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arXiv:2603.17807

Emergent superconformal symmetry in the phase diagram of a 1D $\mathbb{Z}_{2}$ lattice gauge theory

Bachana Beradze, Mikheil Tsitsishvili, Sergej Moroz

Published Mar 18, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the phase diagram and critical properties of a one-dimensional $\mathbb{Z}_{2}$ lattice gauge theory describing an orthogonal metal, where spinless fermions and Ising spins are minimally coupled to a deconfined $\mathbb{Z}_{2}$ gauge field. Working at half-filling of fermions, we derive an exact gauge-invariant formulation that maps the model onto decoupled XXZ and transverse-field Ising chains. This mapping enables a controlled low-energy field-theory description in terms of a perturbed Luttinger liquid and Ising conformal field theories. Combining analytical arguments with numerical simulations, we determine the full phase diagram and identify various critical and multi-critical regimes. Along a specific multi-critical line, where the fermionic and bosonic velocities coincide, we find strong evidence for an emergent superconformal symmetry. Our results establish a minimal lattice realization of emergent superconformal criticalities in a gauge-matter system and provide a route toward its exploration in quantum simulators.

DOI
10.48550/arxiv.2603.17807

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Quantum phases of two-dimensional Z2\mathbb{Z}_2Z2​ gauge theory coupled to spinless fermion matter
We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with U(1)U(1)U(1) symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure Z2\mathbb{Z}_2Z2​ even and odd gauge theories, (ii) free fermions in a static background of deconfined Z2\mathbb{Z}_2Z2​ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of Z2\mathbb{Z}_2Z2​ gauge-invariant spin 1/21/21/2 degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.
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We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.
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