HQS Quantum Solver

Many Particles System Toolkit

HQStage Module

Simulation

The HQS Quantum Solver stands as HQS' comprehensive toolkit to tackle quantum systems in the many particle wave function description. It combines high-speed code, written in compiled programming languages, with a user-friendly interface. With its consistent and adaptable design, the HQS Quantum Solver provides functions for building Hamiltonians and operators in the many-particle description allowing the exploitation of symmetries like particle number or spin Sz conservation. It enables the study of eigen states, time propagation including various quench schemes, and the calculation of static and dynamic correlation functions.

Benefits

  • Simple calculation of band structures, even for interacting systems.

  • User-Friendly Interface: With intuitive interfaces and comprehensive examples, HQS Quantum Solver is accessible to both experienced quantum researchers and beginners.

  • Efficient Computation: The optimized Krylov implementation and dyadic representation significantly boost the speed and accuracy of computations, saving valuable time and resources.

  • Tailored Solutions: HQS Quantum Solvers' extensibility allows users to customize the toolkit according to their specific research needs, ensuring compatibility with their algorithms and tools.

Features

  • User-Friendly Interface: The HQS Quantum Solver provides an a user-friendly interface for creating lattice models. It also connects to the HQS Spin Mapper and struqture and allows for arbitrary user-defined models. Making it easy for users to construct Hamiltonians and operators effortlessly.

  • Enables exploitation of symmetries like particle number, spin Sz conservation, or just the fermion parity for BCS type models for superconductivity.

  • Extensibility and Backends: The HQS Quantum Solver offers multiple backends for efficient property evaluation, catering to users' specific needs. Its consistent protocol allows users to create their backends, tools, and algorithms while ensuring compatibility with HQS Quantum Solver's suite.

  • Calculation of static and dynamical correlations functions in frequency domain including the correction vector approach and the expansion in Chebyshev polynomials.

  • Protocols: HQS Quantum Solver introduces innovative concepts like Protocol, simplifying the customization of the package.

Use Case

HQS Quantum Solver is a powerful tool for researchers and enthusiasts in the field of condensed matter physics and beyond. It can be used for a wide range of applications, including but not limited to:

  • Simulating time-evolution of spin and fermionic systems

  • Evaluating spectral functions of interacting fermionic systems and dynamic correlation function for fermionic and spin-spin problems.

  • Exploring quench scenarios in various lattice structures

  • Studying interacting band structures for spinless and spinful fermion lattices using CPT

Theoretical Background

Empfohlen
Applicability and limitations of cluster perturbation theory for Hubbard models
Applicability and limitations of cluster perturbation theory for Hubbard models

Authors: Nicklas Enenkel, Markus Garst, Peter Schmitteckert
Journal reference: Eur. Phys. J. Spec. Top. 10.1140, 2023

We present important use cases and limitations when considering results obtained from Cluster Perturbation Theory (CPT). CPT combines the solutions of small individual clusters of an infinite lattice system with the Bloch theory of conventional band theory in order to provide an approximation for the Green's function in the thermodynamic limit. To this end we are investigating single-band and multi-band Hubbard models in one- and two-dimensional systems. A special interest is taken in the supposed pseudo gap regime of the two-dimensional square lattice at half filling and intermediate interaction strength (U≤3t) as well as the metal-insulator transition. We point out that the finite-size level spacing of the cluster limits the resolution of spectral features within CPT. This restricts the investigation of asymptotic properties of the metal-insulator transition, as it would require much larger cluster sizes that are beyond computational capabilities.

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