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Physical review. B, Condensed matter

Phase separation in at-Jmodel

Michael P Marder, N. Papanicolaou, G. C. Psaltakis

Published Apr 1, 1990• 116 citations
Publisher

Abstract

We study a simple extension of the Heisenberg model that is abstracted from the large-U limit of the Hubbard Hamiltonian and includes charge fluctuations. An attempt is made to elucidate some basic features of the T=0 phase diagram within a suitable 1/N expansion. We find that the ferromagnetic boundary dictated by a naive application of the Nagaoka theorem is actually incorrect because of an instability induced by phase separation. We derive what we believe to be the correct ferromagnetic boundary for sufficiently high dimension, and provide a detailed description of the ensuing phase separation. We also find that a uniform canted antiferromagnetic state is stable over a nontrivial region of the phase diagram. Potential implications of these results for the physics of the original Hubbard model are briefly discussed.

DOI
10.1103/physrevb.41.6920

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We study a simple extension of the Heisenberg model that is abstracted from the large-U limit of the Hubbard Hamiltonian and includes charge fluctuations. An attempt is made to elucidate some basic features of the T=0 phase diagram within a suitable 1/N expansion. We find that the ferromagnetic boundary dictated by a naive application of the Nagaoka theorem is actually incorrect because of an instability induced by phase separation. We derive what we believe to be the correct ferromagnetic boundary for sufficiently high dimension, and provide a detailed description of the ensuing phase separation. We also find that a uniform canted antiferromagnetic state is stable over a nontrivial region of the phase diagram. Potential implications of these results for the physics of the original Hubbard model are briefly discussed.
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.
The Hubbard model is a "highly oversimplified model" for electrons in a solid which interact with each other through extremely short ranged repulsive (Coulomb) interaction. The Hamiltonian of the Hubbard model consists of two pieces; H_hop which describes quantum mechanical hopping of electrons, and Hint which describes nonlinear repulsive interaction. Either H_hop or H_int alone is easy to analyze, and does not favor any specific order. But their sum H=H_hop+H_int is believed to exhibit various nontrivial phenomena including metal-insulator transition, antiferromagnetism, ferrimagnetism, ferromagnetism, Tomonaga-Luttinger liquid, and superconductivity. It is believed that we can find various interesting "universality classes" of strongly interacting electron systems by studying the idealized Hubbard model. In the present article we review some mathematically rigorous results on the Hubbard model which shed light on "physics" of this fascinating model. We mainly concentrate on magnetic properties of the model at its ground states. We discuss Lieb-Mattis theorem on the absence of ferromagnetism in one dimension, Koma-Tasaki bounds on decay of correlations at finite temperatures in two-dimensions, Yamanaka-Oshikawa-Affleck theorem on low-lying excitations in one-dimension, Lieb's important theorem for half-filled model on a bipartite lattice, Kubo-Kishi bounds on the charge and superconducting susceptibilities of half-filled models at finite temperatures, and three rigorous examples of saturated ferromagnetism due to Nagaoka, Mielke, and Tasaki. We have tried to make the article accessible to nonexperts by describing basic definitions and elementary materials in detail.
The Hubbard model is a `highly oversimplified model' for electrons in a solid which interact with each other through extremely short-ranged repulsive (Coulomb) interaction. The Hamiltonian of the Hubbard model consists of two parts: which describes quantum mechanical hopping of electrons, and which describes non-linear repulsive interaction. Either or alone is easy to analyse, and does not favour any specific order. But their sum is believed to exhibit various non-trivial phenomena including metal-insulator transition, antiferromagnetism, ferrimagnetism, ferromagnetism, Tomonaga-Luttinger liquid, and superconductivity. It is believed that we can find various interesting `universality classes' of strongly interacting electron systems by studying the idealized Hubbard model. In the present article we review some mathematically rigorous results relating to the Hubbard model which shed light on the `physics' of this fascinating model. We mainly concentrate on the magnetic properties of the model in its ground states. We discuss the Lieb-Mattis theorem on the absence of ferromagnetism in one dimension, Koma-Tasaki bounds on the decay of correlations at finite temperatures in two dimensions, the Yamanaka-Oshikawa-Affleck theorem on low-lying excitations in one dimension, Lieb's important theorem for the half-filled model on a bipartite lattice, Kubo-Kishi bounds on the charge and superconducting susceptibilities of half-filled models at finite temperatures, and three rigorous examples of saturated ferromagnetism due to Nagaoka, Mielke, and Tasaki. We have tried to make the article accessible to non-experts by giving basic definitions and describing elementary materials in detail.
The authors use an unrestricted self-consistent mean-field approach to the one-dimensional periodic Hubbard model to study its ground-state phase diagram. Their approach allows one to incorporate spin and electron correlations as well as spin and charge fluctuations. The authors find that a homogeneous antiferromagnetic state exists only at half-filling, where the state is also insulating. Off half-filling, it was found that the ground state of the Hubbard model consists of clusters with different magnetic and charge properties. For certain values of the parameters of the system the cluster formation develops to a full phase separation. The effects of the intersite repulsive or attractive interaction on the ground-state properties were also examined. Implications of the authors results for the existence of a superconducting ground state as well as comparison with other studies will be briefly discussed.
We investigate the instability of the saturated ferromagnetic ground state (Nagaoka state) in the Hubbard model on various lattices in dimensions d=2d=2d=2 and d=3d=3d=3. A variational resolvent approach is developed for the Nagaoka instability both for $U=\ensuremath{\infty}$ and for $U<\ensuremath{\infty}$ which can easily be evaluated in the thermodynamic limit on all common lattices. Our results significantly improve former variational bounds for a possible Nagaoka regime in the ground-state phase diagram of the Hubbard model. We show that a pronounced particle-hole asymmetry in the density of states and a diverging density of states at the lower band edge are the most important features in order to stabilize Nagaoka ferromagnetism, particularly in the low-density limit.