Excited State Quantum Phase Transitions Studied from a Non-Hermitian Perspective

Abstract

A main distinguishing feature of non-Hermitian quantum mechanics is the presence of exceptional points (EPs). They correspond to the coalescence of two energy levels and their respective eigenvectors. Here, we use the Lipkin-Meshkov-Glick (LMG) model as a testbed to explore the strong connection between EPs and the onset of excited state quantum phase transitions (ESQPTs). We show that for finite systems, the exact degeneracies (EPs) obtained with the non-Hermitian LMG Hamiltonian continued into the complex plane are directly linked with the avoided crossings that characterize the ESQPTs for the real (physical) LMG Hamiltonian. The values of the complex control parameter $\alpha$ that lead to the EPs approach the real axis as the system size $N\to \infty$. This happens for both, the EPs that are close to the separatrix that marks the ESQPT and also for those that are far away, although in the latter case, the rate the imaginary part of $\alpha$ reduces to zero as $N$ increases is smaller. With the method of Padé approximants, we can extract the critical value of $\alpha$.

5 pages, 4 figures

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• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model
• Exceptional points near first- and second-order quantum phase transitions
• Characterizing the excited-state quantum phase transition via the dynamical and statistical properties of the diagonal entropy
• Complex density of continuum states in resonant quantum tunneling
• Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Continuum analogues of excited-state quantum phase transitions
• Superradiance in finite quantum systems randomly coupled to continuum
• Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model
• Emergent non-Hermitian conservation laws at exceptional points
• Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians