arXiv subjects

Rafael Flores-Calderón

Publications and source records attributed to Rafael Flores-Calderón.

5 recordsLinked to original sources

arXiv2026

Non-Abelian Anyon Condensation: a Path-Integral Monte Carlo Approach

Transitions out of non-Abelian topological order are difficult to describe in microscopic quantum models with numerical methods that remain tractable at large scales. We develop a sign-free path-integral framework for Kitaev quantum doubles $\mathcal D(G)$ by organizing single-link perturbations in terms of non-invertible electric and magnetic 1-form symmetries that proliferate distinct anyon species. For any finite group $G$, an exact $\textit{matterization}$ isometry introduces vertex degrees of freedom and maps the link-only model onto a $G$ gauge--Higgs theory. Furthermore, the 1-form symmetries of the fixed point allow us to define generalized Fredenhagen--Marcu order parameters that become finite when the corresponding anyons condense. For $G = S_3$, quantum Monte Carlo simulations show that proliferating a non-Abelian electric anyon drives a first-order transition in which all nontrivial electric anyons condense. In the purely magnetic limit, the model reduces to a $(2+1)$D pure $G$ gauge theory; for $G=S_3$, it exhibits a first-order confinement transition, diagnosed by the onset of a Wilson-loop area law and the restoration of an emergent magnetic 1-form symmetry. These results provide a unified numerical framework for non-Abelian anyon condensation, confinement, and generalized symmetry breaking.

cond-mat.str-el↗

arXiv2026

Non-invertible Lattice 1-Form Symmetries for Non-Abelian Topological Order

Higher-form symmetries generalize conventional global symmetries and act on lower-dimensional submanifolds of a quantum system. While Abelian topological phases can be organized by 1-form symmetries that form a group, non-Abelian topological phases based on finite groups require 1-form symmetry operators governed by non-invertible fusion algebras. In this work, we make this statement precise in quantum double lattice models $\mathcal D(G)$ for finite non-Abelian groups $G$. We construct the electric, magnetic, and dyonic 1-form operators directly at the lattice fixed point and show that together they form a complete nonlocal diagnostic algebra for the topological Hilbert space. Using these operators, we explicitly determine the cylinder and torus ground-state subspaces for arbitrary finite $G$. Furthermore, we calculate the microscopic fusion and gluing of the 1-form symmetries and show that their topological deformation properties emerge after projection to the defect-free topological subspace. Our results establish ground states of non-Abelian quantum double models as a concrete microscopic realization of spontaneous non-invertible 1-form symmetry breaking and provide an operator language that may be useful for characterizing such states in quantum processors.

cond-mat.str-el↗

arXiv2025

Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model

Motivated by recent experiments, we investigate the spin-1/2 XXZ model on the triangular lattice with strong Ising anisotropy, combining large-scale numerical simulations and analytical methods to uncover unconventional spin dynamics. First, we compute the dynamical spin structure factor using density matrix renormalization group (DMRG) simulations and find excellent agreement with inelastic neutron scattering data on the layered compound $\text{K}_2\text{Co}(\text{SeO}_3)_2$. The low-energy spectrum reveals a roton-like minimum at the $M$ point, absent in linear spin-wave theory, accompanied by peak intensity and a broad continuum above it. Near the $Γ$ point, we observe an approximately linear dispersion with vanishing spectral weight. Second, we compare two analytical frameworks that reproduce the observed features. The first is a hard-core boson approach, which includes: (i) an effective staggered boson model (ESBM) at zero magnetic field, (ii) perturbation theory applied to the one-third magnetization plateau, and (iii) a self-consistent mean-field Schwinger boson theory (SBT). The second framework is based on a variational supersolid quantum dimer model (QDM) ansatz, combined with a single-mode approximation. The SBT captures the broad continuum, the $M$-point minimum, and linear dispersion at $Γ$, whereas the QDM reproduces the roton minimum and linear dispersion at finite momentum near $Γ$. Remarkably, both the QDM wavefunction and the DMRG ground state exhibit nearly identical structure factors with pronounced transverse photon-like excitations. Together, our comprehensive theoretical and numerical analysis elucidates the microscopic origin of supersolid excitations in the XXZ triangular lattice model and their proximity to a spin liquid phase observed experimentally.

cond-mat.str-el↗

arXiv2025

Higgs Phases and Boundary Criticality

Motivated by recent work connecting Higgs phases to symmetry protected topological (SPT) phases, we investigate the interplay of gauge redundancy and global symmetry in lattice gauge theories with Higgs fields in the presence of a boundary. The core conceptual point is that a global symmetry associated to a Higgs field, which is pure-gauge in a closed system, acts physically at the boundary under boundary conditions which allow electric flux to escape the system. We demonstrate in both Abelian and non-Abelian models that this symmetry is spontaneously broken in the Higgs regime, implying the presence of gapless edge modes. Starting with the U(1) Abelian Higgs model in 4D, we demonstrate a boundary phase transition in the 3D XY universality class separating the bulk Higgs and confining regimes. Varying the boundary coupling while preserving the symmetries shifts the location of the boundary phase transition. We then consider non-Abelian gauge theories with fundamental and group-valued Higgs matter, and identify the analogous non-Abelian global symmetry acting on the boundary generated by the total color charge. For SU($N$) gauge theory with fundamental Higgs matter we argue for a boundary phase transition in the O($2N$) universality class, verified numerically for $N=2,3$. For group-valued Higgs matter, the boundary theory is a principal chiral model exhibiting chiral symmetry breaking. We further demonstrate this mechanism in theories with higher-form Higgs fields. We show how the higher-form matter symmetry acts at the boundary and can spontaneously break, exhibiting a boundary confinement-deconfinement transition. We also study the electric-magnetic dual theory, demonstrating a dual magnetic defect condensation transition at the boundary. We discuss some implications and extensions of these findings and what they may imply for the relation between Higgs and SPT phases.

cond-mat.str-el↗

arXiv2025

Effective field theory of the quantum skyrmion Hall effect

Motivated by phenomenology of myriad recently-identified topologically non-trivial phases of matter, we introduce effective field theories (EFTs) for the quantum skyrmion Hall effect (QSkHE). We employ a single, unifying generalisation for this purpose: in essence, a lowest Landau level projection defining a non-commutative, fuzzy sphere with position coordinates proportional to SU(2) generators of matrix representation size $N\times N$, may host an intrinsically 2+1 dimensional, topologically non-trivial many-body state for small $N$ as well as large $N$. That is, isospin degrees of freedom associated with a matrix Lie algebra with $N \times N$ generators potentially encode some finite number of spatial dimensions for $N\ge 2$, a regime in which isospin has previously been treated as a label. This statement extends to more general $p$-branes subjected to severe fuzzification as well as membranes. As a consequence of this generalisation, systems with $d$ Cartesian spatial coordinates and isospin degrees of freedom encoding an additional $δ$ fuzzy coset space coordinates can realise topologically non-trivial states of intrinsic dimensionality up to $d$+$δ$+1. We therefore identify gauge theories with extra fuzzy dimensions generalised to retain dependence upon gauge fields over fuzzy coset spaces even for severe fuzzification (small $N$), as EFTs for the QSkHE. We furthermore generalise these EFTs to space manifolds with local product structure exploiting the dimensional hierarchy of (fuzzy) spheres. For this purpose, we introduce methods of anisotropic fuzzification and propose formulating topological invariants on fuzzy coset spaces as artifacts of projecting matrix Lie algebras to occupied subspaces. Importantly, we focus on phenomenology indicating the 2+1 D SU(2) gauge theory should be generalised using this machinery, and serves as a minimal EFT of the QSkHE.

hep-th↗