Adrian Del Maestro

The Motzkin spin chain is a well-known mathematical model with connections to symmetry-protected topological phases, such as the Haldane phase, as well as to concepts in the AdS/CFT correspondence. They exhibit highly entangled ground states that violate the area law and are exceptionally difficult to simulate with conventional numerical methods. Numerical simulations of the Motzkin ground state become further challenging at large system sizes due to their high-dimensional spin structure, rendering it a natural test bed for quantum simulation with ultracold systems. Here, we propose a Rydberg-atom based quantum simulation scheme that effectively realizes Motzkin spins using an experimentally accessible set of parameters. We show that the resulting effective Motzkin ground state reproduces the characteristic entanglement scaling and the block-structure properties of the reduced density matrix associated with the ideal Motzkin state. Our results establish a pathway toward a concrete experimental realization of Motzkin spins beyond purely mathematical constructions, opening avenues for exploring other similar exotic non-area-law entangled phases in programmable Rydberg simulators.

We study interaction-driven edge reconstruction in a quantum spin Hall insulator described by the Bernevig-Hughes-Zhang model with Kanamori-Hubbard interactions using the real-space density matrix renormalization group method in both the grand-canonical and canonical ensembles. For a two-dimensional cylinder with a smooth edge, we identify discrete particle-number transitions that lead to a spin-polarized edge state stabilized by an emergent ferromagnetic exchange interaction. The reconstruction is orbital-selective, occurring predominantly in the s -orbital channel. Our results reveal a microscopic mechanism for emergent fluctuating moments at the edge that could compromise the topological protection of helical edge states by time-reversal symmetry.

One-dimensional bosonic systems, such as helium confined to nanopores, exhibit Luttinger liquid behavior characterized by density waves as collective excitations. We investigate the impact of a scattering potential on a low-dimensional quantum liquid. We consider a microscopic model of ^{4}He inside a perturbed nanopore with a localized constriction and employ quantum Monte Carlo simulations to analyze the density of the core within an effective low-energy framework. Our results reveal the emergence of Friedel oscillations in a bosonic quantum liquid without a Fermi surface. Furthermore, we utilize the Luttinger liquid model to predict experimentally observable signatures of this pinning phenomenon in elastic scattering and via the temperature and pressure dependence of mass transport through the deformed nanopore.

The accurate modeling of non-covalent interactions between helium and graphitic materials is important for understanding quantum phenomena in reduced dimensions, with the helium–benzene complex serving as the fundamental prototype. However, creating a quantitatively reliable potential energy surface (PES) for this weakly bound system remains a significant computational challenge. In this study, we present a comprehensive, multi-level investigation of the He–benzene interaction, establishing benchmark energies using high-level coupled-cluster singles-and-doubles with perturbative triples [CCSD(T)] methods extrapolated to the complete basis set limit and assessing higher-order contributions. We use symmetry-adapted perturbation theory to benchmark it against CCSD(T) and to decompose the interaction into its physical components—confirming it is dominated by a balance between dispersion and exchange-repulsion. A continuous, three-dimensional PES is constructed from discrete ab initio points using multifidelity Gaussian process regression that combines density functional theory results with sparse coupled-cluster energies. The result is a highly accurate PES with sub-cm−1 accuracy that obeys physical laws. This new PES is applied to path integral Monte Carlo (PIMC) simulations to study the solvation of 4He atoms on benzene at low temperatures. Our PIMC results reveal qualitatively different solvation behavior, particularly in the filling of adsorption layers, when compared to simulations using commonly employed empirical Lennard-Jones potentials. This study provides a benchmark PES essential for accurate many-body simulations of helium on larger polycyclic aromatic hydrocarbons toward graphene.

We propose an improved Path Integral Monte Carlo (PIMC) algorithm called harmonic PIMC (H-PIMC) and its generalization, mixed PIMC (M-PIMC). PIMC is a powerful tool for studying quantum condensed phases. However, it often suffers from a low acceptance ratio for solids and dense confined liquids. We develop two sampling schemes especially suited for such problems by dividing the potential into its harmonic and anharmonic contributions. In H-PIMC we generate the imaginary time paths for the harmonic part of the potential exactly and accept or reject it based on the anharmonic part. In M-PIMC we restrict the harmonic sampling to the vicinity of local minimum and use standard PIMC otherwise, in order to optimize efficiency. We benchmark H-PIMC on systems with increasing anharmonicity, improving the acceptance ratio and lowering the autocorrelation time. For weakly to moderately anharmonic systems, at βℏω=16, H-PIMC improves the acceptance ratio by a factor of 6-16 and reduces the autocorrelation time by a factor of 7-30. We also find that the method requires a smaller number of imaginary time slices for convergence, which leads to another two- to threefold acceleration. For strongly anharmonic systems, M-PIMC converges with a similar number of imaginary time slices as standard PIMC but allows the optimization of the autocorrelation time. We extend M-PIMC to periodic systems and apply it to a sinusoidal potential. Finally, we combine H- and M-PIMC with the worm algorithm, allowing us to obtain similar efficiency gains for systems of indistinguishable particles.

The accurate modeling of non-covalent interactions between helium and graphitic materials is important for understanding quantum phenomena in reduced dimensions, with the helium-benzene complex serving as the fundamental prototype. However, creating a quantitatively reliable potential energy surface (PES) for this weakly bound system remains a significant computational challenge. In this work, we present a comprehensive, multi-level investigation of the He-Bz interaction, establishing benchmark energies using high-level coupled-cluster singles-and-doubles with perturbative triples (CCSD(T)) methods extrapolated to the complete basis set limit and assessing higher-order (CCSDT(Q)) contributions. We use symmetry-adapted perturbation theory (SAPT) to benchmark it against CCSD(T) and to decompose the interaction into its physical components-confirming it is dominated by a balance between dispersion and exchange-repulsion. A continuous, three-dimensional PES is constructed from discrete ab initio points using multifidelity Gaussian process regression that combines density functional theory results with sparse coupled-cluster energies. The result is a highly accurate PES with sub-cm-1 accuracy that obeys physical laws. This new PES is applied to path integral Monte Carlo (PIMC) simulations to study the solvation of 4He atoms on benzene at low temperatures. Our PIMC results reveal qualitatively different solvation behavior, particularly in the filling of adsorption layers, when compared to simulations using commonly employed empirical Lennard-Jones potentials. This work provides a benchmark PES essential for accurate many-body simulations of helium on larger polycyclic aromatic hydrocarbons towards graphene.

We present a controlled numerical study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in the one-dimensional Bose-Hubbard model at unit filling, providing evidence of the characteristic logarithmic finite-size scaling of the BKT transition. Employing density matrix renormalization group and quantum Monte Carlo simulations under periodic boundary conditions, together with a systematic finite-size scaling analysis of bipartite particle number fluctuations, we resolve boundary-induced complications that previously obscured critical scaling. We demonstrate that a suitably chosen central region under open boundaries reproduces universal renormalization group signatures, reconciling earlier discrepancies. Finally, leveraging a nonparametric Bayesian analysis, we determine the critical interaction strength with high precision to be U c / J = 3.275 ( 2 ) , establishing a benchmark for BKT physics in one-dimensional quantum models.