Quantum lozenge tiling and entanglement phase transition

Abstract

While volume violation of area law has been exhibited in several quantum spin chains, the construction of a corresponding ground state in higher dimensions, entangled in more than one direction, has been an open problem. Here we construct a 2D frustration-free Hamiltonian with maximal violation of the area law. We do so by building a quantum model of random surfaces with color degree of freedom that can be viewed as a collection of colored Dyck paths. The Hamiltonian may be viewed as a 2D generalization of the Fredkin spin chain. It relates all the colored random surface configurations subject to a Dirichlet boundary condition and hard wall constraint from below to one another, and the ground state is therefore a superposition of all such classical states and non-degenerate. Its entanglement entropy between subsystems undergoes a quantum phase transition as the deformation parameter is tuned. The area- and volume-law phases are similar to the one-dimensional model, while the critical point scales with the linear size of the system $L$ as $L\log L$. Further it is conjectured that similar models with entanglement phase transitions can be built in higher dimensions with even softer area law violations at the critical point.

References in corpus (34)

• Entanglement entropy and conformal field theory
• An Area Law for One Dimensional Quantum Systems
• Topological Quantum Distillation
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Topological Order and Conformal Quantum Critical Points
• A variational principle for domino tilings
• Thermalization dynamics of a gauge theory on a quantum simulator
• Power law violation of the area law in quantum spin chains
• Violation of area-law scaling for the entanglement entropy in spin 1/2 chains
• Criticality without frustration for quantum spin-1 chains
• Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain
• From conformal to volume-law for the entanglement entropy in exponentially deformed critical spin 1/2 chains
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Deformed Fredkin Spin Chain with Extensive Entanglement
• Violation of Cluster Decomposition and Absence of Light-Cones in Local Integer and Half-Integer Spin Chains
• Unconventional Fusion and Braiding of Topological Defects in a Lattice Model
• Gapless quantum spin chains: multiple dynamics and conformal wavefunctions
• An area law for 2D frustration-free spin systems
• Quantum spin chains with multiple dynamics
• Holographic rainbow networks for colorful Motzkin and Fredkin spin chains
• Entropy, gap and a multi-parameter deformation of the Fredkin spin chain
• Multicolored quantum dimer models, resonating valence-bond states, color visons, and the triangular-lattice t_2g spin-orbital system
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Prime Suspects in a Quantum Ladder
• Exact holographic tensor networks for the Motzkin spin chain
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• The gap of the area-weighted Motzkin spin chain is exponentially small
• Hidden Bethe states in a partially integrable model
• The frustration-free fully packed loop model
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
• Two-dimensional Anisotropic KPZ growth and limit shapes
• Entanglement blossom in a simplex matryoshka
• Bicolor loop models and their long range entanglement
• Ergodic Archimedean dimers

Cited by in corpus (1)

• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian