Hilbert Space Fragmentation and Ashkin-Teller Criticality in Fluctuation Coupled Ising Models

Abstract

We discuss the effects of exponential fragmentation of the Hilbert space on phase transitions in the context of coupled ferromagnetic Ising models in arbitrary dimension with special emphasis on the one dimensional case. We show that the dynamics generated by quantum fluctuations is bounded within spatial partitions of the system and weak mixing of these partitions caused by global transverse fields leads to a zero temperature phase with ordering in the local product of both Ising copies but no long range order in either species. This leads to a natural connection with the Ashkin-Teller universality class for general lattices. We confirm this for the periodic chain using quantum Monte Carlo simulations. We also point out that our treatment provides an explanation for pseudo-first order behavior seen in the Binder cumulants of the classical frustrated $J_1-J_2$ Ising model and the $q=4$ Potts model in 2D.

References in corpus (21)

• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• "Deconfined" quantum critical points
• Quantum annealing with more than one hundred qubits
• Stochastic series expansion method with operator-loop update
• Quantum Glassiness
• Fractons
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Deconfined quantum critical points: symmetries and dualities
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Higher dimensional realizations of activated dynamic scaling at random quantum transitions
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• A semi-classical limit for the many-body localization transition
• Analysis of the phase transition for the Ising model on the frustrated square lattice
• Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model
• Universal ratios along a line of critical points. The Ashkin--Teller model
• Quantum-criticality and percolation in dimer-diluted 2D antiferromagnets

Cited by in corpus (7)

• Hilbert-Space Fragmentation from Strict Confinement
• Statistical localization: from strong fragmentation to strong edge modes
• Non-Hermitian skin clusters from strong interactions
• Height-conserving quantum dimer models
• Non-monotonic behavior of the Binder Parameter in the discrete spin systems
• Phase determination with and without deep learning
• Protecting Hilbert space fragmentation through quantum Zeno dynamics