Edge exponents in work statistics out of equilibrium and dynamical phase transitions from scattering theory in one dimensional gapped systems

Abstract

I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped, one-dimensional system. I show that the edge exponent in the probability density function of the work is insensitive to the presence of interactions and can take only one of three values: +1/2, -1/2 and -3/2. It also turns out that there is an interesting interplay between spontaneous symmetry breaking or the presence of bound states and the exponents. For instantaneous global protocols, I find that the presence of the one-particle channel creates dynamical phase transitions in the time evolution.

5 pages, 2 figures. Revised version published in PRB

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• Fluctuation theorems: Work is not an observable
• Quantum Quench in the Transverse Field Ising Chain
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Topological classification of dynamical phase transitions
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Work measurement as a generalized quantum measurement
• First order dynamical phase transitions
• Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
• Large deviations and universality in quantum quenches
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Boundary State in an Integrable Quantum Field Theory Out of Equilibrium
• One-point functions in massive integrable QFT with boundaries
• Quantum quenches in two spatial dimensions using chain array matrix product states
• Quench echo and work statistics in integrable quantum field theories

Cited by in corpus (34)

• Dynamical quantum phase transitions: a review
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Mixed state dynamical quantum phase transition and emergent topology
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Coherent and dissipative dynamics at quantum phase transitions
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Initial states in integrable quantum field theory quenches from an integral equation hierarchy
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain
• Dynamical Topological Quantum Phase Transitions at Criticality
• Dynamical Quantum Phase Transitions in Extended Transverse Ising Models
• Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model
• Observing Dynamical Quantum Phase Transitions through Quasilocal String Operators
• Finite temperature dynamical quantum phase transition in a non-Hermitian system
• Quench action and large deviations: work statistics in the one-dimensional Bose gas
• Anomaly in dynamical quantum phase transition in non-Hermitian system with extended gapless phases
• Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model
• Scaling properties of work fluctuations after quenches at quantum transitions
• Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath
• Integrable quenches in nested spin chains II: fusion of boundary transfer matrices
• Dynamical Quantum Phase Transitions in Extended Toric-Code Models
• Effects of the Dzyaloshinsky-Moriya interaction on nonequilibrium thermodynamics in the $XY$ chain in a transverse field
• Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems
• Dynamics of edge current in a linearly quenched Haldane model
• Non-equilibrium aspects of integrable models
• Quantum Work of an Optical Lattice
• Persistent anomaly in dynamical quantum phase transition in long-range non-Hermitian $p$-wave Kitaev chain
• The role of quantum work statistics in many-body physics
• Role of topology on the work distribution function of a quenched Haldane model of graphene
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions