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Zhongguo kexue. Wulixue Lixue Tianwenxue

Excited-state quantum phase transitions in nuclear system and nucleon-pair transfer intensity

Lin CONG, Chang Xiu, Wenting Dong, Yu Zhang

Published Sep 16, 2019• 1 citation
Publisher

Abstract

Structural evolutions in the U(5)-O(6) quantum phase transition are investigated within the framework of the interacting boson model by comparing the two types of effective order parameters in the ground-state quantum phase transition and excited-state quantum phase transition. It is found that the monopole-pair transfer intensities can show critical behaviors not only in the ground-state quantum phase transition but also in the excited-state quantum phase transition. It is thus suggested that the main features of the ESQPT should persist in nuclear systems.

DOI
10.1360/sspma-2019-0210

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Structural evolutions in the U(5)-O(6) quantum phase transition are investigated within the framework of the interacting boson model by comparing the two types of effective order parameters in the ground-state quantum phase transition and excited-state quantum phase transition. It is found that the monopole-pair transfer intensities can show critical behaviors not only in the ground-state quantum phase transition but also in the excited-state quantum phase transition. It is thus suggested that the main features of the ESQPT should persist in nuclear systems.
The series of articles [Ann. Phys. 345, 73 (2014) and Ann. Phys. 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with f=2f=2f=2 degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. The intrinsic Hamiltonian formalism with angular momentum fixed to L=0L=0L=0 is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a nontrivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.
We study the structure of the eigenstates and the dynamics of a system that undergoes an excited-state quantum phase transition (ESQPT). The analysis is performed for two-level pairing models characterized by a U(n+1)\mathrm{U}(n+1)U(n+1) algebraic structure. They exhibit a second-order phase transition between two limiting dynamical symmetries represented by the U(n)\mathrm{U}(n)U(n) and SO(n+1)\mathrm{SO}(n+1)SO(n+1) subalgebras. They are, or can be mapped onto, models of interacting bosons. We show that the eigenstates with energies very close to the ESQPT critical point, EESQPT{E}_{\text{ESQPT}}EESQPT​, are highly localized in the U(n)\mathrm{U}(n)U(n) basis. Consequently, the dynamics of a system initially prepared in a U(n)\mathrm{U}(n)U(n)-basis vector with energy $\mathcal{E}\ensuremath{\sim}{E}_{\text{ESQPT}}$ may be extremely slow. Signatures of an ESQPT can therefore be found in the structures of the eigenstates and in the speed of the system evolution after a sudden quench. Our findings can be tested experimentally with trapped ions.
Abstract The spectral fluctuations and transition intensity fluctuations in the excited-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by adopting three statistical measures, including the nearest neighbor level spacing distribution P ( S ) measuring the chaoticity (regularity) in energy spectra, the Δ 3 ( L ) statistics of Dyson and Mehta measuring the spectral rigidity and the intensity distribution P ( y ) measuring the chaoticity (regularity) in B ( E 0) transitions. The results indicate that that the ESQPT as a function of the excitation energy may occur as a transition from regular (or semiregular) to highly chaotic if only the associated whole spectrum is chaotic, which fits most of the deformed situations in the IBM including those in the U(5)–SU(3) and SU(3)–O(6) transitional regions. Otherwise, the ESQPT will appear as a transition from regular (or semiregular) to regular such as the cases in the U(5)–O(6) transitional region or those on the ‘Alhassid–Whelan arc’, which represents a nearly regular parameter region connecting the U(5) and SU(3) limits in the IBM.
This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann. Phys. 323, 1106 (2008). In many‐body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel with a singularity in the energy spectrum that propagates to higher energies as the control parameter increases beyond the QPT critical point. The analysis of the spectrum has been a main tool for the detection of these ESQPTs. Studies of the effects of this transition on the system dynamics are more limited. Here, we extend our previous works and show that the evolution of an initial state with energy close to the ESQPT critical point may be extremely slow. This result is surprising, because it may take place in systems with long‐range interactions, where the dynamics is usually expected to be very fast. A timely example is the one‐dimensional spin‐1/2 model with infinite‐range Ising interaction studied in experiments with ion traps. Its Hamiltonian has a U(2) algebraic structure. More generally, the slow dynamics described here occurs in two‐level bosonic or fermionic models with pairing interactions and a Hamiltonian exhibiting a QPT between its limiting and dynamical symmetries. In this work, we compare the results for , and 3.
Excited-state quantum phase transitions (ESQPTs) generalize the concept of quantum phase transitions to excited levels. Here we investigate how such ESQPTs can emerge in Kerr nonlinear oscillators, where a bosonic mode with a Kerr nonlinearity is subject to both coherent (one-photon) and parametric (two-photon) driving. We determine the structure and properties of the complete phase diagram by defining proper dimensionless parameters. Rich phases and phase transitions exist in the phase diagram, including phases with two or four critical energies above the ground-state level and first-order quantum phase transitions. We characterize the ESQPTs by singularities in the density of states, which show universal logarithmic divergence or discontinuity at the critical energies. Furthermore, we find that observables such as the photon number also exhibit singular behaviors at the critical energies and obey scaling laws. These results may extend our understanding of the driven Kerr oscillator and ESQPTs in finite-component systems.