Stable Real-Space Invariants Reveal Topology Beyond Symmetry Indicators

A new study has introduced a theoretical framework for identifying topological phases of matter that elude traditional classification based on symmetry indicators. Researchers have developed a set of real-space invariants that are stable under local perturbations and can distinguish between different topological states, even in the absence of crystalline symmetries. This advancement is crucial for understanding and designing materials with exotic electronic properties, opening the door to exploring a broader range of topological phenomena. Traditionally, the classification of topological insulators and semimetals has relied on the presence of crystallographic symmetries, which allow for the definition of symmetry indicators to characterize topological phases. However, many interesting topological materials, such as amorphous topological insulators or disordered systems, lack these symmetries, limiting the applicability of existing methods. The new approach overcomes this limitation by focusing on intrinsic properties of the quantum state that persist even when symmetries are broken. The proposed method is based on constructing real-space invariants from Wannier functions, which describe localized electronic states in the material. These invariants quantify topological properties such as the Chern number or the Z2 number, but in a way that does not require explicit knowledge of the band structure or the system's symmetries. The stability of these invariants against the addition of disorder or material deformation is a key feature that makes them powerful tools for characterizing topological phases in complex systems. This development has significant implications for condensed matter physics, providing a robust tool for identifying new topological materials and understanding their properties under realistic conditions. The ability to classify topology beyond symmetries opens new avenues for engineering materials with advanced functionalities, such as quantum computing or spintronics, where the robustness of topological states is fundamental. This framework is expected to drive the experimental search for exotic topological phases in disordered and amorphous systems.

Pseudo-gauge Ambiguities in Local Equilibrium Angular Momentum Resolved

Researchers have addressed the inherent ambiguity in decomposing total angular momentum into its orbital and spin components. This freedom, known as pseudo-gauge ambiguity, has affected the definition of local-equilibrium density operators and, consequently, spin polarization estimates in heavy-ion collisions. The new approach reformulates this ambiguity, along with others associated with improvements of conserved currents, in terms of spurious symmetries corresponding to conserved currents with vanishing total charge. The central problem lies in the existence of multiple valid ways to separate the total angular momentum, which introduces an indeterminacy in how the state of a system in local equilibrium is described. This indeterminacy is particularly relevant in the study of phenomena such as heavy-ion collisions, where the spin polarization of produced particles is a key observable for understanding the properties of the quark-gluon plasma. To resolve this issue, a prescription has been introduced for the unambiguous definition of a local-equilibrium density operator. This prescription is based on the use of currents associated with genuine symmetries of the system. The resulting density operator is invariant under transformations that add improvement terms to local currents, including the energy-momentum tensor. This advance promises greater precision in characterizing local equilibrium states and their spin properties.