Deconfined Quantum Criticality and Phase Transitions in 3D Classical Loop Models

Flavio S. Nogueira, Asle Sudbø

Adam Nahum, J. T. Chalker, Pablo Serna +2 more

Two-dimensional Mott insulators allow for a remarkable ``deconfined'' quantum phase transition. A new theoretical and computational study shows that this controversial critical point may be even stranger than previously thought.

Bowen Zhao

Guoyi Zhu, Ji-Yao Chen, Peng Ye +1 more

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→∞ 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 N→∞ limit, appears to coexist with a gapless deconfined fracton state.

Sena Watanabe, Yukitoshi Motome, Haruki Watanabe

We develop a self-contained theoretical framework that classifies the topological phases and critical phenomena of classical pyrochlore magnets with arbitrary spin S , subject to competing exchange and single-ion anisotropies. We work first in the monopole-free (ice-rule) limit. In the small- w regime, where the single-ion term favors low spin amplitudes, dualities reveal a dichotomy: Integer spins exhibit a continuous 3D X Y deconfinement transition, whereas half-integer spins remain in a U(1) Coulomb liquid without any transition. In the large- w regime, where the local spin amplitudes are maximized ( | S z | = S ), the macroscopic flux is quantized to multiples of 2 S . By mapping the defect structure to topological loop gases, we prove that the compatibility between the physical ice rule and the modular Z 2 S flux conservation holds at the vertex level if and only if S ≤ 3 / 2 . For S = 3 / 2 , this maps the system to the three-state Potts model, whose symmetry-allowed cubic invariant drives a first-order transition. For S ≥ 2 , no mapping to a discrete clock model exists. Using a decomposition of the partition function, we show that the only processes sensitive to the discrete Z 2 S structure carry exponentially small statistical weight and correspond to irrelevant operators at the 3D X Y fixed point, so the deconfinement transition is of the 3D X Y type. Finally, incorporating thermal monopoles, we show that they act as a symmetry-breaking effective magnetic field that severs defect strings. Consequently, the continuous transitions are rounded into crossovers, whereas the first-order S = 3 / 2 transition is predicted to survive at finite temperatures, terminating at a critical end point. Classical Monte Carlo simulations for S up to 7 / 2 corroborate the predicted crossover behavior at the accessible temperatures; these temperatures lie above the estimated critical end point, so the predicted survival of the S = 3 / 2 first-order transition remains to be tested directly.

Bowen Zhao, Anders W. Sandvik