Effective Field Theories for Condensed Matter and Statistical Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 704

Special Issue Editor


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Guest Editor
Laboratorio Tandar, Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica, Av. Libertador 8250, Buenos Aires C1429, Argentina
Interests: effective field theories; conformal field theories; bosononization; W-infinity algebras

Special Issue Information

Dear Colleagues,

Effective field theories can be utilized for the investigation of the low-energy, long-distance properties of strongly correlated condensed matter and statistical systems. In particular, in systems displaying universality and exactness in some of their observables, such as the quantum Hall effect, these theories provide analytic tools with access to non-perturbative regimes. For quantum systems with one-dimensional degrees of freedom or two-dimensional statistical systems at criticality, conformal field theories yield a mathematical framework providing results that are otherwise difficult to attain.

We are pleased to invite researchers to share their findings regarding the quantum Hall effect, bosonization, quantum hydrodynamics, collective field theories, W-infinity and related algebras, Calogero–Sutherland models, 2D critical phenomena, renormalization group, quantum phases, statistical mechanics models and related subjects. We seek papers that provide a deeper understanding of the physical properties of well-known and new systems, including quantum excitations with novel properties, and that propose experiments for testing them on real samples.

Prof. Dr. Guillermo Raúl Zemba
Guest Editor

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Keywords

  • effective field theories
  • conformal field theories
  • bosonization
  • quantum hall effect
  • statistical mechanics models
  • quantum hydrodynamics
  • calogero–sutherland models

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Published Papers (1 paper)

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Research

8 pages, 248 KB  
Article
Fermi Sea Topology and Boundary Geometry for Free Particles in One- and Two-Dimensional Lattices
by Guillermo R. Zemba
Mathematics 2026, 14(2), 303; https://doi.org/10.3390/math14020303 - 15 Jan 2026
Viewed by 341
Abstract
Free gases of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds Rd/Γ, where Γ is the crystallographic [...] Read more.
Free gases of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds Rd/Γ, where Γ is the crystallographic group of symmetry in d-dimensional momentum space, are used to accomplish this task. Two topological classes exist for d=1: an interval, which is identified as a conductor, and a circumference, which corresponds to an insulator. The number of topological classes increases to 17 for d=2: 8 have the topology of a disk, that are generally recognized as conductors, and 4 correspond to a two-sphere, matching insulators. Both sets eventually contain a finite number of conical singularities and reflection corners at the boundaries. The remaining cases in the listing relate to conductors (annulus, Möbius strip) and insulators (two-torus, real projective plane, Klein bottle). Examples that fall under this list are given, along with physical interpretations of the singularities. It is anticipated that the findings of this classification will be robust under perturbative interactions due to its topological character. Full article
(This article belongs to the Special Issue Effective Field Theories for Condensed Matter and Statistical Systems)
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