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Philosophical Magazine B

Phase diagram regions deduced for strongly correlated systems via unitary transformation

Zsolt Gulácsi

Published Mar 1, 2001• 0 citations
Publisher

Abstract

From known phase diagram regions of different model Hamiltonians describing strongly correlated systems we deduced new domains of the ground state phase diagram of the same model by an unitary transformation.Different types of extended Hubbard Hamiltonians were used for the starting point and the existence of new stable spin-density wave, charge-density wave, ferromagnetic state and a paramagnetic insulator is demonstrated.The used procedure itself is dimension independent.

DOI
10.1080/13642810010029391

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From known phase diagram regions of different model Hamiltonians describing strongly correlated systems we deduced new domains of the ground state phase diagram of the same model by an unitary transformation.Different types of extended Hubbard Hamiltonians were used for the starting point and the existence of new stable spin-density wave, charge-density wave, ferromagnetic state and a paramagnetic insulator is demonstrated.The used procedure itself is dimension independent.
From known phase diagram regions of different model Hamiltonians describing strongly correlated systems we deduced new domains of the ground state phase diagram of the same models by a unitary transformation. Different types of extended Hubbard Hamiltonians were used for the starting point and the existence of new stable spin-density waves, charge-density waves, ferromagnetic states and a paramagnetic insulator is demonstrated. The procedure used is dimension independent. The ground state phase diagrams of several strongly correlated systems modelled by extended Hubbard-like Hamiltonians are analysed using unitary transformations. New stable spin-density wave, charge-density wave, ferromagnetic or paramagnetic insulator phases are obtained in different cases. The results are true in any dimensions. SUMMARY In this paper, we have presented a procedure based on an explicitly given unitary transformation which allows the rigorous deduction of new phase diagram domains starting from known ground state solutions of a given model. The method is not model dependent and can be applied for arbitrary dimensions. We have applied this method to find new stable spin-density wave, charge-density wave, ferromagnetic and paramagnetic insulator domains of different extended Hubbard type models.
Exact results related to extended Hubbard model containing couplings up to next-nearest-neighbour terms were deduced for restricted regions of parameter space in arbitrary D > 1 dimensions at half-filling and T = 0 temperature. Different types of commensurate charge-density waves and spin-density waves, a ferromagnetic domain and a phase separation region were found, the last being for the first time signalled at the level of approximation-free results in dimensions higher than one. In connection with other presented phases we extended their stability domains in comparison with previously published data. The deduced phase diagram is complete in the localized limit. The dependences on the interaction range and dimension were studied. The obtained results emphasize the importance of next-nearest neighbour terms in the development of ordered phases within the studied system.
Exact results related to extended Hubbard model containing couplings up to next-nearest-neighbour terms were deduced for restricted regions of parameter space in arbitrary D > 1 dimensions at half-filling and T = 0 temperature. Different types of commensurate charge-density waves and spin-density waves, a ferromagnetic domain and a phase separation region were found, the last being for the first time signalled at the level of approximation-free results in dimensions higher than one. In connection with other presented phases we extended their stability domains in comparison with previously published data. The deduced phase diagram is complete in the localized limit. The dependences on the interaction range and dimension were studied. The obtained results emphasize the importance of next-nearest neighbour terms in the development of ordered phases within the studied system.
Phase diagram of the extended Hubbard model with on-site repulsion and nearest-neighbor attraction is obtained for various band fillings, covering the strong-correlation regime, in one dimension by mapping the system to the Tomonaga-Luttinger model with use of exact diagonalization of finite systems. We find that the strong electron correlation makes the superconducting region, which is sandwiched between spin-density wave and phase-separation regions, significantly wider than expected from the weak-coupling g-ology.
The Hubbard model is a simple but profound theoretical tool for understanding the physics underlying strongly correlated systems. This phenomenology includes, but is not limited to, metal-insulating transitions, charge and spin order (charge density/spin density waves), superconducting phases, non-Fermi liquid physics, among others. Examining one dimensional physical models described by the Hubbard Hamiltonian can teach us much about the related physics of higher dimensional systems. Applying advanced numerical computational techniques such as density matrix numerical renormalization group (DMRG) to one-dimensional manypbody model Hamiltonians allows for the calculation of ground state energies and dynamical spectral functions with extremely high precision and accuracy. This thesis explores the application of DMRG numerical techniques to one-dimensional physical systems described by Hamiltonians beyond the conventional Hubbard model, and the nuanced physical effects observed for these systems across various regimes and phases. A Wannier Hubbard chain composed of non-orthogonal overlapping atomic orbitals was transformed to an orthogonal atomic basis using a non-unitary Lowdin transformation. The calculation of energies, dynamical spectral functions and the photoemission spectrum for this Wannier Hubbard chain revealed phases not previously observed for Hubbard chains at half-filling. Additional analysis and calculations were performed for a CuO chain described by the Luther-Emery Hamiltonian that epitomizes charge-transfer physics. The motivation for studying this CuO chain was previous literature on transition metal oxides (TMOs) and the mapping of multiband Hamiltonians to single band models in certain energy regimes. Finally, we performed computational analysis for a spin-3/2 generalized Hubbard chain. By spanning the full phase space of our spin-3/2 Hubbard chain in terms of chemical potential μ\muμ and external magnetic field hhh we observed non-typical Cooper pairing states and novel phases for different symmetries of our Hamiltonian.--Author's abstract
We use the correlated-random-field approximation and a conditional coherent-potential approximation to study the ground-state phase diagram of the one-band Hubbard model. Our approach incorporates both spin and electron correlations. It has been found that for certain values of the parameters of the model, in addition to paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass or spin-liquid phases found in our earlier studies, a phase-separated phase is found to be favored for 0.7\ensuremath{\le}n\ensuremath{\le}1.0 and U/B\ensuremath{\ge}2 in good agreement with results obtained in the t-J model using the technique of the 1/N expansion. The present approach also allows one to watch the dependence of the electron density of states on the number of electrons per site and gives a single physical picture for the occurrence of a metal-insulator transition. Implications of these results for the existence of superconducting ground state as well as comparison to other studies will be briefly discussed.