arXiv subjects

Olai B. Mykland

Publications and source records attributed to Olai B. Mykland.

3 recordsLinked to original sources

arXiv2026

Exact critical exponents of the Motzkin and Fredkin Chains

The Motzkin and Fredkin chains are frustration-free spin models with exactly solvable ground states whose $q$-deformations realize an exotic quantum phase transition from a disordered phase to an ordered one under domain-wall boundary conditions. Previous work has mainly focused on their entanglement scaling and spectral gaps, particularly in color-enriched variants. Here we systematically characterize the critical behavior of this transition with three main advances. First, we interpret bulk magnetic order as arising from correlations with boundary spins subject to an effective edge field, directly relating the ordered phase to the domain-wall boundary condition. Second, using the transfer matrix (TM) constructed from the exact matrix product state (MPS) representation, together with a continuum and RG analysis, we derive the algebraic decay of spin correlations and obtain the critical exponent $η= \frac{3}{2}$. We further generalize this TM/dual-Hamiltonian method to translationally invariant gapless states with generic power-law correlations, via a zero-dimensional Hamiltonian dual to the one-dimensional TM. Third, the TM spectrum reveals a duality between the ordered and disordered phases which, combined with scale invariance at criticality and the scaling dimension of the spin operator, yields $ν_\pm = \frac{2}{3}$ from an RG analysis of the $q$-deformed ground states. Both exponents are confirmed numerically by MPS simulations and by direct diagonalization of the TM.

cond-mat.str-el↗

arXiv2026

Highly Entangled Quantum Spin Chains on Fermat's Spiral

We investigate the entanglement entropy (EE) and spectral gap properties of highly entangled spin chains arranged along a Hamiltonian path on a two-dimensional (2D) lattice with geometries reminiscent of Fermat's spiral. Interpreting the interactions along the spin chain as the strongly anisotropic limit of a 2D model, with couplings oriented along different directions in different quadrants, we construct an exactly solvable ground state (GS) that exhibits volume scaling of EE across bipartition through the center in any direction. This provides another mechanism for realizing 2D GSs with local interactions that violate the entanglement area law. As in the previously studied coupled-chains paradigm, the new construction features an entanglement phase transition, but with distinct scaling at the critical point and in the weakly entangled phase, and a faster closing of the spectral gap in the highly entangled phase. The corresponding tensor network representation uses lower-rank tensors while preserving a global geometry similar to that of coupled-chains model. Finally, the Fermat-spiral layout naturally generalizes to two highly entangled 1D chains coupled by a quantum junction at the center of the 2D system.

quant-ph↗

arXiv2025

Highly Entangled 2D Ground States: Tensor Network, Order Parameter and Correlation

In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement entropy. The tensor networks constructed are one dimension higher than the lattices of the physical systems, allowing entangled physical degrees of freedoms to be paired with one another arbitrarily far away. Contraction rules of the internal legs are specified by a simple translationally invariant set of rules in terms of the tesselation of cubes or prisms in 3D space. The networks directly generalize the previous holographic tensor networks for 1D Fredkin and Motzkin chains. We also analyze the correlation in the spin and color sectors from the scaling of the height function of random surfaces, revealing additional characterizations of the exotic phase transitions.

quant-ph↗