TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.2.044
TI  - Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
PY  - 2023/08/02
UR  - https://www.scipost.org/SciPostPhys.15.2.044
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 2
SP  - 044
A1  - Zhang, Zhao
AU  - Klich, Israel
AB  - We generalize the area-law violating models of Fredkin and Motzkin spin chains into two dimensions by building quantum six- and nineteen-vertex models with correlated interactions. The Hamiltonian is frustration free, and its projectors generate ergodic dynamics within the subspace of height configuration that are non negative. The ground state is a volume- and color-weighted superposition of classical bi-color vertex configurations with non-negative heights in the bulk and zero height on the boundary. The entanglement entropy between subsystems has a phase transition as the $q$-deformation parameter is tuned, which is shown to be robust in the presence of an external field acting on the color degree of freedom. The ground state undergoes a quantum phase transition between area- and volume-law entanglement phases with a critical point where entanglement entropy scales as a function $L\log L$ of the linear system size $L$. Intermediate power law scalings between $L\log L$ and $L^2$ can be achieved with an inhomogeneous deformation parameter that approaches 1 at different rates in the thermodynamic limit. For the $q>1$ phase, we construct a variational wave function that establishes an upper bound on the spectral gap that scales as $q^{-L^3/8}$.
ER  -

@Article{10.21468/SciPostPhys.15.2.044,
	title={{Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models}},
	author={Zhao Zhang and Israel Klich},
	journal={SciPost Phys.},
	volume={15},
	pages={044},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.2.044},
	url={https://scipost.org/10.21468/SciPostPhys.15.2.044},
}