Study Of Quantum Many-body Physics From The Perspective Of Temporal Dimension

This thesis focuses on quantum many-body physics from the perspective of temporal dimension and is aimed at uncovering the underline essence of physical questions,discovering new phenomena as well as new physics.In all the included studies,we pay much attention to the understanding of the associated fundamental concepts,which include phase,time period,duality,critical phenomenon and geometry.We present results on several important aspects and related themes.Classifying quantum many-body phases is a fundamental question of contemporary quantum physics.We propose time order,as a general concept and use it to classify quantum many-body phases in the temporal dimension,whose acceptance would make time order a new paradigm of classifying quantum many-body phases.We present time order phase diagrams and the associated time order phases in several quantum many-body systems,including spin-1 Bose-Einstein condensate(BEC),quantum Rabi model,and two non-Hermitian multi-spin interaction lattice models.Time crystals are interesting and attractive quantum many-body phases.We illustrate fractional and higher-order discrete time crystals in spin-exchange dynamics dominated spin-1 BEC system.Moreover,we present a general method to investigate quantum manybody non-equilibrium dynamics by investigating the Fourier transform spectrum's structure in the(frequency,parameter)plane of the observable's dynamical evolution.Through the investigation of symmetry-based time order,we uncover the essence of continuous time crystal.We also discuss the phenomenon of finite-size induced time-crystalline property,and demonstrate it in spin-1 BEC.Quantum phase transition exhibits the universal critical behavior,while duality connects different objects.These two concepts are important research topics in physics.We study the excited-state quantum phase transition(ESQPT)in the spin-1 BEC system.In addition,we propose eigenstate duality and spectrum structure duality,and illustrate them in concrete systems.The celebrated Kibble-Zurek(KZ)mechanism governs the defect/excitation generation during the process of adiabatic crossing of a quantum phase transition critical point.It has general and wide applications.Here we propose a generalized KZ mechanism,and we provide the general KZ phase diagram about KZ physics.In the spin-exchange dynamics dominated spin-1 BEC,we illustrate the results based on our generalized KZ mechanism.Geometric structure is deeply rooted in quantum mechanics,where geometry has important meanings.We use the geometric phase(Berry phase)and quantum geometric tensor to investigate the spin-exchange dynamics of spin-1 BEC,and we show that these two physical quantities can detect(characterize)the ground state first-order(second-order)quantum phase transition as well as the ESQPT in the system.We find an intriguing oddeven effect whose difference grows with system size ,an counterintuitive effect that needs more investigation and understanding.