New progress in quantum simulation at USTC: revealing the relationship between thermalization dynamics and quantum criticality in lattice gauge theory

Pan Jianwei and Yuan Zhensheng from the University of Science and Technology of China, in collaboration with Zhai Hui from Tsinghua University and Mo Zhiyuan from Lanzhou University, studied the relationship between non-equilibrium thermalization process and quantum criticality in lattice gauge field theory using a self-developed ultranuclear quantum simulator. The rule that the multibody system with gauge symmetry is easy to thermalize to the equilibrium state when it is in the critical region of quantum phase transition is revealed. The research results were recently published in the form of "editor's recommendation" in the international authoritative academic journal Physical Review Letters.

Note: Maxwell equations are a gauge theory that satisfies U(1) gauge invariance. Therefore, an important question is: Can the physical system described by the gauge theory reach the equilibrium state through the thermal process? Solving these questions could help answer complex physics questions about the early evolution of the universe that are far from equilibrium.

Gauge theory and statistical mechanics are two important basic theories of physics. From Maxwell's equations of classical electrodynamics to quantum electrodynamics describing the interaction of elementary particles, the standard Model, etc., are all gauge theories satisfying specific group symmetries. Statistical mechanics, based on the maximum entropy principle proposed by Boltzmann et al., is a discipline that connects the microscopic state of an ensemble composed of a large number of microscopic particles (atoms, molecules, etc.) with its macroscopic statistical laws, such as how the energy distribution of a microscopic particle affects its pressure, volume, temperature and other macroscopic quantities. So, can quantum many-body systems described by gauge theory, which are far from equilibrium, heat up to thermodynamic equilibrium? Answering this question will advance the understanding of gauge theory, statistical mechanics and the relationship between them. Although theoretical physicists have proposed various models to analyze this problem, it is experimentally difficult to construct a physical system that is described by gauge theory and can be manually manipulated and observed.

In recent years, the emergence of ultraindicated atomic quantum simulators provides an ideal experimental platform for the simultaneous study of gauge theory and statistical physics. In 2020, a research team at the University of Science and Technology of China developed a 71-lattice optical lattice quantum simulator for ultra-cold atoms, and experimentally simulated the quantum phase transition process of the U(1) lattice gauge theory - Schwinger Model for the first time [Nature 587, 392 (2020)]. In 2022, they simulated the thermalization dynamics of non-equilibrium transition to equilibrium in lattice gauge field theory, and experimentally confirmed for the first time the "loss" of initial state information caused by quantum multibody thermalization under gauge symmetry constraints [Science 377, 311 (2022)]. Recently, Zhai Hui and Mo Zhiyuan, collaborators of this work, have shown through theoretical research that there is a correlation between quantum thermalization and quantum phase transitions in such lattice gauge models, and starting from the antiferromagnetic Neel state, It is predicted that the complete thermalization of the system can only be achieved near the quantum phase transition point [Phys. Rev. B 105,125123 (2022)]. Further observation of the relationship between quantum thermalization and quantum phase transitions in lattice gauge theory poses a new challenge to the previous experimental capabilities: how to manipulate and detect multibody quantum states in situ with single lattice accuracy and atomic number differentiation.

Note: a, schematic diagram of high-resolution imaging device; b, lattice specification model diagram; c, phase transition diagram.

Based on their existing ultracold atomic quantum simulator, the team of Jianwei Pan and Zhensheng Yuan combined quantum gas microscopy, spin-dependent superlattices and programmable optical potential Wells to develop single-lattice precision and particle number resolvable atom manipulation and detection techniques. Based on this, they can prepare and detect multiatomic quantum states of any atomic configuration, and trace the dynamic evolution of multibody quantum states under the constraint of gauge symmetry. In this work, they experimentally prepared the initial state of a special atomic configuration, used the method of adiabatic evolution to study the quantum phase transition process satisfying the constraint of gauge symmetry, and determined the phase transition point for the first time experimentally by the finite scale theory. At the same time, they study the annealing kinetics of the initial state of the same configuration away from the equilibrium condition, and reveal the rule that the multi-body system with normal symmetry is easy to thermalize to the equilibrium state when it is near the critical point of quantum phase transition.

Figure Note: Above, the position of phase transition point is determined by finite size effect; In the following figure, the thermodynamic process of annealing is used to study whether the thermalization of the system satisfies the eigenstate thermalization hypothesis

The paper was selected as an "Editor's recommendation" paper by Phys.Rev.Lett. It was reported by the American Physical Society "Physics" under the title "Watching a Quantum System Thermalize" : https://physics.aps.org/articles/v16/s115.

Hanyi Wang, PhD student at the University of Science and Technology of China, Weiyong Zhang, postdoctoral fellow, and Zhiyuan Yao, a young researcher at Lanzhou University, are co-first authors of the paper. The research was supported by the National Natural Science Foundation of China, the Ministry of Science and Technology, Anhui Province, Beijing City, and the Scientific Exploration Award.

Paper link:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.050401

(Hefei National Research Center for Microscale Matter Science, School of Physics, Institute of Quantum Information and Quantum Technology Innovation, Chinese Academy of Sciences, Department of Scientific Research)

Source: China University of Science and Technology News