Ground State Instability Research Articles

Analytical wave function and reduced Hamiltonian for the weakly coupled two-dimensional Hubbard model.

We introduce a many-body wave function that is shown to describe accurately the ground state of the positive-U, two-dimensional Hubbard model on finite lattices close to half-filling. The wave function is used to demonstrate the absence of a conventional BCS ground state and pairing instability. A simple reduced Hamiltonian describing transverse spin fluctuations is obtained as the fixed-point Hamiltonian in the limit U\ensuremath{\simeq}\ensuremath{\Delta}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{s}}$ where \ensuremath{\Delta}${\mathrm{\ensuremath{\epsilon}}}_{\mathit{s}}$ is the single-particle energy-level spacing at the Fermi surface.

Hadronic matter in a nontopological soliton model.

We have calculated ground-state properties of hadronic matter in a mean-field approximation to a nontopological soliton model in one spatial dimension. The high-density phase of the model is a free Fermi gas of massless fermions. The low-density phase, on the other hand, is a soliton crystal characterized by spatial density oscillations. For certain values of the parameters there is an additional uniform phase in which the underlying chiral symmetry of the Lagrangian is broken and the fermion mass is dynamically generated. A stability analysis of this uniform phase via linear response theory revealed ground-state instabilities at low density and for strong coupling. These findings were consistent with the predictions obtained by solving the mean-field equations by direct matrix diagonalization. In the weak-coupling limit the soliton crystal is characterized by fermion clustering around regions of strongest attraction (shallow bags). The strong-coupling limit, on the other hand, is reminiscent of the soliton kink solution where fermions are excluded from sectors of strongest attraction and are, instead, concentrated in regions where they are effectively massless.

Ground state instability in a gauge theory model of a doped planar antiferromagnet

We study the spectrum of bound states in the (2 + 1)-dimensional C P 1 model coupled to N flavours of Dirac fermions. The case N=2 corresponds to the long-wavelength limit of a microscopic model of the dynamics of holes in a planar antiferromagnet. Fermions of opposite charge with respect to the C P 1 gauge field are found to be subject to attractive forces corresponding to a 1 R two-body potential in the large- N limit. For N<N c= 8 π the corresponding quantum mechanical model is closely related to the problem of an electron moving in a supercritical Coulomb field. At zero temperature the formation of fermion bound states is energetically favoured and this is interpreted as leading to hole-pair condensation and a stable superconducting ground state. The zero temperature mass-gap and coherence length are calculated in this approach. Finite temperature corrections to the two-body potential are derived and the existence of a critical temperature at which superconductivity is extinguished is demonstrated. The model is generalised to include additional four-fermion operators which arise naturally in the underlying statistical model. These are found to have a large effect on the coherence length, reducing it by a factor of about 50. The possible relation of this model to high- T c superconductivity is discussed.

Boson-star formation by classical instability.

A new mechanism to form boson and minisoliton stars is proposed. These objects could be generated by the second-order phase transition due to the ground-state instability of a gravitational interacting scalar field. It is shown that this process manifests itself as a conventional gravitational collapse.

Ground state instability and attractive interactions in the extended Hubbard model

The extended Hubbard model for high temperature superconductors is studied for infinite systems in the strong coupling limit. The attractive interaction between added holes that has been noted for nearly degenerate copper and oxygen energy levels arises because the ground state is near an instability. Adding holes nucleates small regions of this unstable, infinitely compressible phase. Three distinct bound states of two holes occur in the strong coupling limit when double occupation is forbidden. In this limit, the attractive interaction results in phase separation rather than pairing when many holes are present. Perturbative calculations suggest that a pairing state is stable in a narrow parameter range as t increases.

Comment on "Ground-state instability of a random system"

Comment on "Ground-state instability of a random system"

Ground-state instability of interfaces in random systems.

Received 3 February 1988DOI:https://doi.org/10.1103/PhysRevLett.60.2701©1988 American Physical Society

Ground state instability of a random system.

The problem of finding the best path in a random medium is investigated. If the random medium is allowed to undergo slow drifts, the best path can be drastically different. The scaling of the excited states is also discussed. A host of new exponents are found for the 2d problem. The implications for the growing surfaces are also pointed out.

The effective mass of the quasi-particle in an electron liquid at metallic densities

The effective mass of the quasi-particle in an electron liquid is studied, based on Fermi liquid theory. It is shown that the effective-mass ratio m*/m remains smaller than unity throughout the whole region of metallic densities as well as in the high density region. As the electron density is lowered, the effective-mass ratio m*/m decreases very slowly in almost all the metallic region and drops suddenly to zero in the immediate vicinity of the critical density (rs approximately=5.3) where the compressibility becomes divergent. Such a drastic feature of the effective mass can be interpreted as a sign of the ground-state instability of the electron liquid model.

Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains

Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekul\'e states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin $s=\frac{1}{2}$ and $s=1$ chains are carried out in a test of this argument.

Stability and supersymmetry: General formalism and explicit two-loop applications

A complete account of a perturbative investigation of ground state instability is presented for a massless theory involving scalar, pseudoscalar, and Majorana spinor fields. The effective potential, dimensional regularization, and renormalization group formalisms are briefly reviewed and then applied in detail to show the semiclassical vacuum of the model is unstable due to radiative corrections when the (pseudo)scalar self-interaction strength, f, is less than the fermion-(pseudo)scalar coupling, g 2. Models with stable ground states are found when f ⩽ g 2, and when f = g 2 a supersymmetric theory is obtained. The supersymmetric case is thus encountered as a boundary between stable and unstable models. This results is discussed and is conjectured to be a general feature of supersymmetric theories. All perturbative calculations in the analysis are methodically carried out to the level of two-loop Feynman diagrams, and to this level, a variety of renormalization prescriptions are considered. The correlation of the various ultraviolet divergences for the supersymmetric model is explicitly demonstrated and shown not to hold in the general theory.