Devil's staircases, quantum dimer models, and stripe formation in strong coupling models of quantum frustration

Abstract

We construct a two-dimensional microscopic model of interacting quantum dimers that displays an infinite number of periodic striped phases in its T=0 phase diagram. The phases form an incomplete devil's staircase and the period becomes arbitrarily large as the staircase is traversed. The Hamiltonian has purely short-range interactions, does not break any symmetries of the underlying square lattice, and is generic in that it does not involve the fine-tuning of a large number of parameters. Our model, a quantum mechanical analog of the Pokrovsky-Talapov model of fluctuating domain walls in two dimensional classical statistical mechanics, provides a mechanism by which striped phases with periods large compared to the lattice spacing can, in principle, form in frustrated quantum magnetic systems with only short-ranged interactions and no explicitly broken symmetries.

21 pages, 27 figures

References in corpus (31)

• Anyons in an exactly solved model and beyond
• How to detect fluctuating order in the high-temperature superconductors
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Electronic Liquid Crystal Phases of a Doped Mott Insulator
• An RVB phase in the triangular lattice quantum dimer model
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Experimental realization of a 2D fractional quantum spin liquid
• Stripe phases in high-temperature superconductors
• Topological Order and Conformal Quantum Critical Points
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Fractionalization in an Easy-axis Kagome Antiferromagnet
• Algebraic spin liquid as the mother of many competing orders
• Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
• Charge order, superconductivity, and a global phase diagram of doped antiferromagnets
• Putting competing orders in their place near the Mott transition
• Relaxation time for a dimer covering with height representation
• Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids
• Universal Aspects of Coulomb Frustrated Phase Separation
• Separation of Spin and Charge Quantum Numbers in Strongly Correlated Systems
• Phase separation frustrated by the long range Coulomb interaction I: Theory
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Spin nematics and magnetization plateau transition in anisotropic Kagome magnets
• SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Competing orders II: the doped quantum dimer model
• Quasi-1D dynamics and nematic phases in the 2D Emery model
• Stripes and holes in a two-dimensional model of spinless fermions and hardcore bosons
• Quantum Disordered Ground States in Frustrated Antiferromagnets with Multiple Ring Exchange Interactions
• Superfluid-Insulator transitions of bosons on Kagome lattice at non-integer fillings
• Lifting of Multiphase Degeneracy by Quantum Fluctuations

Cited by in corpus (18)

• Emerging 2D Gauge theories in Rydberg configurable arrays
• Incomplete devil's staircase in the magnetization curve of SrCu2(BO3)2
• Geometric frustration in compositionally modulated ferroelectrics
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
• Evidence for deconfined $U(1)$ gauge theory at the transition between toric code and double semion
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Phase diagram of an extended quantum dimer model on the hexagonal lattice
• First- order versus unconventional phase transitions in three-dimensional dimer models
• Incommensurate spin density modulation in a copper-oxide chain compound with commensurate charge order
• Resonating Valence Bond States in an Electron-Phonon System
• Emergent topological excitations in a two-dimensional quantum spin system
• Criticality of a classical dimer model on the triangular lattice
• Devil's staircases without particle-hole symmetry
• Extended Quantum Dimer Model and novel valence-bond phases
• Topological properties of a Valence-Bond-Solid
• Quantum dimer models and exotic orders