Non-perturbative solutions to quasi-one-dimensional strongly correlated systems

F. Siano

Fabian H. L. Eßler

Chia‐Wei Yang, ARMEN N. KOCHARIAN, Y. L. Chiang +1 more

A new efficient converging perturbation technique valid for arbitrary interaction strength U/t and electron concentration n is applied to study strongly correlated electrons within the repulsive Hubbard model. We test the new perturbation expansion theory in terms of interacting quasi-particles about generalized self-consistent field (GSCF) solution in an entire parameter space. The developed perturbation formalism for strong interaction and large perturbation region differs from the traditional theory on the vicinity of non-interacting electrons by incorporating systematically fluctuations of quasi-particles around self-consistent solution. Performed analytical calculations of the ground state properties in the extreme conditions of one dimensionality provide quite reasonable numerical agreement with the Bethe-ansatz results in the intermediate range of U/t and n. The results are compared with the predictions of traditional perturbation theory.

Neil J. Robinson

Quasi-one-dimensional quantum models are ideal for theoretically exploring the physical phenomena associated with strong correlations. In this thesis we study three examples where strong correlations play an important role in the static or dynamic properties of the system. Firstly, we examine the behaviour of a doped fermionic two-leg ladder in which umklapp interactions are present. Such interactions arise at special band fillings and can be induced by the formation of charge density wave order in an array of two-leg ladders with long-range (three-dimensional) interactions. For the umklapp which arises from the half-filling of one of the bands, we show that the low-energy theory has a number of phases, including a strong coupling regime in which the dominant fluctuations are superconducting in nature. These superconducting fluctuations carry a finite wave vector – they are the one-dimensional analogue of Fulde-Ferrell-Larkin-Ovchinnikov superconductivity. In a second example, we consider a quantum spin model which captures the essential one-dimensional physics of CoNb2O6, a quasi-one-dimensional Ising ferromagnet. Motivated by high-resolution inelastic neutron scattering experiments, we calculate the dynamical structure in the paramagnetic phase and show that a small misalignment of the transverse field can lead to quasi-particle breakdown – a surprising broadening in the single particle mode observed in experiment. Finally, we study the out-of-equilibrium dynamics of a model with tuneable integrability breaking. When integrability is broken by the presence of weak interactions, we show that the system relaxes to a non-thermal state on intermediate time scales, the so-called “prethermalization plateau”. We describe the approximately stationary behaviour in this regime by constructing a generalised Gibbs ensemble with charges deformed to leading order in perturbation theory. Expectation values of these charges are time-independent, but interestingly the charges do not commute with the Hamiltonian to leading order in perturbation theory. Increasing the strength of the integrability breaking interactions leads to behaviour compatible with thermalisation. In each case we use a combination of perturbative analytical calculations and non-perturbative numerical computations to study the problem at hand.

Alexei M. Tsvelik

In these Lectures we discuss some aspects of theory of strongly correlated low-dimensional systems. In (1+1) and two dimensions availability of non-perturbative techniques makes it possible to obtain solutions of non-trivial models. One of such techniques is called bosonization. In this course we discuss a generalization of this technique for systems with isotopic symmetry.

Seungwook Ma