arXiv subjects

Pedro R. S. Gomes

Publications and source records attributed to Pedro R. S. Gomes.

At least 19 recordsLinked to original sources

arXiv2026

Gauging Modulated Symmetries: Bond Algebras, Higher-Form Symmetries, and Symmetry-Enriched Topological Order

We develop a constructive framework for characterizing modulated symmetries and their gauging in $d$-dimensional lattice systems. The modulation profiles are organized as a finite-dimensional representation of the space group acting on a finite Abelian internal symmetry group. Since the corresponding automorphism group is finite, the nontrivial spatial action factors through a finite quotient of the space group, leading to periodic modulation patterns and providing a classification framework for discrete Abelian modulated symmetries. The symmetry-allowed local interactions are systematically obtained from a kernel construction, which also yields an algebra of open operators. Upon gauging, its elements are transmuted into extended Wilson and boundary operators while retaining their algebraic relations. In the deconfined regime, the resulting algebra realizes a mixed 't Hooft anomaly, providing a microscopic route to Abelian crystalline symmetry-enriched topological phases (SETs). These SETs do not mix electric and magnetic sectors, which transform in mutually contragredient representations, thereby preserving their braiding pairing. We illustrate the framework through explicit examples and show that several models present in the literature fit naturally within our construction.

cond-mat.str-el↗

arXiv2026

Non-Abelian Zero Modes in Fractional Quantum Hall-Superconductor Heterostructure

We discuss the emergence of non-Abelian zero modes from twist defects in Abelian topological phases. We consider a setup built from a fractional quantum Hall (or a fractional Chern insulator)-superconductor heterostructure, which effectively induces a phase transition, leading to a topological phase endowed with new anyonic symmetries, and accordingly supporting distinct types of zero modes at fixed filling. These defects are modeled at the interface between two copies of the same heterostructure arranged side by side, which produces counterpropagating modes that can be gapped by interactions that realize the anyonic symmetries. We characterize the parafermions associated with each anyonic symmetry and discuss how their presence affect the periodicity of Josephson tunneling current.

cond-mat.str-el↗

arXiv2025

Generalized Modulated Symmetries in $\mathbb{Z}_2$ Topological Ordered Phases

We study $\mathbb{Z}_2$ topological ordered phases in 2+1 dimensions characterized by generalized modulated symmetries. Such phases have explicit realizations in terms of fixed-point Hamiltonians involving commuting projectors with support $h=3,5,7,\ldots$ in the horizontal direction, which dictates the modulation of the generalized symmetries. These symmetries are sensitive to the lattice sizes. For certain sizes, they are spontaneously broken and the ground state is degenerated, while for the remaining ones, the symmetries are explicitly broken and the ground state is unique. The ground state dependence on the lattice sizes is a manifestation of the ultraviolet/infrared (UV/IR) mixing. The structure of the modulated symmetries implies that the anyons can move only in rigid steps of size $h$, leading to the notion of position-dependent anyons. The phases exhibit rich boundary physics with a variety of gapped phases, including trivial, partial and total symmetry-breaking, and SPT phases. Effective field theory descriptions are discussed, making transparent the relation between the generalized modulated symmetries and the restrictions on anyon mobility, incorporating the boundary physics in a natural way, and showing how the short-distance details can be incorporated into the continuum by means of twisted boundary conditions.

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

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

Bosonization, Duality, and the $C$-Theorem in the Non-Abelian Thirring Model

We revisit the two dimensional non-Abelian Thirring model in order to investigate its fixed point structure and the corresponding renormalization group (RG) flow. For this purpose we discuss the bosonization of the model, and we present different, but of course equivalent, bosonic versions of the theory. The bosonic theories are illuminating in that they exhibit the fixed points in a manifest way, and also possess a remarkable strong/weak duality that sheds light on the fixed point structure of the theory. We study the RG flow through the computation of the Zamolodchikov $C$-function and of the $β$-function in the large-level limit. Within this framework, we discuss how close to the infrared fixed point the RG flow can reach, since this point is strictly unachievable due to an emergent gauge invariance.

hep-th↗

arXiv2023

An Introduction to Higher-Form Symmetries

These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and effervescent topics of theoretical physics in recent years. Gauge theories are central in the study of higher-form symmetries, with Wilson and 't Hooft operators corresponding to the charged objects. Along these notes, we discuss in detail some basic aspects, including Abelian Maxwell and Chern-Simons theories, and $SU(N)$ non-Abelian gauge theories. We also discuss spontaneous breaking of higher-form symmetries.

hep-th↗

arXiv2022

Topological Superconductor from the Quantum Hall Phase: Effective Field Theory Description

We derive low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global $U(1)$ symmetry. We couple this symmetry with a background gauge field and compute the effective action by integrating out the gapped fermions. In spite of the fact that the corresponding Dirac operator governing the dynamics of the original fermions is nonrelativistic, the leading contribution in the effective action is a usual Abelian $U(1)$ Chern-Simons term. The proximity to a conventional superconductor induces a pairing potential in the quantum Hall state, favoring the formation of Cooper pairs. When the pairing is strong enough, it drives the system to a topological superconducting phase, hosting Majorana fermions. Even though the continuum $U(1)$ symmetry is broken down to a $\mathbb{Z}_2$ one, we can forge fictitious $U(1)$ symmetries that enable us to derive the effective action for the topological superconducting phase, also given by a Chern-Simons theory. To eliminate spurious states coming from the artificial symmetry enlargement, we demand that the fields in the effective action are $O(2)$ instead of $U(1)$ gauge fields. In the $O(2)$ case we have to sum over the $\mathbb{Z}_2$ bundles in the partition function, which projects out the states that are not $\mathbb{Z}_2$ invariants. The corresponding edge theory is the $U(1)/\mathbb{Z}_2$ orbifold, which contains Majorana fermions in its operator content.

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↗

arXiv2022

Quantum wires, Chern-Simons theory, and dualities in the quantum Hall system

Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and particle-vortex duality, which enable a unified approach for the Laughlin states of the fractional quantum Hall system. Starting from the so-called quantum wires system, which is a semi-microscopic description in terms of 1+1 dimensional theories, we discuss the emergence of 2+1 dimensional low-energy effective field theories by using different maps connecting the microscopic degrees of freedom with the macroscopic ones. We show the origin of these maps by embedding the bosonized version of the original quantum wires model in a gauge invariant theory and using particle vortex-duality.

cond-mat.str-el↗

arXiv2022

Field Theories for type-II fractons

We derive an effective field theory for a type-II fracton starting from the Haah code on the lattice. The effective topological theory is not given exclusively in terms of an action; it must be supplemented with a condition that selects physical states. Without the constraint, the action only describes a type-I fracton. The constraint emerges from a condition that cube operators multiply to the identity, and it cannot be consistently implemented in the continuum theory at the operator level, but only in a weaker form, in terms of matrix elements of physical states. Informed by these studies and starting from the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory that does not need a constraint or projector, and yet has no mobile excitations. Whether this continuum theory admits a lattice counterpart remains unanswered.

cond-mat.str-el↗

arXiv2021

Spontaneous Symmetry Breaking and Frustrated Phases

We study a system involving a single quantum degree of freedom per site of the lattice interacting with a few neighbors (up to second neighbors), with the interactions chosen as to produce frustration. At zero temperature, this system undergoes several quantum phase transitions from both gapped-to-gapless and gapless-to-gapless phases, providing a very rich phase structure with disordered, homogeneous and modulated ordered phases meeting in a quantum Lifshitz point. The gapless phases spontaneously break spatial lattice translations as well as internal symmetries of the form $U(1)^{\mathsf{N}_c}$, where $\mathsf{N}_c$ is the number of independent pitch vectors that arise in the homogeneous and modulated ordered phases. We carry out a detailed analysis of the quantum critical behavior discussing the mechanism leading to the phase transitions. We also discuss a proper characterization of all the gapless phases as well as the nature of the Goldstone excitations. We study the behavior of the correlation functions and identify regions in the phase diagram where the system exhibits generalized symmetries, such as polynomial shift symmetry. This type of symmetry plays an important role in the so-called fractonic phases, which is an exotic form of matter recently discovered.

cond-mat.stat-mech↗

arXiv2021

Lattice Clifford fractons and their Chern-Simons-like theory

We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.

cond-mat.str-el↗

arXiv2020

Bosonization of the Thirring Model in 2+1 Dimensions

In this work we provide a bosonized version of the Thirring model in 2+1 dimensions in the case of single fermion species, where we do not have the benefit of large N expansion. In this situation there are very few analytical methods to extract nonperturbative information. Meanwhile, nontrivial behavior is expected to take place precisely in this regime. To establish the bosonization of the Thirring model, we consider a deformation of a basic fermion-boson duality relation in 2+1 dimensions. The bosonized model interpolates between the ultraviolet and infrared regimes, passing several consistency checks and recovering the usual bosonization relation of the web of dualities in the infrared limit. In addition the duality predicts the existence of a nontrivial ultraviolet fixed point in the Thirring model.

hep-th↗

arXiv2020

Supersymmetric Quantum Spherical Spins with Short-Range Interactions

This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent $z=2$. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric $O(N)$ nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large $N$ limit.

cond-mat.stat-mech↗

arXiv2019

Chiral Edge States in 2+1 Dimensional Topological Phases

Chiral edge states of 2+1 dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and non-integer values of central charge, respectively. In this work we describe certain edge states in terms of constrained fermionic fields that realize chiral coset CFT structures. This construction arises naturally in the so-called quantum wires approach for topological phases and allows for representing fractionalized edge states directly in terms of fermionic degrees of freedom. At the same time, the constrained fermions description introduces some subtleties concerning gauge anomalies since it involves the coupling of chiral fermions to gauge fields. We describe in this article how to handle these issues.

hep-th↗

arXiv2019

From Quantum Wires to the Chern-Simons Description of the Fractional Quantum Hall Effect

We show the explicit connection between two distinct and complementary approaches to the fractional quantum Hall system (FQHS): the quantum wires formalism and the topological low-energy effective description given in terms of an Abelian Chern-Simons theory. The quantum wires approach provides a description of the FQHS directly in terms of fermions arranged in an array of one-dimensional coupled wires. In this sense it is usually referred to as a microscopic description. On the other hand, the effective theory has no connection with the microscopic modes, involving only the emergent topological degrees of freedom embodied in an Abelian Chern-Simons gauge field, which somehow encodes the collective motion of the strongly correlated electrons. The basic strategy pursued in this work is to bosonize the quantum wires system and then consider the continuum limit. By examining the algebra of the bosonic operators of the Hamiltonian, we are able to identify the bosonized microscopic fields with the components of the field strength (electric and magnetic fields) of the emergent gauge field. Thus our study provides a bridge between the microscopic physical degrees of freedom and the emergent topological ones, without relying on the bulk-edge correspondence.

cond-mat.str-el↗

arXiv2018

Supersymmetric Quantum Spherical Spins

In this work we investigate properties of a supersymmetric extension of the quantum spherical model from an off-shell formulation directly in the superspace. This is convenient to safely handle the constraint structure of the model in a way compatible with supersymmetry. The model is parametrized by an interaction energy, $U_{{\bf r},{\bf r}'}$, which governs the interactions between the superfields of different sites. We briefly discuss some consequences when $U_{{\bf r},{\bf r}'}$ corresponds to the case of first-neighbor interactions. After computing the partition function via saddle point method for a generic interaction, $U_{{\bf r},{\bf r}'}\equiv U(|{\bf r}-{\bf r}'|)$, we focus in the mean-field version, which reveals an interesting critical behavior. In fact, the mean-field supersymmetric model exhibits a quantum phase transition without breaking supersymmetry at zero temperature, as well as a phase transition at finite temperature with broken supersymmetry. We compute critical exponents of the usual magnetization and susceptibility in both cases of zero and finite temperature. Concerning the susceptibility, there are two regimes in the case of finite temperature characterized by distinct critical exponents. The entropy is well behaved at low temperature, vanishing as $T \rightarrow 0$

cond-mat.stat-mech↗