Dr. Natalia Chepiga

Abstract:

We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the \mathbb{Z}_2 ℤ 2 -orbifold of the c=1 c = 1 compactified boson boundary conformal field theory, we construct microscopic lattice boundary terms that renormalize to the stable conformal boundary conditions, utilizing simple current extensions and the underlying \mathrm{SU}(2) S U ( 2 ) symmetry to explicitly characterize the four-state Potts point. We validate these theoretical identifications via finite-size spectroscopy of the lattice energy spectra, confirming their consistency with D_4 D 4 symmetry and Kramers-Wannier duality. Finally, we discuss the boundary renormalization group flows among these identified fixed points to propose a global phase diagram for the boundary criticality.

Abstract:

We report an extremely rich ground-state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zigzag ladder. A particular feature of the phase diagram is the extended quantum phase transition in the Ashkin-Teller universality class that separates the plaquette phase, which spontaneously breaks translation symmetry, and the uniform disordered phase. The former is connected to the Haldane phase, stabilized by large interchain coupling, via the topological Gaussian transition. Upon decreasing the interchain interactions, this intermediate disorder phase vanishes, giving place to a dimerized phase separated from the plaquette phase on one side via a nonmagnetic Ising transition and from the Haldane phase on the other side by a topological weak first-order transition. Finally, in the limit of two decoupled chains, we recover a quantum critical point that corresponds to two copies of the Wess-Zumino-Witten $\mathrm{SU}{\left(2\right)}_2$ criticality with a total central charge $c=3$ .

Abstract:

Using a combination of time-dependent density matrix renormalization group and single mode approximation, we investigate the dynamical structure factor of spin chains with antiferromagnetic nearest-neighbor J1, next-nearest-neighbor J2, and three-site J3 interactions and show that, in all gapped phases and at the transitions between them, a simple physical picture can be obtained in terms of magnons and spin-1/2 domain-wall excitations or spinons. This applies to the fully dimerized phase, where a magnon mode clearly pops out of the two-spinon continuum for spin-1 and spin-3/2, and to the transition between the dimerized phase and the Haldane phase (resp. partially dimerized phase) for spin-1 (resp. spin-3/2), where spinons are deconfined along the transition but get confined across it when it is first order. Implications for the interpretation of inelastic neutron scattering in spin chains are briefly discussed.

Abstract:

Quantum phase transitions are characterized by the universal scaling laws in the critical region surrounding the transitions. This universality is also manifested in the critical real-time dynamics through the quantum Kibble-Zurek mechanism. In recent experiments on a Rydberg atom quantum simulator, the Kibble-Zurek mechanism was used to probe the nature of quantum phase transitions. In this paper, we analyze the caveats associated with this method and develop strategies to improve its accuracy. Focusing on two minimal models—transverse-field Ising and quantum three-state Potts, both in one dimension—we study the effect of boundary conditions, the location of the endpoints, and some subtleties in the definition of the kink operators. In particular, we show that the critical scaling of the most intuitive types of kinks is extremely sensitive to the correct choice of endpoint, while more advanced types of kinks exhibit remarkably robust universal scaling. Furthermore, we show that when kinks are tracked over the entire chain, fixed boundary conditions improve the accuracy of the scaling. Surprisingly, the Kibble-Zurek critical scaling appears to be equally accurate whether the fixed boundary conditions are chosen to be symmetric or antisymmetric. We also show that the density of kinks extracted in the central part of long chains obeys the predicted universal scaling for all types of boundary conditions. Finally, we test our kink definition for the Ising transition on the period-2 phase of the Rydberg model and show that it is more robust against the endpoint than the standard definition.

Abstract:

Chains of Rydberg atoms have emerged as a powerful platform for exploring low-dimensional quantum physics. This success originates from the precise control of lattice geometries provided by optical tweezers, which allows access to a wide range of synthetic quantum phases. Experiments on one-dimensional arrays have stimulated tremendous progress in understanding quantum phase transitions into crystalline phases. However, the finite width of tweezers introduces small variations in interatomic distances, leading to quenched disorder in the interactions. In this Letter, we numerically study how such disorder alters the nature of two critical regimes observed in experiments. First, following experimental protocols, we analyze Kibble-Zurek dynamics and find a crossover from the clean Ising transition to the infinite-randomness fixed point as system size and disorder strength increase. Second, we show that the floating phase-an incommensurate Luttinger liquid phase emerging at stronger interactions-is localized by the disorder, yet preserves short-range incommensurate correlations with the same leading wave vector. Our results clearly reveal an additional conceptual challenge in understanding critical phenomena using Rydberg-based quantum simulators.