Finite-Size Spectral Signatures of Order by Quantum Disorder: A Perspective from Anderson's Tower of States

Abstract

In frustrated magnetic systems with a subextensive number of classical ground states, quantum zero-point fluctuations can select a unique long-range ordered state, a celebrated phenomenon referred to as \emph{order by quantum disorder} (ObQD). For frustrated spin-$\frac{1}{2}$ models, unbiased numerical methods able to expose ObQD are necessary. We show that ObQD can be identified from exact diagonalization (ED) calculations through an analysis akin to the Anderson tower of states associated with spontaneous symmetry breaking. By defining an effective quantum rotor model, we describe the competition between ObQD-induced localization of the rotor and its tunneling between symmetry-related ground states, identifying the crossover lengthscale from the finite-size regime where the rotor is delocalized, to the infinite system-size limit where it becomes localized. This rotor model relates the characteristic splittings in the ED energy spectrum to the ObQD selection energy scale, providing an estimate that can be compared to spin wave calculations. We demonstrate the general applicability of this approach in one-, two- and three-dimensional frustrated spin models that exhibit ObQD.

arXiv commentMain text (7 pages including 4 figures), 1 page End Matter including 2 figures, and the supplemental material (7 pages including 4 figures )

References in corpus (51)

• Anyons in an exactly solved model and beyond
• The density-matrix renormalization group in the age of matrix product states
• Quantum Spin Liquids
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Quantum Monte Carlo with Directed Loops
• Spin-Orbit Physics Giving Rise to Novel Phases in Correlated Systems: Iridates and Related Materials
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Computational Studies of Quantum Spin Systems
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
• An investigation of the quantum $J_1-J_2-J_3$ model on the honeycomb lattice
• Er2Ti2O7: Evidence of Order by Disorder in a Frustrated Antiferromagnet
• Finite size and temperature effects in the AF Heisenberg model
• Frustrated quantum rare-earth pyrochlores
• Definitive Evidence for Order-by-Quantum-Disorder in Er2Ti2O7
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Quantum order by disorder and accidental soft mode Er2Ti2O7
• Recent Developments of World-Line Monte Carlo Methods
• A Short Introduction to Numerical Linked-Cluster Expansions
• Order-by-Disorder from Bond-Dependent Exchange and Intensity Signature of Nodal Quasiparticles in a Honeycomb Cobaltate
• Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories
• Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Order by Disorder Spin Wave Gap in the XY Pyrochlore Magnet Er2Ti2O7
• Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited
• $J_1-J_2$ quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder
• Order from structural disorder in $XY$ pyrochlore antiferromagnet $\mathrm{E}{\mathrm{r}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions
• Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb
• Comprehensive study of the phase diagram of the spin-1/2 Kitaev-Heisenberg-Gamma chain
• Unravelling competing microscopic interactions at a phase boundary: a single crystal study of the metastable antiferromagnetic pyrochlore Yb${}_2$Ge${}_2$O${}_7$
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Transition from the ${\mathbb{Z}}_2$ spin liquid to antiferromagnetic order: spectrum on the torus
• Extended degeneracy and order by disorder in the square lattice J${}_1$-J${}_2$-J${}_3$ model
• Spectrum of the Wilson-Fisher conformal field theory on the torus
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Quantum versus thermal fluctuations in the fcc antiferromagnet: alternative routes to order by disorder
• Pseudo-Goldstone modes and dynamical gap generation from order-by-thermal-disorder
• Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point
• Rotor/spin-wave theory for quantum spin models with U(1) symmetry
• State selection in frustrated magnets
• Effective theories for quantum spin clusters: Geometric phases and state selection by singularity
• Order-by-disorder without quantum zero-point fluctuations in the pyrochlore Heisenberg ferromagnet with Dzyaloshinskii-Moriya interactions
• Berry phase in the rigid rotor: the emergent physics of odd antiferromagnets
• Effective Hamiltonian and low-lying energy clustering patterns of four-sublattice antiferromagnets
• Ground state properties of the Heisenberg-compass model on the square lattice
• Left-left-right-right magnetic order in spin-1/2 Kitaev-Heisenberg chain
• The quantum spin quadrumer