arXiv subjects

Guilherme Delfino

Publications and source records attributed to Guilherme Delfino.

11 recordsLinked to original sources

arXiv2026

Kitaev spin liquid in superconducting networks

We propose a realization of the Kitaev honeycomb Hamiltonian -- an archetypal spin-liquid model -- in a superconducting metamaterial. The architecture consists of Cooper-pair boxes coupled through depleted semiconductor--superconductor heterostructures that do not require spin--orbit coupling. The Cooper-pair boxes encode effective spin degrees of freedom, while normal and anomalous virtual propagation through the heterostructures mediate bond-directional interactions. Two key control parameters are an out-of-plane magnetic flux and the semiconductor Fermi energy. The former controls interference and distinguishes the bond directions, while tuning the latter close to the bottom of the band gives rise to an emergent Nambu-exchange symmetry that enforces the required bond directionality. Through numerical calculations, we identify an operating regime with controlled corrections, with associated energy and length scales within experimental reach. These results establish a route toward equilibrium quantum spin liquids in engineered superconducting networks.

cond-mat.str-el↗

arXiv2026

Nonplanar qubit with tunable gauge symmetry

Circuit quantum electrodynamics embeds Josephson junction qubits within superconducting cavities, and has emerged as a leading approach to quantum computing and quantum simulation. Despite the many permutations of circuit geometry that have been explored, Josephson connectivities have so far been planar, making them effectively low-dimensional. Here we show that a non-planar qubit -- a $3\times3$ crossbar Josephson array -- gives rise to flux-tunable $\mathbb{Z}_3$ combinatorial gauge symmetry (CGS), potentially enabling spin-liquid behavior when networked into a lattice. The observed excitation spectrum shows excellent agreement with predictions from a neural network trained to generate variational quantum states, demonstrating that we have predictive power over our high-dimensional quantum system. Fine-structure splittings near the CGS point are compatible with weak tunneling or symmetry breaking due to experimental imperfections. We additionally use the superconducting cavity to externally induce symmetry breaking, observing a restoration of symmetry at the CGS point where ground states differ only by a $\mathbb{Z}_3$ phase. This work initiates a general program exploring lattice gauge theories using the toolbox of circuit quantum electrodynamics. More broadly, introducing non-planar Josephson connectivities opens a vast space for experimental and theoretical exploration of structures in almost any imaginable dimensionality and geometry.

quant-ph↗

arXiv2026

Graph-based emulation of $d$-dimensional curved spaces with superconducting arrays

We introduce a framework for emulating graphs and, through them, curved spaces of arbitrary dimension, using arrays of superconducting wires. The array consists of two stacked layers of wires, horizontal and vertical, such that wires are parallel within each layer and perpendicular between layers. By discretizing a space into a graph, assigning a superconducting wire with a rigid phase to each vertex, and coupling pairs of wires through Josephson junctions according to the graph edges, arbitrary geometries and topologies can be engineered in a controlled setting. The superconducting phases then realize scalar field theories on the emergent geometry. We establish experimentally realistic conditions for implementing these architectures and develop a dictionary relating measurable circuit observables to quantities in the emulated field theory. As an application, we develop the implementation of hyperbolic (Anti-de Sitter) spaces of constant negative curvature and use them as an experimentally accessible platform to explore holographic duality in arbitrary dimensions. We investigate the effects of disorder in the Josephson couplings, which translate into metric variations in the bulk-boundary correspondence, and analyze their impact on boundary scaling exponents both analytically and numerically, finding that holographic duality remains robust even in the presence of strong disorder. Beyond holography, the framework opens a broad range of architectural possibilities, including the exploration of physics on highly nontrivial graphs and toy models of dynamical spacetimes.

cond-mat.supr-con↗

arXiv2026

Topological order and Fractons from Gauging Exponential Symmetries

We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with unconventional charge-conservation laws, which we term \textit{exponential polynomial symmetries}. Gauging these symmetries yields $\mathbb{Z}_N$ gauge theories in 2D that exhibit topological order whose quasiparticles have constrained mobility and whose ground-state degeneracy shows ultraviolet (UV) dependence. These features are reminiscent of spatial symmetry-enriched topological order, wherein quasiparticle excitations transform nontrivially under lattice translations. We further propose a Chern-Simons variant that produces non-CSS stabilizer codes and outline a framework for exponentially symmetric subsystem SPT phases. Finally, we extend this gauging procedure to 3D, obtaining new variants of fracton topological order.

cond-mat.str-el↗

arXiv2025

Cooper-pair splitters as circuit elements for realizing topological superconductors

Advances in materials and fabrication of superconducting devices allows the exploration of novel quantum effects in synthetic superconducting systems beyond conventional Josephson junction arrays. As an example, we introduce a new circuit element, the Y-splitter, a superconducting loop with three leads and three Josephson junctions, smaller or comparable in size to the superconducting coherence length of the material. By tuning magnetic flux through an array of Y-splitters, Cooper-pair transport can be made to interfere destructively, while spatially separated split Cooper pairs propagate coherently. We consider an array of Y-splitters connected in a two-dimensional star [Archimedean (3,$12^2$)] geometry, deformable into the kagome lattice, and find a rich phase diagram that includes topological superconducting phases with Chern numbers $\pm 2$. Experimental realization appears feasible.

cond-mat.supr-con↗

arXiv2025

Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections

Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in ${1+1}$ dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models.

cond-mat.str-el↗

arXiv2024

Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory

This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II fracton physics dictated by a fractal subsystem symmetry. We obtain an expression for the ground state degeneracy, which depends intricately on the sizes of the plane, signaling a strong manifestation of ultraviolet/infrared (UV/IR) mixing. The ground state degeneracy can be interpreted in terms of spontaneous/explicit breaking of fractal subsystem symmetries. We also study the boundary physics, which in turn is useful to understand the connection with certain two-dimensional phases. Finally, we derive a low-energy but not long-distance effective field theory, by Higgsing a fractal $U(1)$ symmetry and taking the deep IR limit. This description embodies in a natural way several aspects of the phases, such as the content of generalized global symmetries, the role of fractal symmetries on the mobility of excitations, the anomalies, and the boundary physics.

cond-mat.str-el↗

arXiv2024

Anyon condensation web and multipartite entanglement in 2D modulated gauge theories

In this work, we introduce an anyon condensation web that interconnects a broad class of 2D fracton gauge theories with multipolar conservation laws at a microscopic level. We find that condensation of anyons triggers the emergence of additional spatially modulated symmetries, which has the general effect of increasing the number of super-selection anyon sectors, as well as the ground state degeneracy for systems with periodic boundary conditions. As explicit examples, we start with the rank-2 toric code model and implement various anyon condensation protocols, resulting in a range of 2D fracton-like theories, each with a distinct gauge structure. We also expand the scope of anyon condensation by introducing lattice defects into spatially modulated gauge theories and demonstrate that these geometric defects can be viewed as effective anyon condensations along the branch cut. Furthermore, we introduce the Multipartite Entanglement Mutual Information measure as a diagnostic tool to differentiate among various distinct multipole conserving phases. A captivating observation is the UV sensitivity of the mutual information sourced from multipartite entanglement in such spatially modulated gauge theories, which depends on the geometric cut and the system size, and exhibits periodic oscillations at large distances.

cond-mat.str-el↗

arXiv2024

Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing

In this work, we study unconventional anisotropic topologically ordered phases in $3d$ that manifest type-II fractonic physics along submanifolds. While they behave as usual topological order along a preferred spatial direction, their physics along perpendicular planes is dictated by the presence of fractal subsystem symmetries, completely restricting the mobility of anyonic excitations and their bound states. We consider an explicit lattice model realization of such phases and proceed to study their properties under periodic boundary conditions and, later, in the presence of boundaries. We find that for specific lattice sizes, the system possesses line and fractal membrane symmetries that are mutually anomalous, resulting in a nontrivially gapped ground state space. This amounts to the spontaneous breaking of the fractal symmetries, implying a subextensive ground state degeneracy. For the remaining system sizes the fractal symmetries are explicitly broken by the periodic boundary conditions, which is intrinsically related to the uniqueness of the ground state. Despite that, the system is still topologically ordered since locally created quasiparticles have nontrivial mutual statistics and, in the presence of boundaries, it still presents anomalous edge modes. The intricate symmetry interplay dictated by the lattice size is a wild manifestation of ultraviolet/infrared (UV/IR) mixing.

cond-mat.str-el↗

arXiv2023

$U(1)$ symmetry-enriched toric code

We propose and study a generalization of Kitaev's $\mathbb Z_2$ toric code on a square lattice with an additional global $U(1)$ symmetry. Using Quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state manifold with indications of UV/IR mixing, i.e., the topological degeneracy of the ground state depends on the microscopic details of the lattice. Specifically, the ground state degeneracy depends on the lattice tilt relative to the directions of the torus cycles. In particular, we observe that while the usual compactification along the vertical/horizontal lines of the square lattice shows a two-fold ground state degeneracy, compactifying the lattice at $45^\circ$ leads to a three-fold degeneracy. In addition to its unusual topological properties, this system also exhibits Hilbert space fragmentation. Finally, we propose a candidate experimental realization of the model in an array of superconducting quantum wires.

cond-mat.str-el↗

arXiv2022

Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid

In this work we propose a $\mathbb{Z}_N$ clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with $N^2$ (and diverges rapidly as a function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hoping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system are captured by a peculiar realization of the translation group.

cond-mat.str-el↗