Order-by-disorder and quantum Coulomb phase in quantum square ice

Abstract

We reconstruct the equilibrium phase diagram of quantum square ice, realized by the transverse-field Ising model on the checkerboard lattice, using a combination of quantum Monte Carlo, degenerate perturbation theory and gauge mean-field theory. The extensive ground-state degeneracy of classical square ice is lifted by the transverse field, leading to two distinct order-by-disorder phases, a plaquette valence-bond solid for low field, and a canted Neel state for stronger fields. These two states appear via a highly non-linear effect of quantum fluctuations, and they can be identified with the phases of a lattice gauge theory (quantum link model) emerging as the effective Hamiltonian of the system within degenerate perturbation theory up to the 8th order. The plaquette valence-bond solid melts at a very low temperature, above which the system displays a thermally induced quantum Coulomb phase, supporting deconfined spinons.

5+5 pages, 4+3 figures

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Cited by in corpus (24)

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• Dynamics of Topological Excitations in a Model Quantum Spin Ice
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• Classical and quantum theories of proton disorder in hexagonal water ice
• Spinon walk in quantum spin ice
• Hierarchy of energy scales and field-tunable order by disorder in dipolar-octupolar pyrochlores
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• Generation of ice states through deep reinforcement learning
• Free coherent spinons in quantum square ice
• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Monte Carlo study of the discontinuous quantum phase transition in the transverse-field Ising model on the pyrochlore lattice
• Prethermal time-crystalline spin ice and monopole confinement in a driven magnet
• Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach
• Quantum phase diagram of two-dimensional transverse field Ising model: unconstrained tree tensor network and mapping analysis
• Solving the quantum dimer and six vertex models one electric field line at a time
• Tuning the two-step melting of magnetic orders in a dipolar kagome spin ice by quantum fluctuations
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Synchronization transition in the double dimer model on the cubic lattice
• Classical fully-packed loop model with attractive interactions on the square lattice
• Symmetry-deformed toric codes and the quantum dimer model
• Crystalline phases and devil's staircase in qubit spin ice
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• Ice on curved surfaces: defect rings and differential local dynamics