Multiple phases and return to equilibrium

Jürg Martin Fröhlich, Marco Merkli

Jürg Martin Fröhlich, Marco Merkli

Leigh Hume, Derek W. Robinson

Ritesh Kumar Palai, Rajiv Kumar, Venktesh Singh +1 more

We investigate dynamical quantum phase transitions (DQPTs) in the extended Agassi model following sudden quenches of same level pairing ($Σ$), monopole-monopole ($χ$) and cross level pairing ($Λ$) strengths. Using exact diagonalization, we characterize the non-equilibrium dynamics through the Loschmidt echo and intensive return-rate function. Quenches across equilibrium phase boundaries produce cusp-like structures in the return rate that shows non-analyticities with increasing system size. Equilibrium finite size to large scaling identifies the $χ$-driven transition as a second order phase transition similar to mean-field, Dicke, and Lipkin-Meshkov-Glick (LMG) models critical behaviour with the exponent of the order parameter $β\simeq 1/2$, while the $Σ$- and $Λ$-driven transitions are first order. We further characterize the associated dynamical singularities through a local scaling exponent $α$, with $α_χ\simeq 2/3$, $α_Λ\simeq 1/3$, and $α_Σ\simeq 3/2$ of all three parameters. The distinct scaling behaviours across the parameter channels show that dynamical criticality is not determined solely by the equilibrium order of the transition, revealing multiple dynamical scaling regimes. These non-analyticities are associated with the Fisher zeros of the Loschmidt amplitude, which cross the real time axis at critical times and the time derivatives of the return-rate function to characterize the order of DQPTs within the extended Agassi model.

Vojkan Jakšić, Jane Panangaden, Annalisa Panati +1 more

Jad C. Halimeh, Maarten Van Damme, Valentin Zauner-Stauber +1 more

This paper establishes a direct connection between the equilibrium quasiparticle spectrum of a model and the nonanalytic behavior appearing in its Loschmidt return rate. For small quenches within the ordered phase, nonanalytic behavior in the form of so-called anomalous cusps occurs in the return rate only when the lowest-lying quasiparticles are local excitations.