Dynamical Quantum Phase Transitions of Quantum Spin Chains with the Loschmidt-rate Critical Exponent equal to $\frac{1}{2}$

Abstract

We describe a new universality class of dynamical quantum phase transitions of the Loschmidt amplitude of quantum spin chains off equilibrium criticality. We demonstrate that in many cases it is possible to change the conventional linear singularity of the Loschmidt rate function into a smooth peak by tuning one parameter of the quench protocol. Exactly at the point when this change-over occurs, the singularity of the Loschmidt rate function persists, with a critical exponent equal to $\frac{1}{2}$ . The non-equilibrium renormalization group fixed-point controlling this universality class is described. An asymptotically exact renormalization group recursion relation is derived around this fixed-point to obtain the critical exponent.

References in corpus (36)

• Many-Body Physics with Ultracold Gases
• Quantum Simulation
• The large deviation approach to statistical mechanics
• Efficient simulation of one-dimensional quantum many-body systems
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Relaxation and Pre-thermalization in an Isolated Quantum System
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Time-dependent variational principle for quantum lattices
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Unifying time evolution and optimization with matrix product states
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Dynamical quantum phase transitions: a review
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Observation of a dynamical topological phase transition
• Time-evolving a matrix product state with long-ranged interactions
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Dynamical phase transitions after quenches in non-integrable models
• Dynamical quantum phase transitions: scaling and universality
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• Disentangling dynamical phase transitions from equilibrium phase transitions
• Dynamical phase diagram of spin chains with long-range interactions
• First order dynamical phase transitions
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Quenches and dynamical phase transitions in a non-integrable quantum Ising model
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Tuning the presence of dynamical phase transitions in a generalized $XY$ spin chain
• Quantum Criticality and the Kondo Lattice
• Dynamical quantum phase transitions in the quantum Potts chain
• Dynamical Quantum Phase Transitions in Extended Transverse Ising Models
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions
• Non-equilibrium Renormalization Group Fixed-Points of the Quantum Clock Chain and the Quantum Potts chain
• Dynamical quantum phase transitions in many-body localized systems

Cited by in corpus (12)

• Local measures of dynamical quantum phase transitions
• Finite-component dynamical quantum phase transitions
• Dynamical quantum phase transition from a critical quantum quench
• Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
• Dynamical quantum phase transitions in spin-$S$ $\mathrm{U}(1)$ quantum link models
• Unconventional critical exponents at dynamical quantum phase transitions in a random Ising chain
• Hybrid infinite time-evolving block decimation algorithm for long-range multi-dimensional quantum many-body systems
• Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points
• Detecting quantum phase transitions in the quasi-stationary regime of Ising chains
• Environment induced dynamical quantum phase transitions in two-qubit Rabi model
• Exotic signature of dynamical quantum phase transition in the time evolution of engineered initial state
• Quantum Supercritical Crossover with Dynamical Singularity