Quantum phase transitions in a strongly entangled spin-orbital chain: A field-theoretical approach

Abstract

Motivated by recent experiments on quasi-1D vanadium oxides, we study quantum phase transitions in a one-dimensional spin-orbital model describing a Haldane chain and a classical Ising chain locally coupled by the relativistic spin-orbit interaction. By employing a field-theoretical approach, we analyze the topology of the ground-state phase diagram and identify the nature of the phase transitions. In the strong coupling limit, a long-range Néel order of entangled spin and orbital angular momentum appears in the ground state. We find that, depending on the relative scales of the spin and orbital gaps, the linear chain follows two distinct routes to reach the Néel state. First, when the orbital exchange is the dominating energy scale, a two-stage ordering takes place in which the magnetic transition is followed by melting of the orbital Ising order; both transitions belong to the two-dimensional Ising universality class. In the opposite limit, the low-energy orbital modes undergo a continuous reordering transition which represents a line of Gaussian critical points. On this line the orbital degrees of freedom form a Tomonaga-Luttinger liquid. We argue that the emergence of the Gaussian criticality results from merging of the two Ising transitions in the strong hybridization region where the characteristic spin and orbital energy scales become comparable. Finally, we show that, due to the spin-orbit coupling, an external magnetic field acting on the spins can induce an orbital Ising transition.

13 pages, 2 figures

References in corpus (18)

• Anyons in an exactly solved model and beyond
• Bosonization and Strongly Correlated Systems
• Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
• One-Dimensional Magnetism
• One-dimensional spin-liquid without magnon excitations
• Orbital ordering and frustration of $p$-band Mott-insulators
• SU(4) spin-orbit critical state in one dimension
• Thermodynamics of the one-dimensional SU(4) symmetric spin-orbital model
• Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays
• Phase diagram of a 1 dimensional spin-orbital model
• Orbital order in Mott insulators of spinless p-band fermions
• Equal Time Correlations in Haldane Gap Antiferromagnets
• NMR relaxation rate and dynamical structure factors in nematic and multipolar liquids of frustrated spin chains under magnetic fields
• Theory of Nuclear Magnetic Relaxation in Haldane Gap Antiferromagnets
• Single Crystal Growth, Crystallography, Magnetic Susceptibility, Heat Capacity, and Thermal Expansion of the Antiferromagnetic S = 1 Chain Compound CaV2O4
• Magnetic Structure and Interactions in the Quasi-1D Antiferromagnet CaV${}_2$O${}_4$
• Model for frustrated spin-orbital chains: application to CaV2O4
• Quantum criticality of vanadium chains with strong relativistic spin-orbit interaction

Cited by in corpus (5)

• Fingerprints of spin-orbital entanglement in transition metal oxides
• Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
• Orbital multicriticality in spin gapped quasi-1D antiferromagnets
• Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model
• Orbital- and spin-driven lattice instabilities in quasi-one-dimensional CaV${}_2$O${}_4$