Pseudoscalar susceptibilities and quark condensates: chiral restoration and lattice screening masses

We derive the formal Ward identities relating pseudoscalar susceptibilities and quark condensates in three-flavor QCD, including consistently the 77-n' sector and the U-A(1) anomaly. These identities are verified in the low-energy realization provided by ChPT, both in the standard SU(3) framework for the octet case and combining the use of the SU(3) framework and the large-Nc expansion of QCD to account properly for the nonet sector and anomalous contributions. The analysis is performed including finite temperature corrections as well as the calculation of U(3) quark condensates and all pseudoscalar susceptibilities, which together with the full set of Ward identities, are new results of this work. Finally, the Ward identities are used to derive scaling relations for pseudoscalar masses which explain the behavior with temperature of lattice screening masses near chiral symmetry restoration.

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase-an interaction-driven topological insulator-using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest-and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.