arXiv subjects

Francisco Peña-Benítez

Publications and source records attributed to Francisco Peña-Benítez.

9 recordsLinked to original sources

arXiv2026

Effective field theory for the superfluid vortex lattice from coset construction

Guided by symmetry principles, we construct an effective field theory that captures the long-wavelength dynamics of two-dimensional vortex crystals observed in rotating Bose-Einstein condensates trapped in a harmonic potential. By embedding the system into Newton--Cartan spacetime and analyzing its isometries, we identify the appropriate spacetime symmetry group for trapped condensates at finite angular momentum. After introducing a coarse-grained description of the vortex lattice we consider a homogeneous equilibrium configuration and discuss the associated symmetry breaking pattern. We apply the coset construction method to identify covariant structures that enter the effective action and discuss the physical interpretation of the inverse Higgs constraints. We verify that Kohn's theorem is satisfied within our construction and subsequently focus on the gapless sector of the theory. In this regime, the effective theory accommodates a single gapless excitation--the Tkachenko mode--for which we construct both the leading-order and next-to-leading-order actions, the latter including cubic interaction terms.

cond-mat.quant-gas↗

arXiv2025

Non-relativistic transport from frame-indifferent kinetic theory

This paper explores the application of Newton-Cartan geometry to the kinetic theory of gases that includes non-relativistic gravitational effects and the principle of general covariance. Starting with an introduction to the basics of Newton-Cartan geometry, we examine the motion of point particles within this framework, leading to a detailed analysis of kinetic theory and the derivation of conservation equations. The equilibrium distribution function is explored, and the example of a rotating gas in a gravitational field is discussed. Further, we develop covariant hydrodynamic equations and extend our analysis through a gradient expansion approach to assess first-order constitutive relations for rotating gases. Finally, we address the frame-dependence paradox, presenting a novel resolution that addresses apparent discrepancies. Our construction resolves a fifty-year-old debate about the frame-indifferent formulation of kinetic theory. The resolution is presented in a modern, symmetry-based approach.

hep-th↗

arXiv2025

Hydrostatic equilibrium in multi-Weyl semimetals

We study the hydrostatic equilibrium of multi-Weyl semimetals, a class of systems with Weyl-like quasi-particles but anisotropic dispersion relation $ω^2 \sim k_\parallel^2 + k_\perp^{2n}$, with $n$ a possitive integer. A characteristic feature of multi-Weyl systems is the lack of Lorentz invariance, instead, they possess the reduced spacetime symmetry $(SO(1,1)\times SO(2))\ltimes \mathbb R^4$. In this work we propose a covariant formulation for the low energy theory, allowing for a minimal coupling of the fermion field to external geometric background and $U(1)$ gauge field. The non-Lorentzian structure of the field theory demands introducing an Aristotelian spacetime analogous to the so-called stringy Newton-Cartan geometry \cite{Andringa:2012uz}. Our proposal allows for a systematic study of the hydrostatic properties via the derivation of the partition function of the system. In addition to multi-Weyl models, our formulation can be applied to systems with similar spacetime symmetry groups, such as Bjorken flow.

cond-mat.str-el↗

arXiv2025

Non-equilibrium charge-vortex duality

Traditionally applied within equilibrium states, the charge-vortex dualities are expanded to address the complex dynamics of superfluids and ideal fluids under non-static conditions. We have constructed explicit mappings of finite temperature fluid dynamics to gauge theories, enabling a dual description where vortices in both superfluids and ideal fluids are interpreted as charges within these theories. We found that vortices in the normal component naturally exhibit mobility restrictions, as manifested by the symmetries and conservation laws. Next, we formulated the Liénard-Wiechert problem for the ideal fluid at finite temperature and extracted the wave dynamics in the system along with the speed of sound corrections for both fluid components. Finally, we computed the correlation functions for the gauge potentials, particularly elucidating explicit cross-correlations between the normal and superfluid components.

hep-th↗

arXiv2025

Quadrupole gauge theory: anti-Higgs mechanism and elastic dual

Motivated by the duality between elasticity and fracton gauge theory, we study an extension of the gauge group that includes the quadrupole moment. Remarkably, we find that spontaneous breaking of the quadrupole symmetry increases the number of massless excitations. This result appears to challenge the well-established paradigm, according to which gauge fields acquire mass through the Higgs mechanism, and the would-be Goldstone bosons are rendered massive. We refer to this phenomenon as the anti-Higgs mechanism. Furthermore, we demonstrate that the quadrupole gauge theory is dual to an exotic class of elastic systems, which we dub incompressible crystals. The anti-Higgs mechanism in the dual theory corresponds to a phase transition from the incompressible crystal state to an ordinary (compressible) solid.

cond-mat.str-el↗

arXiv2024

Dissipative fracton superfluids

We present a comprehensive study of hydrodynamic theories for superfluids with dipole symmetry. Taking diffusion as an example, we systematically construct a hydrodynamic framework that incorporates an intrinsic dipole degree of freedom in analogy to spin density in micropolar (spinful) fluids. Subsequently, we study a dipole condensed phase and propose a model that captures the spontaneous breaking of the $U(1)$ charge. The theory explains the role of the inverse Higgs constraint for this class of theories, and naturally generates the gapless field. Next, we introduce finite temperature theory using the Hamiltonian formalism and study the hydrodynamics of ideal fracton superfluids. Finally, we postulate a derivative counting scheme and incorporate dissipative effects using the method of irreversible thermodynamics. We verify the consistency of the dispersion relations and argue that our counting is systematic.

hep-th↗

arXiv2024

Fracton gauge fields from higher-dimensional gravity

We show that the fractonic dipole-conserving algebra can be obtained as an Aristotelian (and pseudo-Carrollian) contraction of the Poincaré algebra in one dimension higher. Such contraction allows to obtain fracton electrodynamics from a relativistic higher-dimensional theory upon dimensional reduction. The contraction procedure produces several scenarios including the some of the theories already discussed in the literature. A curved space generalization is given, which is gauge invariant when the Riemann tensor of the background geometry is harmonic.

hep-th↗

arXiv2023

Hydrodynamics of dipole-conserving fluids

Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and immobile excitations dubbed fractons. Unfortunately, such systems have so far escaped a complete macroscopic formulation as viscous fluids. In this work, we construct a consistent hydrodynamic description for fluids invariant under translation, rotation, and dipole shift symmetry. We use symmetry principles to formulate a thermodynamic theory for dipole-conserving systems at equilibrium and apply irreversible thermodynamics in order to elucidate dissipative effects. Remarkably, we find that the inclusion of the energy conservation not only renders the longitudinal modes diffusive rather than subdiffusive but also diffusion is present even at the lowest order in the derivative expansion. This work paves the way towards an effective description of many-body systems with constrained dynamics such as ensembles of topological defects, fracton phases of matter, and certain models of glasses.

cond-mat.str-el↗

arXiv2022

Hydrodynamics of ideal fracton fluids

Low-energy dynamics of many-body fracton excitations necessary to describe topological defects should be governed by a novel type of hydrodynamic theory. We use a Poisson bracket approach to systematically derive hydrodynamic equations from conservation laws of scalar theories with fracton excitations. We study three classes of theories. In the first class we introduce a general action for a scalar with a shift symmetry linear in the spatial coordinates, whereas the second one correspond with a complex scalar, while the third class serves as a toy model for disclinations and dislocations propagating along the Burgers vector. We apply our construction to study hydrodynamic fluctuations around equilibrium states and derive the dispersion relations of hydrodynamic modes.

cond-mat.str-el↗