Thermodynamics And Quantum Dynamics Of Quantum Many-body Systems

With the rapid development of modern materials science,low-dimensional sys-tems and quantum dynamics have become the frontiers of modern quantum physics research.In the research of low-dimensional quantum many body systems,it is of great significance to find the exact solution of the strongly correlated quantum many-body models.Its rich mathematical structure and physical connotation play an irreplaceable role in revealing the critical behavior of strongly correlated physical systems.This the-sis mainly focuses on the thermodynamic?quantum criticality?phase diagram in one dimensional integrable model.From the perspective of exact solution,we obtain the thermodynamics and the characteristics of the quantum critical region of the Gruneisen parameter in Lieb-Liniger model and Yang-Gaudin model.In addition,we use the cen-tral spin model to study the dynamic evolution of the energy and power of the quantum battery,and give the relation between the power of battery and number of central spin.The main contents of this thesis are as follows:1.Thermodynamics and quantum criticality of one-dimensional Bose gasWe use the Bethe ansatz(BA)method to rigorously solve the ground state of Lieb-Liniger model,and discuss the ground state properties of the system under the weak and strong interaction limits respectively.Moreover,starting from the BA solution,by using the Yang Yang thermodynamic method,we give the thermodynamic quantities of the system(pressure,density of the particle number,compressibility and specific heat)and phase diagram of the system.And we discuss the thermodynamic behavior,quantum statistics and quantum criticality of the systems.2.Griineisen parameter in one-dimensional interacting quantum gasesUsing the Bethe ansatz solution,we analytically study expansionary,magnetic,and interacting Gruneisen parameters(GPs)for one-dimensional Lieb-Liniger model and Yang-Gaudin model.These different GPs elegantly quantify the dependence of characteristic energy scales of these quantum gases on the volume,the magnetic field,and the interaction strength,revealing the caloric effects resulting from the variations of these potentials.We also present the universal scaling behavior of these GPs in the vicinities of the quantum critical points driven by different potentials.The divergence of the GPs elegantly determines low-temperature phases of the quantum gases.Moreover,the pairing and unpairing features in the 1D attractive Fermi gases can be captured by the magnetic and interacting GPs,facilitating experimental observation of quantum phase transitions.3.Quantum battery in multiple central spin modelWe study the energy transfer process in quantum battery systems consisting of multiple central spins and bath spins.Here with"quantum battery.we refer to the central spins,whereas the bath serves as the "charger".For the single central-spin battery,we analytically derive the time evolutions of the energy transfer and the charging power with arbitrary number of bath spins.For the case of multiple central spins in the battery,we find the scaling-law relation between the maximum power Pmax and the number of central spins NB.It approximately satisfies a scaling law relation Pmax ? NB?,where scaling exponent a varies with the bath spin number N from the lower bound?=1/2 to the upper bound ?=3/2.The lower and upper bounds correspond to the limits N?1 and N?NB,respectively.In thermodynamic limit,by applying the Holstein-Primakoff(H-P)transformation,we rigorously prove that the upper bound is Pmax=0.72BA(?)NB3/2,which shows the same advantage in scaling of a recent charging protocol based on the Tavis-Cummins model.