相关论文: Space-Time Geometry of Topological phases

Quantum link models (QLMs) are generalizations of Wilson's lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant…

Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…

In topological phases of matter, the interplay between intrinsic topological order and global symmetry is an interesting task. In the study of topological orders with discrete global symmetry, an important systematic approach is the…

We study the perturbative large-$N$ expansion of the round three-sphere partition function in a class of M2-brane theories, including flavored SYM and ABJM theories as well as more general 3d theories admitting dual $(p,q)$ 5-brane web…

A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner…

In this work, we explore a microscopic realization of three types of anyonic symmetries in a $\mathbb{Z}_2\times\mathbb{Z}_2$ topological order, corresponding to a double toric code. These symmetries act as nontrivial permutations on the…

Wilson loops are among the most fundamental gauge-invariant observables in quantum field theory, encoding the global structure of gauge fields through their holonomy along closed contours. Originally introduced as order parameters for…

A study of the partition function of a 3-dimensional scalar-vector model formally related via duality to the Rozansky-Witten topological sigma-model is presented. The partition function is shown to consist of such topological quantities of…

We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and…

The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system. However, the original construction is not applicable to all unitary fusion category since…

The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts…

We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and…

We present a general methodology towards the systematic characterization of crystalline topological insulating phases with time reversal symmetry (TRS).~In particular, taking the two-dimensional spinful hexagonal lattice as a proof of…

The partition function of the double-layer $XY$ model in the (dual) Villain form is computed exactly in the limit of weak coupling between layers. Both layers are found to be locked together through the Berezinskii-Kosterlitz-Thouless…

We derive the partition functions of the Schwarz-type four-dimensional topological half-flat 2-form gravity model on K3-surface or T^4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class…

Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a…

The single graphene layer is a novel material consisting of a flat monolayer of carbon atoms packed in a two-dimensional honeycomb-lattice, in which the electron dynamics is governed by the Dirac equation. A pseudo-spin phase-space approach…

Rydberg lattice gases are at the forefront of quantum simulation platforms due to their inherent strong dipole-dipole interactions, long life-times and high degree of control currently achievable in experiments. We propose a simple and…

We review an approach that uses binary relations as the fundamental constituents of the universe, utilizing them as building blocks for both space and matter. The model is defined by an ultraviolet continuous fixed point of a statistical…