Non-equilibrium Renormalization Group Fixed-Points of the Quantum Clock Chain and the Quantum Potts chain

Abstract

We derive an exact renormalization group recursion relation for the Loschmidt amplitude of the quantum $Q$-state clock model and the quantum $Q$-state Potts model in one dimension. The renormalization group flow is discussed in detail. The fixed-points of the renormalization group flow are found to be complex in general. These fixed-points control the dynamical phases of the two models, giving rise to non-analyticities in its Loschmidt rate function, for both the pure and the disordered system. For the quench protocols studied, dynamical quantum phase transitions are found to occur in the clock model for all $Q$s considered, while in the Potts model, they only occur when $Q$ < 4.

arXiv admin note: text overlap with arXiv:1908.04476

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• 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
• Dynamical Quantum Phase Transitions of Quantum Spin Chains with the Loschmidt-rate Critical Exponent equal to $\frac{1}{2}$
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Detecting quantum phase transitions in the quasi-stationary regime of Ising chains
• Dynamical scaling laws in the quantum $q$-state clock chain