We study strong correlation effects in topological insulators via the Lanczos algorithm, which we utilize to calculate the exact many-particle ground-state wave function and its topological properties. We analyze the simple, non-interacting Haldane model on a honeycomb lattice with known topological properties and demonstrate that these properties are already evident in small clusters. Next, we consider interacting fermions by introducing repulsive nearest-neighbor interactions. A first-order quantum phase transition was discovered at finite interaction strength between the topological band insulator and a topologically trivial Mott insulating phase by use of the fidelity metric and the charge-density-wave structure factor. We construct the phase diagram at T = 0 as a function of the interaction strength and the complex phase for the next-nearest-neighbor hoppings. Finally, we consider the Haldane model with interacting hard-core bosons, where no evidence for a topological phase is observed. An important general conclusion of our work is that despite the intrinsic non-locality of topological phases their key topological properties manifest themselves already in small systems and therefore can be studied numerically via exact diagonalization and observed experimentally, e.g., with trapped ions and cold atoms in optical lattices.

We report large scale determinant Quantum Monte Carlo calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian at half-filling. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite-size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the Green's function in momentum space, allowing a more quantitative comparison with time-of-flight optical lattice experiments.

In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. Spatial symmetries are argued to play a fundamental role in the selection of the boundary conditions to be used to locate topological transitions in finite systems. We discuss the theoretical implications of these results, and utilize exact diagonalization to demonstrate its manifestations in the Haldane-Fermi-Hubbard model. Our findings provide an efficient way to detect topological transitions in experiments and in numerical calculations that cannot access the ground-state wave function.

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We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing-cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate the magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures. The extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine the implications of this unusual scenario. The method of bold diagrammatic Monte Carlo simulation (BDMC) [1] allows one to sample contributions from millions of skeleton Feynman diagrams and extrapolate the results to the infinite diagram order, provided the series is convergent (or subject to resummation beyond the convergence radius). Recent experimentally certified application of BDMC to unitary fermions down to the point of the superfluid transition [2] makes a strong case for BDMC method as a generic method for dealing with correlated fermions described by Hamiltonians without small parameters. One intriguing avenue to explore is to apply it to frustrated lattice spin systems, where, on one hand, standard Monte Carlo (MC) simulation fails because of the sign problem [3], and, on the other hand, the system's Hamiltonian can be always written in the fermionic representation [4-6] which contains no large parameters-exactly what is needed for the anticipated convergence of BDMC series with the diagram order.The BDMC approach is based on the sign blessing phenomenon, when, despite the factorial increase in the number of diagrams with expansion order, the series features a finite convergence radius because of dramatic (sign alternation induced) compensation between the diagrams. With the finite convergence radius, the series can be summed either directly, or with resummation techniques that can be potentially applied down to the critical temperature of the phase transition, if any. (At the critical temperature thermodynamic functions become nonanalytic, and the diagrammatic expansion involving explicit symmetry breaking by the finite order parameter is necessary to treat the critical region and the phase with broken symmetry.) In the absence of the sign blessing, the resummation protocols become questionable in view of the known mathematical theorems regarding asymptotic series. At the moment, there is no theory allowing one to prove the existence of a finite convergence radius analytically. The absence of Dyson's collapse [7] in a given fermionic system is merely providing hope that the corresponding diagrammatic series is not asymptotic and cannot be a priori taken as a sufficient condition for the sign blessing. Hence, the applicab...

We demonstrate the formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and stripes in a cluster. We propose to realize such systems in vortex matter (where a vortex is mapped onto a particle with multi-scale interactions) in layered superconducting systems with varying inter-layer thicknesses and different layer materials.

The existence of quantum spin liquids was first conjectured by Pomeranchuk some 70 years ago, who argued that frustration in simple antiferromagnetic theories could result in a Fermi-liquid-like state for spinon excitations. Here we show that a simple quantum spin model on a honeycomb lattice hosts the long sought for Bose metal with a clearly identifiable Bose surface. The complete phase diagram of the model is determined via exact diagonalization and is shown to include four distinct phases separated by three quantum phase transitions.

Microwave-assisted thermal sterilization (MATS) is an advanced thermal process that utilizes microwave (MW) energy for in-package food sterilization. Benefits include much shorter processing times than conventional retort sterilization. This research explores how MATS affects the performance of high-barrier multilayer polymeric films compared with conventional retort sterilization. The gas barrier, morphological, and free volume packaging properties of these films may influence the shelf-life of shelf-stable foods. In this study, we applied X-ray diffraction (XRD) and positron annihilation lifetime spectroscopy in order to investigate film morphology and free volume characteristics, respectively. Results show that the conventional retort process affected gas barrier properties more than MATS processing did which could be explained by the morphological and free volume changes in the polymeric films. XRD revealed improved crystalline morphology of MW-treated films in terms of overall crystallinity as compared with retort sterilization. On the other hand, higher free volume increase in MW-treated films could be explained by the different heating mechanisms involved in MATS and retort sterilization. Overall, the oxygen transmission rate for both films remained below 2 cc/m 2 -day after MATS and retort sterilization required for packaging applications for shelf-stable foods. This work provides the basis for understanding the gas-barrier changes of multilayer polymeric films after MATS application using Materials Science techniques.