 GHz), medical detection (>THz) and rectenna solar cells (optical frequencies). Such a major challenge can be resolved by replacing the conventional semiconductor diodes with tunneling diodes as the rectenna switches. In this work, metal-insulator-metal (MIM) tunneling diodes based on 2D insulating materials were designed, and their performance was evaluated using a comprehensive simulation approach which includes density-function-theory simulation of 2D insulator materials, modeling of the electrical characteristics of tunneling diodes, and circuit simulation for rectifiers. It is found that novel 2D insulators such as monolayer TiO2 can be obtained by oxidizing sulfur-metal layered materials. The MIM diodes based on such insulators exhibit fast tunneling and excellent current rectifying properties. Such tunneling diodes effectively convert the received high-frequency electromagnetic waves into direct current.