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...

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...

"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,...

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...

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...

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...

Thermodynamics has shed light on engines, efficiency, and time’s arrow since the Industrial Revolution. But the steam engines that powered the Industrial Revolution were large and classical. Much of today’s technology and experiments are small-scale, quantum, far from equilibrium, and processing information. Nineteenth-century thermodynamics needs re-envisioning for the 21st century. Guidance...

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...

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...

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...

I will discuss how spontaneous breaking of time reversal symmetry in multiband superconductors leads quite generally to the formation of small Fermi surfaces of Bogoliubov excitations, irrespective of whether inversion symmetry is absent or present in the superconducting state. In the latter case the inversion symmetry is susceptible to being dynamical broken at low temperatures by the...

I will talk about our recent progress on bootstrapping critical gauge theories. In specific, I will first introduce the current understanding that why bootstrap works, for example, why a CFT can sit at a kink of bootstrap bounds and why CFT can be isolated as an island. Then, I will apply these idea to a prototypical critical gauge theory--the scalar QED (i.e. SU(N) deconfined phase...

In frustrated magnets, novel phases characterized by fractionalized excitations and emergent gauge fields can occur. A paradigmatic example is given by the Kitaev model of localized spins 1/2 on the honeycomb lattice, which realizes an exactly solvable quantum spin liquid ground state with Majorana fermions as low-energy excitations. I will demonstrate that the Kitaev solution can be...

In the last few years the concept of symmetry has been significantly expanded. One exotic example of the generalized symmetries, is the “type-II subsystem symmetry”, where the conserved charge is defined on a fractal sublattice of an ordinary lattice. In this talk we will discuss examples of models with the fractal symmetries. In particular, we will introduce a quantum many-body model with a...

"The Thirring Model is a covariant quantum field theory of interacting fermions, sharing many features in common with effective theories of two-dimensional electronic systems with linear dispersion such as graphene.

For a small number of flavors and sufficiently strong interactions the ground state may be disrupted by condensation of particle- hole pairs leading to a quantum critical point....