Modelling equilibration of local many-body quantum systems by random graph ensembles

We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex matrix structures, well beyond Wigner's full or banded random matrices, are required to faithfully model equilibration times. Viewing the random matrices as connectivities of graphs, we analyse the resulting network of classical oscillators in Hilbert space with tools from network theory. One of these tools, called the maximum flow value, is found to be an excellent proxy for equilibration times. Since maximum flow values are less expensive to compute, they give access to approximate equilibration times for system sizes beyond those accessible by exact diagonalisation.

QuSpin: a Python package for dynamics and exact diagonalisation of quantum many body systems part I: spin chains

We present a new open-source Python package for exact diagonalisation and quantum dynamics of spin(-photon) chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary) time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet) systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i) Standard exact diagonalisation of XXZ chain (ii) adiabatic ramping of parameters in the many-body localised XXZ model, (iii) heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv) quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.

GROUND STATE PROPERTIES OF TWO SPIN MODELS WITH EXACTLY KNOWN GROUND STATES ON THE SQUARE LATTICE

We introduce a new two-dimensional model with diagonal four spin exchange and an exactly known ground-state. Using variational ansätze and exact diagonalisation we calculate upper and lower bounds for the critical coupling of the model. Both for this model and for the Shastry–Sutherland model we study periodic systems up to system size 6×6.

QUANTUM DISORDER OF AN ANTIFERROMAGNETIC SPIN MODEL ON THE SIERPIŃSKI GASKET

We study the ground state magnetic order of the quantum antiferromagnet on the fractal Sierpiński gasket, a system with a dimension between one and two. Using exact diagonalisation we analyse the ground state and thermodynamic properties of small finite systems and calculate data like spin-spin correlations and specific heat. We find arguments that the ground state remains disordered for an XY or Ising like anisotropy in the spin exchange away from the isotropic Heisenberg point.

Charge ordering and superconductivity in α-(BEDT-TTF)$_2M$Hg(SCN)4

In the optical spectra of the non-superconducting salt α-(BEDT-TTF)2KHg(SCN)4 a strong feature appears at frequencies of about 200 cm-1 and temperatures below 200 K which indicates the opening of a pseudogap. This is in contrast to the superconducting α-(BEDT-TTF)2NH4Hg(SCN)4 whch exhlbits metallic-like optical properties down to 2 K. Based on exact diagonalisation calculations of the optical conductivity on an extended Hubbard model at quarter-filling we argue that the proximity of these salts to a charge ordering transition is responsible for the observed pseudogap. Our proposed scenario suggests that the different ground states, including superconductivity, are a consequence of the fluctuations associated with short range charge ordering which builds up close to the quantum phase transition.

Superconducting Pairs in Clusters and in the Cu-O Plane

Recently, by exact diagonalisation methods, we reported superconducting pairing and flux quantization in Cu-O Hubbard clusters of up to 21 atoms. The pairing is due to a configuration interaction mechanism driven by symmetry, and arises when the least bound holes have vanishing mutual repulsion ( W =0 pairs). The second-order, spin-flip interaction leads to a net attraction for the singlet and repulsion for the triplet. Here we show that electron bound pairs also exist and show similar flux quantization properties. Then, we extend the theory of pairing to the full plane and to all orders.

STATIC AND DYNAMICAL PROPERTIES OF A SINGLE IMPURITY IN A STRONGLY CORRELATED HOST

We study, using numerical exact diagonalisation, some static and dynamical properties of a single impurity substituted into a one-dimensional repulsive Hubbard chain. A systematic scan of the parameter-space reveals a rich magnetic phase diagram. Interactions on the lattice stabilize the local moment phase of the impurity. A scalar impurity is seen to induce local moments on the neighbouring sites near Half Filling. Static spin and charge correlation functions reflect a non-Fermi liquid character of the ground state in the presence of a scalar impurity.