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Entanglement
Integrability
Renormalization
Symmetry
Tensor Network
Topology
Research Highlights
Research Highlights
Entanglement and Tensor Network
Entanglement and Tensor Network
Ground states (GSs) of gapped quantum systems obey the area law of entanglement entropy (EE), but how entangled can gapless GS be? It turns out that by mapping lattice spin configurations to random surfaces under boundary constraints, local interactions can be designed to make the EE of the GS scale with the volume of the subsystem. Tuning a deformation parameter in the Hamiltonian, the GS undergoes an entanglement phase transition, the first example of its kind.
ZZ, and IK, Quantum Lozenge Tiling and Entanglement Phase Transition. Quantum 8, 1497, 2024.
ZZ, and IK, Coupled Fredkin and Motzkin Chains from Six- and 19-vertex Models. SciPost Physics 15 (2), 044, 2023.
ZZ, et al., Novel Quantum Phase Transition from Bounded to Extensive Entanglement. PNAS, 114 (20) 5142-5146, 2017.
Such GSs can be represented by tensor networks (TNs) in one dimension higher than the physical system. At the critical point, the TNs can be optimized to hierachical structures like the multiscale entanglement renormalization ansatz (MERA).
OM, and ZZ, Reconciling Translational Invariance and Hierarchy. submitted to Quantum, 2025
OM, and ZZ, Highly Entangled 2D Ground States: Tensor Networks and Correlation Functions. submitted to SciPost Physics, 2025
Integrability and Symmetry
Integrability and Symmetry
Spin chains with binary local degrees of freedom and nearest neighbor interactions are either integrable or non-integrable. But for higher spin SU(2) or multicomponent SU(N) chains, the symmetry of the Heisenberg interaction can be broken to the smaller permutation group such that integrability is partially broken. Non-trivial Bethe states can be solved after a clever basis transformation in some non-integrable subspaces.
ZZ, and GM, Hidden Bethe States in a Partially Integrable Model. Phys. Rev. B 106, 134420, 2022.
The ideas of integrability and symmetry can be applied to show the partial resonant valence bond nature of the infinite-U Hubbard model ground states in the singly doped kinetically frustrated lattices of the sawtooth chain and pyrochlore stripe, which can be exactly solved in the thermodynamic limit.
ZZ and CG, Resonating Valence Bond Ground States on Corner-sharing Simplices. submitted to SciPost Physics, 2025
Topology and Ergodicity
Topology and Ergodicity
Spectral gap is the condensed matter physics counterpart of mass in elementary particle physics. Symmetry breaking and interactions are two different ways to open up an energy gap between the ground state and first excited state, just as they are for mass generation. In quantum many-body physics, they are closely related to topological order and Hilbert-space fragmentation. Ring-exchange moves on close-packed dimers and loops in general leads to the latter. But whether the ground state degeneracy is accounted for by topological sectors or Krylov subspaces, depends on the lattice. By showing the necessity of the additional butterfly move on the triangular lattice, we expect the ergodicity of the Rokhsar-Kivelson moves to be behind the resonant valence bond liquid phase of the triangular quantum dimer model.
ZZ, Bicolor Loop Models and Their Long Range Entanglement. Quantum 8, 1268, 2024.
HR, and ZZ, Ergodic Archimedean Dimers. SciPost Physics Core 6 (3), 054, 2023.
ZZ, and H. S. Røising, The Frustration-free Fully Packed Loop Model. J Phys. A: Math. Theor. 56, 194001, 2023.
SS, et al., Coupled Wire Model of Symmetric Majorana Surfaces of Topological Superconductors. Phys. Rev. B (Editors' Suggestion), 94, 165142, 2016.
Renormalization Group
Renormalization Group
When strong disorder is combined with hierarchical lattices, the Schrieffer-Wolff transformation can be applied to perform exact renormalization group calculations that reveal the interplay between entanglement, curvature and topological defects.
ZZ, Entanglement Blossom in a Simplex Matryoshka. Annals of Physics 457, 169395, 2023.
Transfer matrix and renormalization group are two analytical tools for studying many-body physics. They are usually applied to drastically different systems, with either translational invariance or hierarchical structures. With a tensor network realization of the pentagon identity, they were shown to be compatible in the first exact MERA ground states, the critical exponents of which are computed using the transfer matrix.
OM, and ZZ, Exact critical exponents of the Motzkin and Fredkin Chains. submitted to SciPost Physics, 2026
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