Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States,Physical Review Letters

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Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States
Physical Review Letters ( IF 8.1 ) Pub Date : 2023-05-25 , DOI: 10.1103/physrevlett.130.216704
Guo-Yi Zhu ₁ , Ji-Yao Chen _{2,

3} , Peng Ye _{2,

4} , Simon Trebst ₁

Affiliation

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a

Z_{N}

generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wave function deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the

Z_{N}

model we find a family of (weakly) first-order fracton confinement transitions that in the limit of

N \to \infty

converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the