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Physica B Condensed Matter

Dirac's time-dependent variational principle to phase transition of ground state in the quantum double-well model

Hong-Wei Zhong, Haiqing Xu, He Wei-Zhong, Ping-Hua Huang

Published Jan 20, 2009• 0 citations
Publisher
DOI
10.1016/j.physb.2009.01.012

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地面状态阶段转变和量双井模型的声子分散关系借助于变化途径与 Hartree 类型许多身体试用波浪功能相结合的时间依赖者被学习。单个粒子的状态被拿是冻结的 Jackiw 苏格兰教会会员波浪功能。在最小的不确定性关系的条件下面，我们为粒子的期望价值为运动的系统和方程获得有效古典 Hamiltonian。到一个对称的单个井的潜力的从一个对称的双井潜力的有效底层潜力运输，和地面说，这被显示出作为增加量变化的力量从一个破对称阶段展出转变到一个恢复对称阶段。我们也在二个阶段获得声子分散关系和声子差距。

Chinese Physics Letters•Jan 1, 2008•0 citations
Phase transitions are fundamental phenomena in physics, characterized by abrupt changes in the properties of a system. While classical phase transitions occur due to thermal fluctuations, quantum phase transitions (QPTs) are driven by quantum fluctuations at zero temperature. In this work, we explore the presence of QPTs in cavity quantum electrodynamics systems using the Time-Dependent Variational Principle (TDVP), a semi-classical approach for analyzing complex quantum systems. Beginning with the Rabi model, where a single qubit interacts with a single-mode cavity field, we examine the influence of counter-rotating terms on the system's ground state properties. Subsequently, we extend our analysis to the Jaynes-Cummings model, where rotating-wave approximation applies, and finally, to the Dicke model, which considers the collective interaction of multiple qubits with a bosonic mode. For each model, we derive analytical expressions for the ground state properties and identify critical coupling strengths indicative of phase transitions. Our findings reveal second-order quantum phase transitions, including superradiant phases with distinct ground state behaviors, emphasizing the utility of TDVP in understanding QPTs across a variety of systems.
The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle's expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.
地面状态阶段转变和量双井模型的声子分散关系借助于变化途径与 Hartree 类型许多身体试用波浪功能相结合的时间依赖者被学习。单个粒子的状态被拿是冻结的 Jackiw 苏格兰教会会员波浪功能。在最小的不确定性关系的条件下面，我们为粒子的期望价值为运动的系统和方程获得有效古典 Hamiltonian。到一个对称的单个井的潜力的从一个对称的双井潜力的有效底层潜力运输，和地面说，这被显示出作为增加量变化的力量从一个破对称阶段展出转变到一个恢复对称阶段。我们也在二个阶段获得声子分散关系和声子差距。