Conference

Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. However, long experimental state preparation times limit the amount of measurement data that can be generated at reasonable timescales, posing a challenge for the reconstruction and characterization of quantum states. Over the last years, neural networks have been explored as a powerful and systematically tuneable ansatz to represent quantum wavefunctions. These models can be efficiently trained from projective measurement data or through Hamiltonian-guided variational Monte Carlo. In this talk, I will compare the data-driven and Hamiltonian-driven training procedures to reconstruct ground states of two-dimensional Rydberg atom arrays. I will discuss the limitations of both approaches and demonstrate how pretraining on a small amount of measurement data can significantly reduce the convergence time for a subsequent variational optimization of the wavefunction.

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, some notably hard systems such as those exhibiting glassiness and frustration have mainly achieved unsatisfactory results despite their representational power and entanglement content, thus, suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman-Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman-Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape.

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive a competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically-trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the spatial extent of the localized flat-band Wannier wavefunctions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the non-perturbative nature of the problem, we identify an analytically tractable limit associated with a `small' spatial extent of the Wannier functions, and derive a low-energy effective Hamiltonian that can well describe our numerical results.

The sign structure of quantum states is closely connected to quantum phases of matter, yet detecting such fine-grained properties of amplitudes is subtle. We employ as a diagnostic measurement-induced entanglement (MIE)-- the average entanglement generated between two parties after measuring the rest of the system. We propose that for a sign-free state, the MIE upon measuring in the sign-free basis decays no slower than correlations in the state before measurement. Concretely, we prove that MIE is upper bounded by mutual information for sign-free stabilizer states (essentially CSS codes), which establishes a bound between scaling dimensions of conformal field theories describing measurement-induced critical points in stabilizer systems. We also show that for sign-free qubit wavefunctions, MIE between two qubits is upper bounded by a simple two-point correlation function, and we verify our proposal in several critical ground states of one-dimensional systems, including the transverse field and tri-critical Ising models. In contrast, for states with sign structure, such bounds can be violated, as we illustrate in critical hybrid circuits involving both Haar or Clifford random unitaries and measurements, and gapless symmetry-protected topological states.

Two-dimensional gapless Dirac fermions emerge in various condensed-matter settings. In the presence of interactions such Dirac systems feature critical points and the precision determination of their exponents is a prime challenge for quantum many-body methods. In a field-theoretical language, these critical points can be described by Gross-Neveu-Yukawa-type models and in my talk I will show some results on Gross-Neveu critical behavior using field theoretical approaches beyond the leading order. To that end, I will first present higher-loop perturbative RG calculations for generic Gross-Neveu-Yukawa models and compare estimates for the exponents with recent corresponding results from Quantum Monte Carlo simulations and the conformal bootstrap. Then, I will discuss a more exotic variant of Gross-Neveu-Yukawa models which describes the interacting fractionalized excitations of two-dimensional frustrated spin-orbital magnets. Here, we have provided field-theoretical estimates for the critical exponents employing higher-order epsilon expansion, large-N calculations, and functional renormalization group.

In the original field theoretical scenario of deconfined quantum criticality, the deconfined quantum-critical point (DQCP) separating antiferromagnetic (AFM) and singlet-solid phases of quantum magnets is generic, i.e., does not require fine-tuning. Recent numerical studies instead point to a fine-tuned multi-critical DQCP [1] that is also the end-point of a gapless spin liquid phase [2]. An example is the Shastry-Sutherland (SS) model, where a narrow spin liquid phase was recently detected [2,3], instead of the previously argued direct transition between plaquette singlet solid (PSS) and AFM phases. The multi-critical DQCP, followed by a direct transition without intervening spin liquid, can be reached when other interactions are included. Very recent NMR experiments on the SS compound SrCu2(BO3)2 under high pressures and high magnetic fields are consistent with this scenario [4]. Low-temperature (below 0.1 K) direct PSS to XY-AFM transitions were observed that become less strongly first-order at higher pressures. At the highest pressure, quantum-critical scaling of the spin-lattice relaxation was observed, indicating close proximity to a DQCP. This point may be the end-point of a not yet confirmed quantum spin liquid phase existing at slightly higher pressures. [1] B. Zhao, J. Takahashi, and A. W. Sandvik, PRL 125, 257204 (2020). [2] J. Yang, A. W. Sandvik, and L. Wang, PRB 105, L060409 (2022). [3] L. Wang, Y. Zhang, and A. W. Sandvik, arXiv:2205.02476 [4] Y. Cui et al., arXiv:2204.08133.

The Kitaev model with anisotropic interactions on the bonds of a honeycomb lattice is a paradigmatic model for quantum spin liquids. Despite the simplicity of the model, a rich phase diagram with gapless and gapped quantum spin liquid phases, with abelian and non-abelian excitations, are revealed as a function of a magnetic field and bond couplings. Our results of the entanglement entropy, topological entanglement entropy, and the dynamical spin excitation spectrum, are obtained using exact diagonalization and density matrix renormalization group (DMRG) methods. We provide insights into the phases from the underlying effective field theories. In collaboration with Shi Feng, Cullen Gantenberg, Adhip Agarwala, Subhro Bhattacharjee [1] Signatures of magnetic-field-driven quantum phase transitions in the entanglement entropy and spin dynamics of the Kitaev honeycomb model, David C. Ronquillo, Adu Vengal, Nandini Trivedi, Phys. Rev. B 99, 140413 (2019) [2] Magnetic field induced intermediate quantum spin-liquid with a spinon Fermi surface, Niravkumar D. Patel and Nandini Trivedi, Proceedings of the National Academy of Sciences 116, 12199 (2019). [3] Two-Magnon Bound States in the Kitaev Model in a [111]-Field, Subhasree Pradhan, Niravkumar D. Patel, Nandini Trivedi, Phys. Rev. B 101, 180401 (2020) [4] Symmetry Analysis of Tensors in the Honeycomb Lattice of Edge-Sharing Octahedra, Franz G. Utermohlen, Nandini Trivedi, Phys. Rev. B 103, 155124 (2021)

Starting from the Villain formulation with an additional constraint we construct a self-dual lattice version of U(1) field theory with a theta-term. An interesting feature is that the self-dual symmetry gives rise to an action that is local but not ultra-local, similar to lattice actions that implement chiral symmetry. We outline how electric and magnetic matter can be coupled in a self-dual way and discuss the emerging symmetry structure with the theta term. We present results from a Monte Carlo simulation of the self-dual system with electric and magnetic matter and explore spontaneous breaking of the self-dual symmetry.

The sign problem is arguably the greatest weakness of the otherwise highly efficient, non-perturbative Monte Carlo simulations. Recently, considerable progress has been made in alleviating the sign problem by deforming the integration contour of the path integral into the complex plane and applying machine learning to find near-optimal alternative contours. This deformation however requires a Jacobian determinant calculation which has a generic computational cost scaling as volume cubed. In this talk I am going to present a new architecture with linear runtime, based on complex-valued affine coupling layers.