We study the correlations in a family of ground-state wave functions for one-dimensional quantum many-body systems. For a particular ordering of the M particles, these wave functions are given as the absolute value of the free-fermion ground-state wave function, raised to an arbitrary power \ensuremath{\lambda}. For other permutations of the particles, we use the particle statistics---boson or fermion---to construct the wave function. This prescription works equally well on the continuum line of length L or on the discrete lattice of size N. The theory of random matrices singles out the ``special'' values of \ensuremath{\lambda}=1/2, 1, and 2, and provides techniques for calculating all correlations. Results obtained in this work include analytic expressions for the lattice momentum distributions, accurate numerical results for all momentum distributions and their critical exponents, and explicit results for the lattice pair-correlation functions. We emphasize that this is only for the stated special values of \ensuremath{\lambda}. Finally, these wave functions are evaluated as candidates for variational wave functions.We study the correlations in a family of ground-state wave functions for one-dimensional quantum many-body systems. For a particular ordering of the M particles, these wave functions are given as the absolute value of the free-fermion ground-state wave function, raised to an arbitrary power \ensuremath{\lambda}. For other permutations of the particles, we use the particle statistics---boson or fermion---to construct the wave function. This prescription works equally well on the continuum line of length L or on the discrete lattice of size N. The theory of random matrices singles out the ``special'' values of \ensuremath{\lambda}=1/2, 1, and 2, and provides techniques for calculating all correlations. Results obtained in this work include analytic expressions for the lattice momentum distributions, accurate numerical results for all momentum distributions and their critical exponents, and explicit results for the lattice pair-correlation functions. We emphasize that this is only for the stated special values of \ensuremath{\lambda}. Finally, these wave functions are evaluated as candidates for variational wave functions.

Physical review. B, Condensed matterJan 1, 199222 citations

Variational theory for correlated lattice fermions in high dimensions

Walter Metzner

The European Physical Journal BJun 1, 198991 citations

Functional integrals for correlated fermions

Heinz J. Schulz

arXiv:cond-mat/9411059Journal of Low Temperature PhysicsMay 1, 19953 citations

Correlated Lattice Fermions in d = ∞ Dimensions

Walter Metzner, D. Vollhardt

We show that even in $d=\ensuremath{\infty}$ dimensions the Hubbard model, when scaled properly, describes nontrivial correlations among fermions. Diagrammatic treatments are found to be substantially simpler than in finite dimensions. The weak-coupling correlation energy is seen to be a good approximation for that in $d=3$ . Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\ensuremath{\infty}$.We show that even in $d=\ensuremath{\infty}$ dimensions the Hubbard model, when scaled properly, describes nontrivial correlations among fermions. Diagrammatic treatments are found to be substantially simpler than in finite dimensions. The weak-coupling correlation energy is seen to be a good approximation for that in $d=3$. Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\ensuremath{\infty}$.

Physical Review LettersJan 16, 19892,347 citations

Phase diagram of the one-dimensional t-J model from variational theory

C. Stephen Hellberg, E. J. Melé

We study a class of variational wave functions for strongly interacting one-dimensional lattice fermions in which correlations among the particles are specified by a single variational parameter. We find that the wave functions describe the ground-state properties of the one-dimensional t-J model remarkably well over the entire phase diagram in which interaction strength and density are varied. Specifically the wave function describes a Tomonaga-Luttinger liquid at low J/t, a phase-separated state at large J/t, and a stable state with infinite compressibility between these phases at low densities.We study a class of variational wave functions for strongly interacting one-dimensional lattice fermions in which correlations among the particles are specified by a single variational parameter. We find that the wave functions describe the ground-state properties of the one-dimensional t-J model remarkably well over the entire phase diagram in which interaction strength and density are varied. Specifically the wave function describes a Tomonaga-Luttinger liquid at low J/t, a phase-separated state at large J/t, and a stable state with infinite compressibility between these phases at low densities.

Physical Review LettersOct 1, 199192 citations

Correlated Lattice Fermions in High Dimensions

P. G. J. van Dongen, D. Vollhardt

Springer eBooksJan 1, 19910 citations

d=3

. Recent approximations based on slave-boson techniques are recovered by the exact evaluation of explicit variational wave functions in $d=\ensuremath{\infty}$.