Grigorios Makris | Searcharxiv

arXiv2026

Inducing Extraordinary-log Criticality through a Quantum Spin Chain

We demonstrate the emergence of extraordinary-log criticality in a quantum many-body system by coupling a spin-$1/2$ Heisenberg chain to a two-dimensional quantum critical Heisenberg bilayer. Under the quantum-to-classical mapping, the chain acts as a plane defect in a three-dimensional critical environment for which the extraordinary-log universality class has recently been predicted. Using large-scale sign-problem-free quantum Monte Carlo simulations, we directly probe the renormalization-group flow of the effective defect coupling through the spin stiffness. We observe the characteristic logarithmic growth with linear system size $L$, corresponding to a stable weak-coupling fixed point and a running coupling $g(L)\sim 1/\log L$. Furthermore, the extracted step-scaling function quantitatively follows the universal renormalization-group flow predicted for the extraordinary-log universality class, including the leading and subleading universal coefficients. Our results establish extraordinary-log criticality in a genuine quantum many-body setting and show that its universal behavior persists despite the topological $θ$-term present in the low-energy field theory of the isolated spin chain.

cond-mat.str-el↗

arXiv2026

Spectral optimization of spherical lattices and applications to classical and quantum interacting spin systems

We develop an optimization algorithm for spherical lattice discretizations based on the spectrum of the discretized Laplace operator. Starting from refined icosahedral lattices, we minimize the splitting of the $(2\ell+1)$, $\ell=0,1,2,\dots$, continuum multiplets expected from $\mathrm{SO}(3)$ symmetry via gradient descent. This approach simultaneously produces lattices based on triangles with nearly uniform circumradii and perimeters. Although the optimization uses only the free-particle spectrum, we show that the resulting lattices carry over to interacting models. On the optimized lattices, rotational symmetry is restored for the critical Ising and Potts models and primary scaling dimensions are accurately reproduced for the three-dimensional Ising conformal field theory, when appropriate geometry-dependent interaction strengths are used. Higher-angular-momentum descendant states reveal weak residual symmetry breaking beyond the sectors protected by the underlying icosahedral symmetry.

cond-mat.stat-mech↗