Complex dynamics approach to dynamical quantum phase transitions: the Potts model

Abstract

This paper introduces complex dynamics methods to study dynamical quantum phase transitions in the one- and two-dimensional quantum 3-state Potts model. The quench involves switching off an infinite transverse field. The time-dependent Loschmidt echo is evaluated by an exact renormalization group (RG) transformation in the complex plane where the thermal Boltzmann factor is along the positive real axis, and the quantum time evolution is along the unit circle. One of the characteristics of the complex dynamics constituted by repeated applications of RG is the Julia set, which determines the phase transitions. We show that special boundary conditions can alter the nature of the transitions, and verify the claim for the one-dimensional system by transfer matrix calculations. In two dimensions, there are alternating symmetry-breaking and restoring transitions, both of which are first-order, despite the criticality of the Curie point. In addition, there are finer structures because of the fractal nature of the Julia set. Our approach can be extended to multi-variable problems, higher dimensions, and approximate RG transformations expressed as rational functions.

arXiv comment18 pages, 10 figures, 2 tables. Replaced by the published version

References in corpus (27)

• Nonequilibrium dynamics of closed interacting quantum systems
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• 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
• Dynamical quantum phase transitions: scaling and universality
• Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
• A Measure of data-collapse for scaling
• Special invited paper. Large deviations
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Floquet dynamical phase transition and entanglement spectrum
• Floquet dynamical quantum phase transition in the extended XY model: nonadiabatic to adiabatic topological transition
• Boundary Critical Phenomena in the Three-State Potts Model
• Dynamical phase transitions in the two-dimensional transverse-field Ising model
• Dynamical Topological Quantum Phase Transitions at Criticality
• Dynamical quantum phase transitions in the quantum Potts chain
• Finite temperature dynamical quantum phase transition in a non-Hermitian system
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Dynamical quantum phase transition from a critical quantum quench
• Boundaries and unphysical fixed points in Dynamical Quantum Phase Transitions
• Non-equilibrium criticality in quench dynamics of infinite-range spin models
• Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points
• Degenerate groundstates and multiple bifurcations in a two-dimensional q-state quantum Potts model
• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field
• Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line
• Dynamical scaling laws in the quantum $q$-state clock chain

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• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Julia Set in Quantum Evolution: The case of Dynamical Quantum Phase Transitions
• Emergent dynamical quantum phase transition in a $Z_3$ symmetric chiral clock model