Some critical properties for static and dynamic equilibrium superradiant models are discussed, within a Gaussian fluctuation theory. The temperature critical region and the λ-critical region are calculated and the phase diagram of the superradiant phase transition is obtained.
The role of the quantum fluctuations of the order parameter in a second-order phase transition is discussed, for a superradiant model. The mean field equations and the equation of the critical temperature are obtained. The change of the value of the critical exponent of the specific heat α is connected with the supplementary dimension introduced by the frequency dependence of the field variables. The functional integral method is used, most of the calculations being performed within the Gaussian approximation.
Some aspects of the critical behaviour of a single-mode superradiant system are discussed. Using the method of functional integral the free energy and the specific heat are calculated in the neighbourhood of the second-order phase transition exhibited by the system. The results obtained in a mean field and in a Gaussian approximation are compared and the accordance with the Josephson scaling rule is discussed. The importance of the fluctuations of the order parameter for a low-dimensional system ( d = 0) is proved and the width of the critical region using the Ginsburg criterion is evaluated.
The existence of zero-dimensional superradiant quantum phase transitions seems inconsistent with conventional statistical physics. This work clarifies this apparent inconsistency. We demonstrate the corresponding effective field theories and finite-temperature properties of light-matter interacting systems, and show how this zero-dimensional quantum phase transition occurs. We first focus on the Rabi model, which is a minimum model that hosts a superradiant quantum phase transition. With the path-integral method, we derive the imaginary-time action of the photon degrees of freedom. We also define a dynamical critical exponent as the rescaling between the temperature and the photon frequency, and perform dimensional analysis to the effective action. The dynamical critical exponent shows that the effective theory of the Rabi model is a free scalar field, where a true second-order quantum phase transition emerges. These results are also verified by numerical simulations of imaginary-time correlation functions of the order parameter. Furthermore, we also generalize this method to the Dicke model. Our results make the zero-dimensional superradiant quantum phase transition compatible with conventional statistical physics, and pave the way to understand it in the perspective of effective field theories. Published by the American Physical Society 2024
Various light-matter interactions lead to diverse phase diagram structures in superradiant phase transition (SPT) studies. Such systems consist of multiqubit and multimode with anisotropic couplings, one- and two-photon interactions, Stark shifts, inter-cavity hoppings, qubit-qubit interactions and so on. We find a general phase diagram feature that the origin is in normal phase (NP) and SPT happens only once along the radial direction of a chosen coupling parameter vector with the mean-field method at finite temperature. We can calculate the phase boundary and SPT properties by a concise method. We illustrate it with specific models and find SPT can be achieved in strong coupling regime by means of multimode collective behavior. We also find the disorder will shift the phase boundary. These general features facilitate SPT studies and their diverse applications.
Abstract Phase transitions are both thermodynamically and quantum-mechanically ubiquitous in nature and laboratories, and their understanding remains one of the most active issues in modern physics and related disciplines. The Landau theory provides a general framework to describe phenomenologically phase transitions by introducing order parameters and associated symmetry breaking. This theory is also taken as a starting point to explore critical phenomena in connection with phase transitions in the renormalization group, which provides a complete theoretical description of behaviors close to critical points. In this context, the microscopic mechanism of phase transitions remains unclear. In this study, we explore the microscopic mechanism of the superradiant phase transition in the quantum Rabi model (QRM). First, we perform a diagonalization operation in an operator space to obtain three fundamental patterns, denoted as λ 1 , λ 2 , and λ 3 , involved in the QRM. Then, we explicitly analyze the energy evolutions of these patterns with increasing coupling strength. The observed characteristic behaviors reveal the microscopic mechanism of the superradiant phase transition as a consequence of competition between patterns due to different phase relations. In other words, with increasing coupling strength, the pattern λ 1 drives the phase transition, the pattern λ 2 exhibits a similar response speed but less energy compensation than the pattern λ 1 , and the pattern λ 3 exhibits a slow response speed but plays a key role in the balance between it and the pattern λ 1 , which stabilizes the new phase. This type of dissecting mechanism explains why and how the superradiant phase transition occurs in the QRM and paves the way for exploring the microscopic mechanism of phase transitions that occur frequently in nature.
This paper investigates the role of statistical fluctuations about the equilibrium value of the order parameter in the vicinity of a phase-transition temperature. The systems under consideration are assumed to be of finite size, but the behavior in the thermodynamic limit is also described. Our objective is to examine the simplest exactly solvable model of non-Gaussian static fluctuations for samples of finite size. To this end a Landau form is employed for the model Hamiltonian and various expansions are analyzed in order to describe first- and second-order phase transitions, field-induced transitions, and liquid-vapor critical phenomena. The approach differs from previous treatments primarily in the application of a quartic non-Gaussian model for statistical fluctuations which redresses some of the shortcomings of the standard Gaussian approximation. In particular, it is found that for finite values of V (volume) no singularities exist even at the critical temperature. The treatment is generalized by examining a class of non-Gaussian distribution functions, and particular emphasis is placed on strict adherence to the uniform convergence criterion so that general conclusions can be drawn.