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Register a new userGreens functions on finite lattices and their connection to the infinite lattice limit
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Authors
S. Cojocaru
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It is shown that the Greens function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
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We show how few-particle Greens functions can be calculated efficiently for models with nearest-neighbor hopping, for infinite lattices in any dimension. As an example, for one dimensional spinless fermions with both nearest-neighbor and second nearest-neighbor interactions, we investigate the ground states for up to 5 fermions. This allows us not only to find the stability region of various bound complexes, but also to infer the phase diagram at small but finite concentrations.
In this note we present the Greens functions and density of states for the most frequently encountered 2D lattices: square, triangular, honeycomb, kagome, and Lieb lattice. Though the results are well know, we hope that their derivation performed in a uniform way is of some pedagogical value.
We present a further development of methods for analytical calculations of Greens functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we obtain a number of new results. In particular we derive an explicit expression for arbitrary Greens function of an open Kitaev chain and discover non-local fermionic corner states in a 2D p-wave superconductor.
We analyze the cut-off dependence of mesonic spectral functions calculated at finite temperature on Euclidean lattices with finite temporal extent. In the infinite temperature limit we present analytic results for lattice spectral functions calculated with standard Wilson fermions as well as a truncated perfect action. We explicitly determine the influence of `Wilson doublers on the high momentum structure of the mesonic spectral functions and show that this cut-off effect is strongly suppressed when using an improved fermion action.
We present an alternative approach to studying topology in open quantum systems, relying directly on Greens functions and avoiding the need to construct an effective non-Hermitian Hamiltonian. We define an energy-dependent Chern number based on the eigenstates of the inverse Greens function matrix of the system which contains, within the self-energy, all the information about the influence of the environment, interactions, gain or losses. We explicitly calculate this topological invariant for a system consisting of a single 2D Dirac cone and find that it is half-integer quantized when certain assumptions over the damping are made. Away from these conditions, which cannot or are not usually considered within the formalism of non-Hermitian Hamiltonians, we find that such a quantization is usually lost and the Chern number vanishes, and that in special cases, it can change to integer quantization.
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