arXiv subjects

Chih-Yu Lo

Publications and source records attributed to Chih-Yu Lo.

3 recordsLinked to original sources

arXiv2026

Detecting Higher Berry Phase via Boundary Scattering

Higher Berry phase has recently been proposed to study the topology of the space of gapped many-body quantum systems. In this work, we develop a boundary-scattering approach to detect higher Berry phases in one-dimensional gapped free-fermion systems. By coupling a gapless lead to the gapped system, we demonstrate that the higher Berry invariant can be obtained by studying the higher winding number of the boundary reflection matrix. The resulting topological invariant is robust against perturbations such as disorder. Our approach establishes a connection between higher Berry invariants and transport properties, thereby providing a potentially experimentally accessible probe of parametrized topological phases.

cond-mat.str-el↗

arXiv2024

Towards a Topological Proof of the Strong Subadditivity

Topological entanglement entropy (TEE) represents an intrinsic contribution to the entanglement entropy (EE) in topologically ordered systems. In quantum information theory, strong subadditivity (SSA) is a fundamental property of EE, reflecting the non-negativity of conditional mutual information. TEE was originally believed to be a universal correction to the area law of EE, suggesting that its SSA would directly follow from the SSA of EE. However, due to spurious contributions, the correction term is not universal; consequently, the value predicted by topological quantum field theory (TQFT) provides only a lower bound. In this work, we present a topological analysis showing that the SSA for TEE is equivalent to a specific inequality within the TQFT framework. We further verify that this inequality holds for all known unitary modular tensor categories (UMTCs) up to rank 11, supporting the conjecture that SSA holds universally in the TQFT framework. Conversely, assuming the validity of the SSA condition, the inequality can be interpreted as a consistency criterion for candidate UMTCs.

cond-mat.str-el↗

arXiv2023

Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas

The topological R\'enyi and entanglement entropies depend on the bipartition of the manifold and the choice of the ground states. However, these entanglement quantities remain invariant under a coordinate transformation when the bipartition also undergoes the same transformation. In the context of topological quantum field theories, these coordinate transformations reduce to representations of the mapping class group on the manifold of the Hilbert space. We employ this invariant property of the R\'enyi and entanglement entropies under coordinate transformations for TQFTs in (2 + 1) dimensions on a torus with various bipartitions. By utilizing the replica trick and the surgery method to compute the topological R\'enyi and entanglement entropies, the invariant property results in Verlinde-like formulas. Furthermore, for the bipartition with interfaces as two non-intersecting torus knots, an $SL(2, \mathbb{Z})$ transformation can untwist the torus knots, leading to a simple bipartition with an effective ground state. This invariant property allows us to demonstrate that the topological entanglement entropy has a lower bound $-2 \ln D$, where $D$ is the total quantum dimensions of the system.

cond-mat.str-el↗