Publications

One of the demanding frontiers in ultracold science is identifying laser cooling schemes for complex atoms and molecules, out of their vast spectra of internal states. Motivated by a need to expand the set of available ultracold molecules for applications in fundamental physics, chemistry, astrochemistry, and quantum simulation, we propose and demonstrate an automated graph-based search approach for viable laser cooling schemes. The method is time efficient and the outcomes greatly surpass the results of manual searches used so far. We discover new laser cooling schemes for C

Synthetic dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases - two are localized in the synthetic dimension, predicted as zero-temperature ground states in Refs. [Sci. Rep., 8, 1 (2018) and Phys. Rev. A 99, 013624 (2019)], and a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength, for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tri-critical point on the phase boundary. By examining the dependence of the tri-critical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.

The performance of semiconductor devices can be enhanced by understanding and characterizing the bound states of deep defects. However, simulating these states using conventional

In conventional

Using scanning-tunneling-microscopy and theoretical modeling on heterostructures of twisted bilayer graphene and hexagonal Boron-Nitride, we show that the emergent super-moire structures display a rich landscape of moire-crystals and quasicrystals. We reveal a phase-diagram comprised of commensurate moire-crystals embedded in swaths of moire quasicrystals. The 1:1 commensurate crystal, expected to be a Chern insulator, should only exist at one point on the phase-diagram, implying that it ought to be practically undetectable. Surprisingly we find that the commensurate crystals exist over a much wider than predicted range, providing evidence of an unexpected self-alignment mechanism that is explained using an elastic-network model. The remainder of the phase-diagram, where we observe tunable quasicrystals, affords a new platform for exploring the unique electronic-properties of these rarely found in nature structures.

We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically with respect to system sizes and linearly with the number of 𝐤-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with 𝐤-point sampling beyond density functional theory.

We discuss a tensor network method for constructing the adiabatic gauge potential -- the generator of adiabatic transformations -- as a matrix product operator, which allows us to adiabatically transport matrix product states. Adiabatic evolution of tensor networks offers a wide range of applications, of which two are explored in this paper: improving tensor network optimization and scanning phase diagrams. By efficiently transporting eigenstates to quantum criticality and performing intermediary density matrix renormalization group (DMRG) optimizations along the way, we demonstrate that we can compute ground and low-lying excited states faster and more reliably than a standard DMRG method at or near quantum criticality. We demonstrate a simple automated step size adjustment and detection of the critical point based on the norm of the adiabatic gauge potential. Remarkably, we are able to reliably transport states through the critical point of the models we study.

Quantum many-body systems are typically endowed with a tensor product structure. This structure is inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. Considering a particular Hamiltonian and a particular tensor product structure, one can ask: is there a basis in which this Hamiltonian has this desired tensor product structure? In particular, we ask: is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e. it contains only pairwise interactions? Here we show, using numerical and analytical arguments, that generic Hamiltonian (e.g. a large random matrix) can approximately be written as a linear combination of two-body interactions terms with high precision; that is the Hamiltonian is 2-local in a carefully chosen basis. We show that these Hamiltonians are robust to perturbations. Taken together, our results suggest a possible mechanism for the emergence of locality from chaos.

Recent experiments have confirmed the presence of interlayer excitons in the ground state of transition metal dichalcogenide (TMD) bilayers. The interlayer excitons are expected to show remarkable transport properties when they undergo Bose condensation. In this work, we demonstrate that quantum geometry of Bloch wavefunctions plays an important role in the phase stiffness of the Interlayer Exciton Condensate (IEC). Notably, we identify a geometric contribution that amplifies the stiffness, leading to the formation of a robust condensate with an increased BKT temperature. Our results have direct implications for the ongoing experimental efforts on interlayer excitons in materials that have non-trivial quantum geometry. We provide quantitative estimates for the geometric contribution in TMD bilayers through a realistic continuum model with gated Coulomb interaction, and find that the substantially increased stiffness allows for an IEC to be realized at amenable experimental conditions.

Helical twisted trilayer graphene exhibits zero-energy flat bands with large degeneracy in the chiral limit. The flat bands emerge at a discrete set of magic twist angles and feature properties intrinsically distinct from those realized in twisted bilayer graphene. Their degeneracy and the associated band Chern numbers depend on the parity of the magic angles. Two degenerate flat bands with Chern numbers C