Diagnosing order by disorder in quantum spin systems

Abstract

In this paper we study the frustrated J1-J2 quantum Heisenberg model on the square lattice for J2 > 2J1, in a magnetic field. In this regime the classical system is known to have a degenerate manifold of lowest energy configurations, where standard thermal order by disorder occurs. In order to study its quantum version we use a path integral formulation in terms of coherent states. We show that the classical degeneracy in the plane transverse to the magnetic field is lifted by quantum fluctuations. Collinear states are then selected, in a similar pattern to that set by thermal order by disorder, leaving a Z2 degeneracy. A careful analysis reveals a purely quantum mechanical effect given by the tunneling between the two minima selected by fluctuations. The effective description contains two planar (XY -like) fields conjugate to the total magnetization and the difference of the two sublattice magnetizations. Disorder in either or both of these fields produces the locking of their conjugate observables. Furthermore, within this scenario we argue that the quantum state is close to a product state.

8 pages, 3 figures

References in corpus (26)

• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Li${}_2$VO(Si,Ge)O${}_4$, a prototype of a two-dimensional frustrated quantum Heisenberg antiferromagnet
• Critical Exponents of the 3D Ising Universality Class From Finite Size Scaling With Standard and Improved Actions
• Field induced ordering in highly frustrated antiferromagnets
• Ising transition driven by frustration in a 2D classical model with SU(2) symmetry
• Quantum disordered phase on the frustrated honeycomb lattice
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model
• Very low-frequency excitations in frustrated two-dimensional $S=1/2$ Heisenberg antiferromagnets
• From classical to quantum Kagome antiferromagnet in a magnetic field
• Quantum vs. Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains
• A Monte Carlo analysis of the phase transitions in the 2D, $J_1-J_2$ XY model
• Quantum phases in the frustrated Heisenberg model on the bilayer honeycomb lattice
• Geometric phases and the magnetization process in quantum antiferromagnets
• Combined analytical and numerical approach to magnetization plateaux in one-dimensional spin tube antiferromagnets
• Combined analytical and numerical approach to study magnetization plateaux in doped quasi-one-dimensional antiferromagnets
• Statistical transmutation in doped quantum dimer models
• Emergent Criticality and Friedan Scaling in a 2D Frustrated Heisenberg Antiferromagnet
• Statistics of holes and nature of superfluid phases in Quantum dimer models
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Phase diagram study of a dimerized spin-S zig-zag ladder
• Two-dimensional Hubbard Model in the presence of lattice distortions

Cited by in corpus (6)

• Ground-State Ordering of the $J_1$--$J_2$ Model on the Simple Cubic and Body-Centered Cubic Lattices
• Magnon crystals and magnetic phases in a Kagomé-stripe antiferromagnet
• An effective field theory approach for the $S=3/2$ bilayer honeycomb antiferromagnet
• Current jumps in flat band ladders with Dzyaloshinskii-Moriya interactions
• Quantum order by disorder in Frustrated Spin Nanotubes
• Optimizing configurations for determining the magnetic model based on ab-initio calculations