Universal Critical Behaviors in Non-Hermitian Phase Transitions

Abstract

Quantum phase transitions also occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal behaviors for phase transitions in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many-body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems: (i) It bridges the nonanalytic behavior in physical observable and nonanalytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. (ii) It predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being $(1-1/p),2(1-1/p),\cdots ,n(1-1/p),\cdots$ with $p$ being the number of coalesced states at the exceptional point and $n$ being a positive integer. (iii). It reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being $(1-1/p),2(1-1/p),\cdots ,n(1-1/p),\cdots$. These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics and establish foundations for quantum metrology in non-Hermitian systems.

5 pages,2 Figures

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• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Loschmidt echo and fidelity decay near an exceptional point
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Signature of exceptional point phase transition in Hermitian systems
• Quantum Work Relations and Response Theory in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Systems
• Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains
• Links between Dissipation and Rényi Divergences in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Kondo effect in a non-Hermitian, $\mathcal{P}\mathcal{T}$-symmetric Anderson model with Rashba spin-orbit coupling
• Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Tunable tachyon mass in the PT-broken massive Thirring model
• Analytical Study of the Non-Hermitian Semiclassical Rabi Model
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Semi-localization transition driven by a single asymmetrical tunneling
• Continuous phase transition induced by non-Hermiticity in the quantum contact process model
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions