Dynamical Singularities of Glassy Systems in a Quantum Quench

Abstract

We present a prototype of behavior of glassy systems driven by quantum dynamics in a quenching protocol by analyzing the random energy model in a transverse field. We calculate several types of dynamical quantum amplitude and find a freezing transition at some critical time. The behavior is understood by the partition-function zeros in the complex temperature plane. We discuss the properties of the freezing phase as a dynamical chaotic phase, which are contrasted to those of the spin-glass phase in the static system.

arXiv comment6 pages, 5 figures

References in corpus (19)

• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Canonical Typicality
• From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
• Mathematical Foundation of Quantum Annealing
• Thermal Pure Quantum States at Finite Temperature
• Non-equilibrium dynamic critical scaling of the quantum Ising chain
• Dynamics after a sweep through a quantum critical point
• Simple Glass Models and their Quantum Annealing
• A Quantum Approach to Classical Statistical Mechanics
• Thermodynamic formula for the cumulant generating function of time-averaged current
• Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems
• Chaos in Glassy Systems from a TAP Perspective
• Exact Analytic Continuation with Respect to the Replica Number in the Discrete Random Energy Model of Finite System Size
• Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit
• Zon-Cohen singularity and negative inverse temperature in a trapped particle limit
• Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice
• Partition-function zeros of spherical spin glasses and their relevance to chaos
• Replica analysis of partition-function zeros in spin-glass models

Cited by in corpus (11)

• Dynamical quantum phase transitions: a review
• Dynamical Topological Order Parameters far from Equilibrium
• Topological classification of dynamical phase transitions
• Quenching a Quantum Critical State by the Order Parameter: Dynamical Quantum Phase Transitions and Quantum Speed Limits
• Disordered Kitaev chain with long-range pairing: Loschmidt echo revivals and dynamical phase transitions
• Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions
• Zeros of the partition function and dynamical singularities in spin-glass systems
• Disorder-induced dynamical Griffiths singularities after certain quantum quenches
• Dynamical quantum phase transitions in Stark quantum spin chains
• Zeros and amoebas of partition functions
• Krylov Complexity Under Hamiltonian Deformations and Toda Flows