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Energy gap at first-order quantum phase transitions: An anomalous case

淳一津田, Junichi Tsuda, 優輝山中 +3 more

Oct 1, 20130 citations

Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

Zi-Gang Yuan, Ping Zhang

In our previous work [Phys. Rev. A 85 (2012) 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann—Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition (ESQPT) in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.In our previous work [Phys. Rev. A 85 (2012) 044102], we studied the Berry phase of the ground state and exited states in the Lipkin model. In this work, using the Hellmann—Feynman theorem, we derive the relation between the energy gap and the Berry phase closed to the excited state quantum phase transition (ESQPT) in the Lipkin model. It is found that the energy gap is approximately linearly dependent on the Berry phase being closed to the ESQPT for large N. As a result, the critical behavior of the energy gap is similar to that of the Berry phase. In addition, we also perform a semiclassical qualitative analysis about the critical behavior of the energy gap.

arXiv:1405.0636Chinese Physics LettersJun 1, 20153 citations

The Relevance of Berry Phase in Quantum Physics

Pratul Bandyopadhyay

Statistical science and interdisciplinary researchNov 1, 20090 citations

Scaling of the Berry phase close to the excited-state quantum phase transition in the Lipkin model

Zi-Gang Yuan, Ping Zhang, Shu‐Shen Li +2 more

We study the Berry phase of the ground state and excited states in the Lipkin model. Using the Schwinger representation of spin operators, we get the expression for the Berry phase of the ground state in the thermodynamic limit and numerically calculate that of the excited states in finite sizes. We find that the Berry phase of the ground state is nonanalytic, but its derivative (with respect to the control parameter $\ensuremath{\alpha}$, see text) is finite even in the thermodynamic limit. Whereas, for the excited states, the Berry phase tends to be nonanalytic, and its derivative approaches $\ensuremath{\infty}$ in the thermodynamic limit and in the vicinity of the critical point of the excited-state quantum phase transition.We study the Berry phase of the ground state and excited states in the Lipkin model. Using the Schwinger representation of spin operators, we get the expression for the Berry phase of the ground state in the thermodynamic limit and numerically calculate that of the excited states in finite sizes. We find that the Berry phase of the ground state is nonanalytic, but its derivative (with respect to the control parameter $\ensuremath{\alpha}$, see text) is finite even in the thermodynamic limit. Whereas, for the excited states, the Berry phase tends to be nonanalytic, and its derivative approaches $\ensuremath{\infty}$ in the thermodynamic limit and in the vicinity of the critical point of the excited-state quantum phase transition.

Physical Review AApr 25, 201235 citations

Berry Phase in Composite-Fermi-Liquid States

Jie Wang, Scott Geraedts, Edward H. Rezayi +1 more

Bulletin of the American Physical SocietyMar 6, 20180 citations

Excited-state quantum phase transitions in Dicke superradiance models

Tobias Brandes

We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke states, we discuss the singular behavior of the derivative of the density of states and find observables such as the mean (atomic) inversion and the boson (photon) number and its fluctuations at arbitrary energies. Criticality depends on energy and a parameter that quantifies the relative weight of rotating versus counterrotating terms, and we find a close analogy to the logarithmic and jump-type nonanalyticities known from the Lipkin-Meshkov-Glick model.We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke states, we discuss the singular behavior of the derivative of the density of states and find observables such as the mean (atomic) inversion and the boson (photon) number and its fluctuations at arbitrary energies. Criticality depends on energy and a parameter that quantifies the relative weight of rotating versus counterrotating terms, and we find a close analogy to the logarithmic and jump-type nonanalyticities known from the Lipkin-Meshkov-Glick model.

arXiv:1306.6435Physical Review ESep 23, 2013137 citations

Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

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Critical Behavior of the Energy Gap and Its Relation with the Berry Phase Close to the Excited State Quantum Phase Transition in the Lipkin Model

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