Numerical Investigations of SO(4) Emergent Extended Symmetry in Spin-1/2 Heisenberg Antiferromagnetic Chains

Abstract

The antiferromagnetic Heisenberg chain is expected to have an extended symmetry, [SU(2)xSU(2)]/Z 2 , in the infrared limit, whose physical interpretation is that the spin and dimer order parameters form the components of a common 4-dimensional vector. Here we numerically in- vestigate this emergent symmetry using quantum Monte Carlo simulations of a modified Heisenberg chain (the J-Q model) in which the logarithmic scaling corrections of the conventional Heisenberg chain can be avoided. We show how the two- and three-point spin and dimer correlation func- tions approach their forms constrained by conformal field theory as the system size increases and numerically confirm the expected effects of the extended symmetry on various correlation functions.

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• First-principle simulations of 1+1d quantum field theories at $\theta =\pi$ and spin-chains
• Fixed point annihilation for a spin in a fluctuating field
• Dynamical signatures of the one-dimensional deconfined quantum critical point
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• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Emergent O(4) symmetry at an one-dimensional deconfined quantum tricritical point
• Short-imaginary-time quantum critical dynamics in the J-Q${}_3$ spin chain
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet