Research

Various lattice spin models are related with their gauge theories and their effective field theories. Most well-known examples are the relation of the toric code, rank-1 gauge theory, and the BF theory. We have been working on creating the formalism deriving the effective field theory of the lattice spin models based on the constant application of the gauge principle. Furthermore, we analyzed the rank-2 toric code and rank-2 gauge theory and showed the exotic behavior of quasiparticles. Their braiding statistics depends on the initial locations of the quasiparticles, and we tried effective field theoretical analysis.

1. Oh, Y. T., Kim, J., Moon, E. G., & Han, J. H. (2022). Rank-2 toric code in two dimensions. Physical Review B, 105(4), 045128.
2. Oh, Y. T., Kim, J., & Han, J. H. (2022). Effective field theory of dipolar braiding statistics in two dimensions. Physical Review B, 106(15), 155150.
3. Kim, J., Oh, Y. T., & Han, J. H. (2022). Hybrid rank-1 and rank-2 U (1) lattice gauge theory, the F3 model, and its effective field theory. Physical Review B, 106(15), 155154.
4. Oh, Y. T., Pace, S. D., Han, J. H., You, Y., & Lee, H. Y. (2023). Aspects of Z_N rank-2 gauge theory in (2+ 1) dimensions: Construction schemes, holonomies, and sublattice one-form symmetries. Physical Review B, 107(15), 155151.

Tensor networks are useful to represent exact or variational low energy wave functions in many-body Hamiltonian. A network of individual tensors is used to express the wave function as a tensor contraction. Matrix product states and projected entangled pair states are respectively used for 1D and 2D many-body system. Individual tensor structure can impose global symmetries on the wave function. The mathematical structure of the tensor network can also be used to derive strict bounds on quantities like entanglement and correlation length.

1. Kim, J. et al. Path integral for spin-1 chain in the fluctuating matrix product state basis. Phys. Rev. B  102, 041105
2. Kim, J. et al. Construction of variational matrix product states for the Heisenberg spin-1 chain. Phys. Rev. B 102, 085117
3. Kim, J. et al. Matrix product wave function of the ground state and elementary excitations in the spin-1/2 chain. Phys. Rev. B 103, 125157.

Fault-tolerant quantum computing scheme is essential for large-scale quantum computation. Non-fault-tolerant quantum computation leads to the error of multiple qubits consisting of the logical qubit and the error of information after decoding. One of the well-known ways to execute universal fault-tolerant quantum computation is using a three-dimensional cluster state. Quantum computation using a three-dimensional cluster state include various specific methods such as lattice surgery for two-qubit gates computation and planar code construction for high threshold quantum computation. We study three-dimensional cluster state construction, photonic quantum computation, and magic state distillation.

1. Kim, J. et al. Fault-tolerant Quantum Computation Using a Linear Array of Emitters, arxiv 2403.01376