Impact of chaos on precursors of quantum criticality

Abstract

Excited-state quantum phase transitions (ESQPTs) are critical phenomena that generate singularities in the spectrum of quantum systems. {For systems with a classical counterpart,} these phenomena have their origin in the classical limit when the separatrix of an unstable periodic orbit divides phase space into different regions. Using a semiclassical theory of wave propagation based on the manifolds of unstable periodic orbits, we describe the quantum states associated with an ESQPT {for the quantum standard map: a paradigmatic example of a kicked quantum system}. {Moreover, we show that finite-size precursors of ESQPTs shrink as chaos increases due to the disturbance of the system. This phenomenon is explained through destructive interference between principal homoclinic orbits}

6 pages + Supp. Mat. 4+6 Figs. Closest to published version

References in corpus (9)

• Quantum criticality
• Excited-state quantum phase transitions
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Excited-state quantum phase transitions in systems with two degrees of freedom: III. Interacting boson systems
• Excited-state quantum phase transitions in spinor Bose-Einstein condensates
• Scarring by homoclinic and heteroclinic orbits
• Effective time-independent analysis for quantum kicked systems
• Characterizing the excited-state quantum phase transition via the dynamical and statistical properties of the diagonal entropy
• Critical quasienergy states in driven many-body systems

Cited by in corpus (7)

• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Quantum tunneling and level crossings in the squeeze-driven Kerr oscillator
• Effective versus Floquet theory for the Kerr parametric oscillator
• Excited state quantum phase transition and Loschmidt echo spectra in a spinor Bose-Einstein condensate
• Impact of chaos on the excited-state quantum phase transition of the Kerr parametric oscillator
• Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model
• Multifractality and excited-state quantum phase transition in ferromagnetic spin-$1$ Bose-Einstein condensates