Dynamical quantum phase transitions from random matrix theory
arXiv:2208.01659 · doi:10.22331/q-2024-02-29-1271
Abstract
We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the Loschmidt echo. This leads to the study of a random matrix ensemble with a complex weight, whose analysis requires novel technical considerations, that we develop. We obtain three main results: 1) There is a third order phase transition at a rescaled critical time, that we determine. 2) The third order phase transition persists away from the thermodynamic limit. 3) For times below the critical value, the difference between the thermodynamic limit and a finite chain decreases exponentially with the system size. All these results depend in a rich manner on the parity of the number of flipped spins of the quantum state conforming the fidelity.
v2: 60 pages, 18 figures, published version
References in corpus (37)
- Probing many-body dynamics on a 51-atom quantum simulator
- Many body localization and thermalization in quantum statistical mechanics
- Dynamics of Loschmidt echoes and fidelity decay
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Topological classification of dynamical phase transitions
- First order dynamical phase transitions
- Symmetry enriched phases of quantum circuits
- Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
- Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
- Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
- Entanglement view of dynamical quantum phase transitions
- From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in Heisenberg spin chains
- Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition
- Floquet dynamical quantum phase transitions under synchronized periodic driving
- Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain
- Dynamical quantum phase transitions in the quantum Potts chain
- Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
- Entanglement entropy in the Ising model with topological defects
- Dissipative Floquet Dynamical Quantum Phase Transition
- Delayed Deconfinement and the Hawking-Page Transition
- Observing crossover between quantum speed limits
- Determination of dynamical quantum phase transitions in strongly correlated many-body systems using Loschmidt cumulants
- Exceptional Dynamical Quantum Phase Transitions in Periodically Driven Systems
- Dynamical and excited-state quantum phase transitions in collective systems
- Anomaly in dynamical quantum phase transition in non-Hermitian system with extended gapless phases
- Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
- Dynamical quantum phase transitions in spin- quantum link models
- Simulating prethermalization using near-term quantum computers
- Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
- Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems
- Lattice gauge theory and dynamical quantum phase transitions using noisy intermediate scale quantum devices
- Phases of five-dimensional supersymmetric gauge theories
- Dynamical quantum phase transition in diamond: applications in quantum metrology
- Multiple phases and meromorphic deformations of unitary matrix models
- Critical exponents for higher order phase transitions: Landau theory and RG flow
- Exact time evolution formulae in the XXZ spin chain with domain wall initial state
- Classical group matrix models and universal criticality