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arXiv:2609.20755

Engineering Weak Universality with Quantum Dots

Warre Missiaen, Michael Wimmer, Natalia Chepiga

cond-mat.str-elcond-mat.mes-hallquant-phSubmitted Sep 17, 2026• Announced Sep 18, 2026• 0 citations
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Abstract

Quantum critical theories with continuously varying critical exponents remain challenging to access experimentally. Here, we propose quantum-dot architectures for realizing the quantum Ashkin-Teller and XYZ/eight-vertex models using resonator-mediated and direct Coulomb interactions, respectively. We focus on the Ashkin-Teller and eight-vertex critical lines, which are connected by a non-local duality relating local order parameters to topological string operators. The resulting platforms provide microscopic control over the parameters explicitly controlling critical exponents, with the Coulomb-based implementation enabling stronger interaction regimes. We demonstrate that continuously varying critical behavior can already be resolved in short chains. For experimentally realistic parameters, the accessible interaction range is expected to produce changes in the critical exponents of order $10\%$ for the Ashkin-Teller model and substantially larger changes for the eight-vertex model. In both cases, the predicted variations lie well above the estimated measurement uncertainties.

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Journal of Physics A Mathematical and General•Apr 7, 1990•6 citations
Quantum critical theories with continuously varying critical exponents remain challenging to access experimentally. Here, we propose quantum-dot architectures for realizing the quantum Ashkin-Teller and XYZ/eight-vertex models using resonator-mediated and direct Coulomb interactions, respectively. We focus on the Ashkin-Teller and eight-vertex critical lines, which are connected by a non-local duality relating local order parameters to topological string operators. The resulting platforms provide microscopic control over the parameters explicitly controlling critical exponents, with the Coulomb-based implementation enabling stronger interaction regimes. We demonstrate that continuously varying critical behavior can already be resolved in short chains. For experimentally realistic parameters, the accessible interaction range is expected to produce changes in the critical exponents of order 10%10\%10% for the Ashkin-Teller model and substantially larger changes for the eight-vertex model. In both cases, the predicted variations lie well above the estimated measurement uncertainties.
The Ashkin-Teller model can be formulated as a pair of 2D Ising models, interacting via a four-spin interaction. I consider the case of weak anisotropy (slight a-symmetry between the two Ising layers) and weak coupling. I show that the system admits two critical temperatures whose difference varies continuously with the strength of the coupling, scaling with an anomalous exponent as one let the a-symmetry parameter go to zero. The specific heat diverges logarithmically at the critical points (as for Ising) but the constant in front of the logarithm is renormalized by an anomalous critical exponent. The logarithmic divergence of the specific heat dominates only in an exponentially small interval around the critical temperatures and outside it is modified into an anomalous power law behaviour. The proof is based on an exact mapping of Ashkin-Teller into a model of (1+1)D interacting fermions and on the implementation of constructive Renormalization group methods on the fermionic system. This PhD thesis includes: (1) a review of the exact solution of 2D Ising in terms of Grassmann functional integrals; (2) a review of the Grassmann representation for a class of interacting Ising models, including Ashkin-Teller and the 8 vertex model; (3) a detailed discussion of the multiscale analysis of the Ashkin-Teller model, based on fermionic Renormalization Group methods, including the study of the flow of the effective coupling constants (in particular a proof of vanishing of the beta function for this and similar Luttinger-like models, based on modified approximate Ward identities, is included). This thesis is based on joint work with V. Mastropietro.
Abstract Recent advances in quantum dot platforms have opened a new platform for realizing Majorana zero modes (MZMs) and simulating topological quantum computation. Here we propose an experimentally feasible setup for implementing topological X\sqrt{X}X​ X - and X -quantum gates in an interacting Y -shaped quantum-dot array. The proposed architecture enables both braiding and charge readout through simple fusion operations controlled by gate-tunable potentials. Using many-body time-dependent exact diagonalization, we analyze MZM braiding and fusion dynamics in the presence of nearest-neighbor Coulomb interactions, hopping-pairing mismatch, onsite charge fluctuations, and pairing disorder. We compute diabatic errors, braiding fidelity, and the time- and space-resolved electron and hole components of the local density of states to monitor the braiding process. Our results show that even weak interactions or pairing disorder induce oscillations in the braiding fidelity, thereby setting an upper bound on the braiding speed. Furthermore, we demonstrate that comparing fusion outcomes before and after double braiding provides a direct and experimentally accessible signature of the non-Abelian nature of MZMs in quantum-dot systems.
Adaptive quantum circuits—where a quantum many-body state is controlled using measurements and conditional unitary operations—are a powerful paradigm for state preparation and quantum error-correction tasks. They can support two types of nonequilibrium quantum phase transitions: measurement-induced transitions between volume- and area-law-entangled steady states and control-induced transitions where the system falls into an absorbing state or, more generally, an orbit visiting several absorbing states. Within this context, nonlocal conditional operations can alter the critical properties of the two transitions and the topology of the phase diagram. Here, we consider the scenario where the measurements are , in order to engineer efficient control onto dynamical trajectories. Motivated by Rydberg-atom arrays, we consider a locally constrained model with global sublattice magnetization measurements and local correction operations to steer the system’s dynamics onto a many-body orbit with finite recurrence time. The model has a well-defined classical limit, which we leverage to aid our analysis of the control transition. As a function of the density of local correction operations, we find control and entanglement transitions with continuously varying critical exponents. For sufficiently high densities of local correction operations, we find that both transitions acquire a dynamical critical exponent z < 1 , reminiscent of criticality in long-range power-law interacting systems. At low correction densities, we find that the criticality reverts to a short-range nature with z ≳ 1 . In the long-range regime, the control and entanglement transitions are indistinguishable to within the resolution of our finite-size numerics, while in the short-range regime we find evidence that the transitions become distinct. We conjecture that the effective long-range criticality mediated by collective measurements is essential in driving the two transitions together.
Quantum phase transitions are usually classified into discrete universality classes that typically only depend on symmetries and spatial dimensionalities. In this Letter, we demonstrate an opportunity to continuously vary the critical exponents or universalities by tuning experimental parameters in a given physical system. Particularly, we show that critical exponents in long-range spin systems simulated in ion traps can be easily tuned with laser detuning. We suggest that such experiments also effectively simulate some aspects of critical phenomena in conventional spin systems but in artificial non-integer spatial dimensions.
The exact solution of an Ashkin-Teller model, with layer and spatial anisotropy and Z 2 *Z 2 symmetry, is presented. The model is related to the eight-vertex model by a sublattice or orbifold duality and it has the same free energy and magnetisation. The exact solution manifold is a three-dimensional submanifold of the full six-dimensional thermodynamic space. It admits a Z 3 symmetry relating three regimes each exhibiting different partial order. In the spatially isotropic case, these regimes are separated by three lines of continuously varying critical behaviour which coalesce at the four-state Potts critical point. The magnetisations and polarisation are derived using corner transfer matrices giving rise to the appearance of chiral and Virasoro characters. The associated critical exponents confirm the known values. In particular, one obtains the value x sigma =1/8 for the magnetic scaling dimension and identify the next-to-leading thermal field.