Twisted Boundaries, Subtle Anomalies: Unveiling Hidden Symmetries in 2D Fermions
New research demonstrates how the parity anomaly of a 2+1D Dirac fermion can be detected and matched using twisted boundary conditions and crystalline symmetries on a lattice.
![Dysprosium emerges as a promising medium for dark photon research, exhibiting sensitivity to kinetic mixing ε across a range of values-specifically, when [latex]f[/latex] varies from 0.01 to 0.1-and potentially unlocking several orders of magnitude of previously unexplored parameter space.](https://arxiv.org/html/2601.01043v1/x9.png)

![The study demonstrates that in a nonlinear orbital angular momentum lattice, antisymmetric edge states remain stable regardless of nonlinearity strength, while symmetric edge states-present under weak nonlinearity-transition into bulk states and ultimately vanish beyond a critical nonlinearity threshold, a boundary clearly delineated by the system’s parameters [latex]U=gN_{edge}[/latex], [latex]J=1[/latex], and [latex]\delta J=0.3[/latex].](https://arxiv.org/html/2601.02199v1/x10.png)

![The study demonstrates that particle production in a massless scalar field theory, initially predicted by analytical calculations and observed through the evolution of excited state probabilities, is suppressed by even slight interactions introduced via fermion mass, a phenomenon signaled by a decreasing ratio of measured to free-theory probabilities and momentarily obscured by state mixing during rapid level crossings-effects quantified within a system defined by [latex]N=20[/latex], [latex]a=1[/latex], and a lightest meson mass of [latex]M\_1=0.25[/latex].](https://arxiv.org/html/2601.02331v1/x12.png)

![The plotted relationship between [latex]\rho_{\mathbf{q}}[/latex] and [latex]p_{\mathbf{q}}[/latex] as a function of [latex]r[/latex] demonstrates how even the most meticulously constructed theoretical frameworks are ultimately subject to the limitations imposed by the inescapable pull of the unknown, mirroring the inherent fragility of knowledge itself.](https://arxiv.org/html/2601.00929v1/x12.png)