Quantum complexity across thermal phase transition in the transverse field Ising chain with long-range couplings

TL;DR

This paper explores how quantum complexity indicators like entanglement and non-stabiliserness behave near thermal phase transitions in a long-range transverse-field Ising model, revealing quantum signatures at classical critical points.

Contribution

It demonstrates the emergence of quantum complexity signatures at thermal phase transitions using tensor-network simulations of thermal states.

Findings

Quantum observables show pronounced signatures at thermal criticality.

Quantum complexity indicators reveal coherence near classical phase transitions.

Tensor-network methods effectively simulate thermal states in long-range models.

Abstract

We investigate the behavior of the Schmidt gap, the von Neumann entanglement entropy, and the non-stabiliserness in proximity to the classical phase transition of the one-dimensional long-range transverse-field Ising model (LRTFIM). Leveraging the time-dependent variational principle (TDVP) within a tensor-network formulation, we simulate thermal states through their purified tensor-network representations. Our results show that these observables, typically regarded as hallmarks of quantum criticality, exhibit pronounced and coherent signatures even at a classical thermal transition, highlighting the emergence of quantum complexity as the system nears thermal criticality.