Introduction

Introduction#

The aim of the HQS Cloud platform is to enable the study of interacting tight-binding or spin models, which, for simplicity, we just call lattice models, see Physics. Such models consist of a discrete set of sites representing the corresponding orbitals or spin degrees of freedom, respectively. A lattice can be viewed as a regular tiling of space by a primitive cell, where, in the context of condensed matter physics, the primitive cell is usually called unit cell. The lattice is then constructed by repeating the unit cell in the directions of the lattice vectors. The number of linear independent lattice vectors defines the number of dimensions of the system.

In HQS Cloud we have added another layer in the construction of the lattice system, which allows us to define an embedding, see section on cluster embedding. We start with the unit cell as the primitive unit and build a cluster as described above. We can then repeat the cluster to construct a full system. In this way we are able to describe various embedding schemes, described in the Physics section. If the number of repetitions in every direction along a lattice vector is one, which corresponds to system_size = [1, 1, 1] in the input, the system consists of a single cluster ony, in which case no embedding is employed.

It is perfectly fine to define a system consisting of just a single cluster with a large single unit cell which enables the study of amorphous systems.

Currently, our emphasis is on adding functionality for the system_size = [1, 1, 1] mode. At the moment embedding schemes have only been implemented for very simple lattice models.

We are always eager to learn which features are most useful to our user base, so any feedback is highly encouraged. Depending on this user feedback, we envisage to implement the following features in the future:

  • Support for 3D lattices: While 3D lattices do not pose a fundamental challenge to the HQS Cloud solver, in practice, the number of sites in a 3D lattice grows quickly such that the available computational resources become a limitation. (Available via API)

  • Access to all underlying parameters of the HQS Cloud and its DMRG solver: For expert users, access will be granted to all of the parameters which are used in the HQS Cloud software. (Available via API)

  • Access to the HQS Cloud via an API: The HQS Cloud can be used directly by calling the API in a python script. (available)

  • Optional coarse-graining of the bath.

  • BCS-like superconducting pairing terms. (available)

  • Quantum computation as a backend for the HQS Cloud calculations: Of course, this ultimately depends on the development of quantum computing hardware.

  • Expansion of available embedding schemes: Cluster Perturbation Theory (CPT) and Dynamical Mean Field Theory (DMFT) will be added as options for embedding.

Please keep in mind that the current release offers a limited feature set only, but we have plenty of ideas for extensions to the platform.