Numerical study of critical properties and hidden orders in dimerized spin ladders

Abstract

Dimerized antiferromagnetic spin-1/2 ladders are known to exhibit a quantum critical phase transition in the ground state, the existence or absence of which is dependent on the dimerization pattern of the ladder. The gapped phases cannot be distinguished by the conventional Landau long-range order parameter. However, they possess a non-local (hidden) string order parameter, which is non-zero in one phase and vanishes in the other. We use an exact diagonalization technique to calculate ground state energies, energy gaps and string order parameters of dimerized two- and three-leg Heisenberg ladders, as well as a critical scaling analysis to yield estimates of the critical exponents nu and beta.

7 pages, 14 figures. V.2: Extended version to appear in PRB

References in corpus (7)

• Topological Order, Dimerization, and Spinon Deconfinement in Frustrated Spin Ladders
• DMRG Study of Critical Behavior of the Spin-1/2 Alternating Heisenberg Chain
• Quantum Criticality in Dimerized Spin Ladders
• DMRG study of the Bond Alternating \textbf{S}=1/2 Heisenberg ladder with Ferro-Antiferromagnetic couplings
• Spin-Peierls instability in the three-leg Heisenberg ladder
• Critical Lines and Massive Phases in Quantum Spin Ladders with Dimerization
• Twisted Order Parameter applied to Dimerized Ladders

Cited by in corpus (14)

• Local and nonlocal order parameters in the Kitaev chain
• Melting of a frustration-induced dimer crystal and incommensurability in the J_1-J_2 two-leg ladder
• Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
• Topological Order Parameters of the Spin-1/2 Dimerized Heisenberg Ladder in Magnetic Field
• Berry phase investigation of spin-S ladders
• String and conventional order parameters in the solvable modulated quantum chain
• Constructing Landau framework for topological order: Quantum chains and ladders
• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions
• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Brane order and quantum magnetism in modulated anisotropic ladders
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models
• Plaquette Order in a Dimerized Frustrated Spin-Ladder
• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions