PaperPanorama

HEP Lattice·hep-lat

Thu·Aug 20, 2026

3 papers—1 primary·2 cross-listed

All3Primary1Cross-lists2
  1. 01

    Searching for symmetric mass generation with staggered fermions in four dimensions

    Nouman Butt🇺🇸 · Simon Catterall🇺🇸 · Gwen Hartshaw🇺🇸 · Anna Hasenfratz🇺🇸

    We conduct numerical simulations to map out the phase diagram and critical behavior of a lattice Higgs model composed of two massless staggered fermion fields forming a doublet under a global and coupled to a scalar field in the adjoint representation of the group. The scalar action consists of a potential comprising quadratic and quartic terms and a scalar kinetic term. At fixed quartic coupling we explore a two-dimensional parameter space finding a massless symmetric phase at weak coupling and a massive symmetric phase (SMG phase) at strong coupling. An intermediate anti-ferromagnetic phase separates these two regimes. These results are consistent with leading order weak and strong coupling expansions. We find that the critical lines bounding the intermediate phase merge at a unique point where all fermion bilinear condensates vanish but fermion susceptibilities diverge as non-trivial powers of the lattice size. We conjecture that this merged point corresponds to a multicritical point and may describe a phase consisting of a condensate of certain topological defects.

    hep-latcond-mat.str-elhep-th1 citation
  2. 02

    Chern insulator boundary criticality

    Benjamin Moy · Eduardo Fradkin

    We investigate signatures of chirality at Chern insulator transitions in the presence of a boundary. The transition between a trivial insulator and a Chern insulator with Chern number is described by a massless Dirac fermion whose parity anomaly gives a critical Hall conductivity . Using a Dirac mass domain wall construction, we show that the chiral edge mode delocalizes into the bulk at criticality, but the boundary fermion correlation function retains a chiral structure and acquires the scaling dimension of the bulk fermion. We compute current correlation functions and demonstrate that the anomaly of the bulk Hall response is matched by delocalized chiral modes near the boundary. Using only the residual conformal symmetry of a (2+1)d conformal field theory (CFT) in a half-space, we identify parity-odd terms in current and energy-momentum tensor correlation functions that encode these modes and determine their electromagnetic and gravitational anomaly coefficients. Our analysis therefore applies to general time-reversal breaking (2+1)d CFTs, beyond the free Dirac transition. In particular, the analysis of the gravitational anomaly is also applicable to the free Majorana CFT governing the transition between a trivial superconductor and a topological superconductor. We also extend our results to more general Chern number changing transitions and to the transition between a (3+1)d topological insulator and a trivial insulator.

    ↳ cond-mat.str-elcond-mat.mes-hallhep-lathep-th1 citation
  3. 03

    Cluster Representation of Renormalization Group Transformations and a Rigorous Proof for Convergence of the RG-Flow of the Ising Model to Trivial Fixed Points away from Criticality

    Fabio Arz

    Many rigorous results in the modern era of statistical mechanics have been obtained through geometrical representations. A much studied tool in this setting is the random cluster representation of lattice spin models. Another area of statistical mechanics that is of great interest but lacking rigorous results is the theory of the renormalization group. This paper investigates the idea to find a common ground between these two concepts in order to obtain rigorous results on the renormalization group flow. A need for negative cluster-weights weakens the success of this approach. Nevertheless, we managed to establish a relation between the scaling limit of the renormalization group flow of the nearest-neighbour Ising model away from criticality with a simple one-dimensional dynamical system that follows the cluster connectivity of the renormalization group transformation. This allows for a rigorous proof of the convergence of this flow to the zero- and infinite-temperature fixed point respectively for a large family of renormalization group transformations. Explicit results will be established on followed by a discussion of the available generalizations to higher dimensions.

    ↳ math-phcond-mat.stat-mechhep-latmath.MP0 citations

Affiliations

first authorsco-authorsvia INSPIRE